# Entries Tagged 'Entrance Exams' ↓

November 23rd, 2009 — CAT Preparation, Entrance Exams

Thanks to the internet, email, blogging etc- we have all become very tech savvy in terms of communication. Sending and receiving information has become very easy now. However, along with this development, people have become lax about spelling and grammar in day to day writing. For instance, there is a difference between two similar sounding words that we tend to misuse often. Most of us make horrendous grammar mistakes that are can be avoided by keeping the following information in mind:

1) Your and You’re

**Your:** It refers to somebody’s possession. It is used while pertaining to something that is controlled or owned by someone. Example- You shouldn’t have forgotten your umbrella, now you are totally drenched.

**You’re:** It simply means you are. It is often used as a form of contraction. Example- You’re being selfish. Think about others.

2) Than and Then

**Than:** It is used to introduce the other element in a sentence, or when making a comparison. It can also be used as a source of contrast to show exceptions. Example- As per news reports, this year it rained more than the last year.

**Then:** It means at that time. It also indicates the same as after that, afterwards or next. Example- Let’s raise a toast first, and then sing and dance.

3) Lie and Lay

**Lie:** The verb lie refers to a horizontal position to rest and it is not as generic as ‘lay’. Something that remains is also referred to as lie. The noun lie refers to something that is not true, however don’t mistake it for lay. Example- Why don’t you lie on the couch?

**Lay:** It basically refers to putting something down, or to set something in position. It also refers to the past tense of ‘lie’. Example- Lay your differences aside to be a better human being.

4) Choose or Chose

**Choose:** This is in the future tense or present tense of making a decision. The extra ‘o’ can lead to confusion between the words- choose and chose. So you need to be careful. Example- I can’t decide between the pink top and black top. Can you help me choose one?

**Chose:** It is the past tense of choose. When you chose, it means the decision of choosing has already been made. Example- I chose the best jacket for myself. I am happy with my decision.

Likewise, there is a difference between the words ‘insure’ and ‘ensure’, ‘it’ and ‘it’s’, ‘less’ and ‘fewer’, etc. There are a lot more words and phrases that confuse us in daily life. Choose your words correctly. Avoid making these grammar mistakes.

August 2nd, 2009 — CAT, CAT Preparation, Entrance Exams, GMAT, GMAT Preparation

The Verbal Section of the question paper tests English skills. Examiners consider this section very important and this is apparent from the increase in the number of questions in this section.

B-Schools are looking to determine the student’s level of understanding of the language. This is done through an assessment of how well the student comprehends…

- the meaning of words in the given context,

- the message that is being conveyed,

- the undercurrent tones of the passage,

- correct grammar and the right use of punctuation and the conclusion made.

Particular attention is paid to how well the student answers the question after an analysis of the options provided. Students find the reading comprehension section the most difficult because it tests all of these very qualities. The section however, is easier for some who have a firm command over the language. Make it a practice to read textual material on your computer. This will help not only in this section of CAT but also in the General Awareness section of other MBA entrance tests.

To achieve fluency in any language it is imperative to learn the correct meanings of words and their usage instead of memorizing the word and the sentences. Shorter and convoluted passages now feature in the CAT. Read and understand the passage thoroughly before attempting to answer. The passages are mostly excerpts from articles on economic, social and political issues, such as those that feature in The Economist. The passages are generally about 400 words long. Reading longer articles and thinking in English builds up speed. Discussing what you read with your colleagues will help you understand the fundamental points of the article as well as the subtle nuances. It is also important to separate the opinions of the author from the facts stated.

Learning even the less-common words and their use in sentences will help build vocabulary. This again can be achieved through widespread reading. Apart from understanding the examiner’s reasoning, knowing why answers are incorrect will help prevent repetition of those mistakes. In case the options to a question contain a new word, look it up in a thesaurus. Practice makes perfect. Brushing-up your grammar and vocabulary will help you master the language and add considerably to your overall score.

July 28th, 2007 — CAT, CAT Preparation, Entrance Exams, GMAT, GMAT Preparation, GRE, GRE Preparation, MBA, MBA Study Material

A-

Ablutophobia- Fear of washing or bathing.

Acarophobia- Fear of itching or of the insects that cause itching.

Acerophobia- Fear of sourness.

Achluophobia- Fear of darkness.

Acousticophobia- Fear of noise.

Acrophobia- Fear of heights.

Aerophobia- Fear of drafts, air swallowing, or airbourne noxious substances.

Aeroacrophobia- Fear of open high places.

Aeronausiphobia- Fear of vomiting secondary to airsickness.

Agateophobia- Fear of insanity.

Agliophobia- Fear of pain.

Agoraphobia- Fear of open spaces or of being in crowded, public places like markets. Fear of leaving a safe place.

Agraphobia- Fear of sexual abuse.

Agrizoophobia- Fear of wild animals.

Agyrophobia- Fear of streets or crossing the street.

Aichmophobia- Fear of needles or pointed objects.

Ailurophobia- Fear of cats.

Albuminurophobia- Fear of kidney disease.

Alektorophobia- Fear of chickens.

Algophobia- Fear of pain.

Alliumphobia- Fear of garlic.

Allodoxaphobia- Fear of opinions.

Altophobia- Fear of heights.

Amathophobia- Fear of dust.

Amaxophobia- Fear of riding in a car.

Ambulophobia- Fear of walking.

Amnesiphobia- Fear of amnesia.

Amychophobia- Fear of scratches or being scratched.

Anablephobia- Fear of looking up.

Ancraophobia- Fear of wind. (Anemophobia)

Androphobia- Fear of men.

Anemophobia- Fear of air drafts or wind.(Ancraophobia)

Anginophobia- Fear of angina, choking or narrowness.

Anglophobia- Fear of England or English culture, etc.

Angrophobia - Fear of anger or of becoming angry.

Ankylophobia- Fear of immobility of a joint.

Anthrophobia or Anthophobia- Fear of flowers.

Anthropophobia- Fear of people or society.

Antlophobia- Fear of floods.

Anuptaphobia- Fear of staying single.

Apeirophobia- Fear of infinity.

Aphenphosmphobia- Fear of being touched. (Haphephobia)

Apiphobia- Fear of bees.

Apotemnophobia- Fear of persons with amputations.

Arachibutyrophobia- Fear of peanut butter sticking to the roof of the mouth.

Arachnephobia or Arachnophobia- Fear of spiders.

Arithmophobia- Fear of numbers.

Arrhenphobia- Fear of men.

Arsonphobia- Fear of fire.

Asthenophobia- Fear of fainting or weakness.

Astraphobia or Astrapophobia- Fear of thunder and lightning.(Ceraunophobia, Keraunophobia)

Astrophobia- Fear of stars or celestial space.

Asymmetriphobia- Fear of asymmetrical things.

Ataxiophobia- Fear of ataxia. (muscular incoordination)

Ataxophobia- Fear of disorder or untidiness.

Atelophobia- Fear of imperfection.

Atephobia- Fear of ruin or ruins.

Athazagoraphobia- Fear of being forgotton or ignored or forgetting.

Atomosophobia- Fear of atomic explosions.

Atychiphobia- Fear of failure.

Aulophobia- Fear of flutes.

Aurophobia- Fear of gold.

Auroraphobia- Fear of Northern lights.

Autodysomophobia- Fear of one that has a vile odor.

Automatonophobia- Fear of ventriloquist’s dummies, animatronic creatures, wax statues - anything that falsly represents a sentient being.

Automysophobia- Fear of being dirty.

Autophobia- Fear of being alone or of oneself.

Aviophobia or Aviatophobia- Fear of flying.

B-

Bacillophobia- Fear of microbes.

Bacteriophobia- Fear of bacteria.

Ballistophobia- Fear of missiles or bullets.

Bolshephobia- Fear of Bolsheviks.

Barophobia- Fear of gravity.

Basophobia or Basiphobia- Inability to stand. Fear of walking or falling.

Bathmophobia- Fear of stairs or steep slopes.

Bathophobia- Fear of depth.

Batophobia- Fear of heights or being close to high buildings.

Batrachophobia- Fear of amphibians, such as frogs, newts, salamanders, etc.

Belonephobia- Fear of pins and needles. (Aichmophobia)

Bibliophobia- Fear of books.

Blennophobia- Fear of slime.

Bogyphobia- Fear of bogeys or the bogeyman.

Botanophobia- Fear of plants.

Bromidrosiphobia or Bromidrophobia- Fear of body smells.

Brontophobia- Fear of thunder and lightning.

Bufonophobia- Fear of toads.

C-

Cacophobia- Fear of ugliness.

Cainophobia or Cainotophobia- Fear of newness, novelty.

Caligynephobia- Fear of beautiful women.

Cancerophobia or Carcinophobia- Fear of cancer.

Cardiophobia- Fear of the heart.

Carnophobia- Fear of meat.

Catagelophobia- Fear of being ridiculed.

Catapedaphobia- Fear of jumping from high and low places.

Cathisophobia- Fear of sitting.

Catoptrophobia- Fear of mirrors.

Cenophobia or Centophobia- Fear of new things or ideas.

Ceraunophobia or Keraunophobia- Fear of thunder and lightning.(Astraphobia, Astrapophobia)

Chaetophobia- Fear of hair.

Cheimaphobia or Cheimatophobia- Fear of cold.(Frigophobia, Psychophobia)

Chemophobia- Fear of chemicals or working with chemicals.

Cherophobia- Fear of gaiety.

Chionophobia- Fear of snow.

Chiraptophobia- Fear of being touched.

Chirophobia- Fear of hands.

Cholerophobia- Fear of anger or the fear of cholera.

Chorophobia- Fear of dancing.

Chrometophobia or Chrematophobia- Fear of money.

Chromophobia or Chromatophobia- Fear of colors.

Chronophobia- Fear of time.

Chronomentrophobia- Fear of clocks.

Cibophobia- Fear of food.(Sitophobia, Sitiophobia)

Claustrophobia- Fear of confined spaces.

Cleithrophobia or Cleisiophobia- Fear of being locked in an enclosed place.

Cleptophobia- Fear of stealing.

Climacophobia- Fear of stairs, climbing, or of falling downstairs.

Clinophobia- Fear of going to bed.

Clithrophobia or Cleithrophobia- Fear of being enclosed.

Cnidophobia- Fear of stings.

Cometophobia- Fear of comets.

Coimetrophobia- Fear of cemeteries.

Coitophobia- Fear of coitus.

Contreltophobia- Fear of sexual abuse.

Coprastasophobia- Fear of constipation.

Coprophobia- Fear of feces.

Consecotaleophobia- Fear of chopsticks.

Coulrophobia- Fear of clowns.

Counterphobia- The preference by a phobic for fearful situations.

Cremnophobia- Fear of precipices.

Cryophobia- Fear of extreme cold, ice or frost.

Crystallophobia- Fear of crystals or glass.

Cyberphobia- Fear of computers or working on a computer.

Cyclophobia- Fear of bicycles.

Cymophobia or Kymophobia- Fear of waves or wave like motions.

Cynophobia- Fear of dogs or rabies.

Cypridophobia or Cypriphobia or Cyprianophobia or Cyprinophobia - Fear of prostitutes or venereal disease.

D-

Decidophobia- Fear of making decisions.

Defecaloesiophobia- Fear of painful bowels movements.

Deipnophobia- Fear of dining or dinner conversations.

Dementophobia- Fear of insanity.

Demonophobia or Daemonophobia- Fear of demons.

Demophobia- Fear of crowds. (Agoraphobia)

Dendrophobia- Fear of trees.

Dentophobia- Fear of dentists.

Dermatophobia- Fear of skin lesions.

Dermatosiophobia or Dermatophobia or Dermatopathophobia- Fear of skin disease.

Dextrophobia- Fear of objects at the right side of the body.

Diabetophobia- Fear of diabetes.

Didaskaleinophobia- Fear of going to school.

Dikephobia- Fear of justice.

Dinophobia- Fear of dizziness or whirlpools.

Diplophobia- Fear of double vision.

Dipsophobia- Fear of drinking.

Dishabiliophobia- Fear of undressing in front of someone.

Domatophobia- Fear of houses or being in a house.(Eicophobia, Oikophobia)

Doraphobia- Fear of fur or skins of animals.

Doxophobia- Fear of expressing opinions or of receiving praise.

Dromophobia- Fear of crossing streets.

Dutchphobia- Fear of the Dutch.

Dysmorphophobia- Fear of deformity.

Dystychiphobia- Fear of accidents.

E-

Ecclesiophobia- Fear of church.

Ecophobia- Fear of home.

Eicophobia- Fear of home surroundings.(Domatophobia, Oikophobia)

Eisoptrophobia- Fear of mirrors or of seeing oneself in a mirror.

Electrophobia- Fear of electricity.

Eleutherophobia- Fear of freedom.

Elurophobia- Fear of cats. (Ailurophobia)

Emetophobia- Fear of vomiting.

Enetophobia- Fear of pins.

Enochlophobia- Fear of crowds.

Enosiophobia or Enissophobia- Fear of having committed an unpardonable sin or of criticism.

Entomophobia- Fear of insects.

Eosophobia- Fear of dawn or daylight.

Ephebiphobia- Fear of teenagers.

Epistaxiophobia- Fear of nosebleeds.

Epistemophobia- Fear of knowledge.

Equinophobia- Fear of horses.

Eremophobia- Fear of being oneself or of lonliness.

Ereuthrophobia- Fear of blushing.

Ergasiophobia- 1) Fear of work or functioning. 2) Surgeon’s fear of operating.

Ergophobia- Fear of work.

Erotophobia- Fear of sexual love or sexual questions.

Euphobia- Fear of hearing good news.

Eurotophobia- Fear of female genitalia.

Erythrophobia or Erytophobia or Ereuthophobia- 1) Fear of redlights. 2) Blushing. 3) Red.

F-

Febriphobia or Fibriphobia or Fibriophobia- Fear of fever.

Felinophobia- Fear of cats. (Ailurophobia, Elurophobia, Galeophobia, Gatophobia)

Francophobia- Fear of France or French culture. (Gallophobia, Galiophobia)

Frigophobia- Fear of cold or cold things.(Cheimaphobia, Cheimatophobia, Psychrophobia)

G-

Galeophobia or Gatophobia- Fear of cats.

Gallophobia or Galiophobia- Fear France or French culture. (Francophobia)

Gamophobia- Fear of marriage.

Geliophobia- Fear of laughter.

Geniophobia- Fear of chins.

Genophobia- Fear of sex.

Genuphobia- Fear of knees.

Gephyrophobia or Gephydrophobia or Gephysrophobia- Fear of crossing bridges.

Germanophobia- Fear of Germany or German culture.

Gerascophobia- Fear of growing old.

Gerontophobia- Fear of old people or of growing old.

Geumaphobia or Geumophobia- Fear of taste.

Glossophobia- Fear of speaking in public or of trying to speak.

Gnosiophobia- Fear of knowledge.

Graphophobia- Fear of writing or handwriting.

Gymnophobia- Fear of nudity.

Gynephobia or Gynophobia- Fear of women.

H-

Hadephobia- Fear of hell.

Hagiophobia- Fear of saints or holy things.

Hamartophobia- Fear of sinning.

Haphephobia or Haptephobia- Fear of being touched.

Harpaxophobia- Fear of being robbed.

Hedonophobia- Fear of feeling pleasure.

Heliophobia- Fear of the sun.

Hellenologophobia- Fear of Greek terms or complex scientific terminology.

Helminthophobia- Fear of being infested with worms.

Hemophobia or Hemaphobia or Hematophobia- Fear of blood.

Heresyphobia or Hereiophobia- Fear of challenges to official doctrine or of radical deviation.

Herpetophobia- Fear of reptiles or creepy, crawly things.

Heterophobia- Fear of the opposite sex. (Sexophobia)

Hexakosioihexekontahexaphobia- Fear of the number 666.

Hierophobia- Fear of priests or sacred things.

Hippophobia- Fear of horses.

Hippopotomonstrosesquippedaliophobia- Fear of long words.

Hobophobia- Fear of bums or beggars.

Hodophobia- Fear of road travel.

Hormephobia- Fear of shock.

Homichlophobia- Fear of fog.

Homilophobia- Fear of sermons.

Hominophobia- Fear of men.

Homophobia- Fear of sameness, monotony or of homosexuality or of becoming homosexual.

Hoplophobia- Fear of firearms.

Hydrargyophobia- Fear of mercurial medicines.

Hydrophobia- Fear of water or of rabies.

Hydrophobophobia- Fear of rabies.

Hyelophobia or Hyalophobia- Fear of glass.

Hygrophobia- Fear of liquids, dampness, or moisture.

Hylephobia- Fear of materialism or the fear of epilepsy.

Hylophobia- Fear of forests.

Hypengyophobia or Hypegiaphobia- Fear of responsibility.

Hypnophobia- Fear of sleep or of being hypnotized.

Hypsiphobia- Fear of height.

I-

Iatrophobia- Fear of going to the doctor or of doctors.

Ichthyophobia- Fear of fish.

Ideophobia- Fear of ideas.

Illyngophobia- Fear of vertigo or feeling dizzy when looking down.

Iophobia- Fear of poison.

Insectophobia - Fear of insects.

Isolophobia- Fear of solitude, being alone.

Isopterophobia- Fear of termites, insects that eat wood.

Ithyphallophobia- Fear of seeing, thinking about or having an erect penis.

J-

Japanophobia- Fear of Japanese.

Judeophobia- Fear of Jews.

K-

Kainolophobia or Kainophobia- Fear of anything new, novelty.

Kakorrhaphiophobia- Fear of failure or defeat.

Katagelophobia- Fear of ridicule.

Kathisophobia- Fear of sitting down.

Kenophobia- Fear of voids or empty spaces.

Keraunophobia or Ceraunophobia- Fear of thunder and lightning.(Astraphobia, Astrapophobia)

Kinetophobia or Kinesophobia- Fear of movement or motion.

Kleptophobia- Fear of stealing.

Koinoniphobia- Fear of rooms.

Kolpophobia- Fear of genitals, particularly female.

Kopophobia- Fear of fatigue.

Koniophobia- Fear of dust. (Amathophobia)

Kosmikophobia- Fear of cosmic phenomenon.

Kymophobia- Fear of waves. (Cymophobia)

Kynophobia- Fear of rabies.

Kyphophobia- Fear of stooping.

L-

Lachanophobia- Fear of vegetables.

Laliophobia or Lalophobia- Fear of speaking.

Leprophobia or Lepraphobia- Fear of leprosy.

Leukophobia- Fear of the color white.

Levophobia- Fear of things to the left side of the body.

Ligyrophobia- Fear of loud noises.

Lilapsophobia- Fear of tornadoes and hurricanes.

Limnophobia- Fear of lakes.

Linonophobia- Fear of string.

Liticaphobia- Fear of lawsuits.

Lockiophobia- Fear of childbirth.

Logizomechanophobia- Fear of computers.

Logophobia- Fear of words.

Luiphobia- Fear of lues, syphillis.

Lutraphobia- Fear of otters.

Lygophobia- Fear of darkness.

Lyssophobia- Fear of rabies or of becoming mad.

M-

Macrophobia- Fear of long waits.

Mageirocophobia- Fear of cooking.

Maieusiophobia- Fear of childbirth.

Malaxophobia- Fear of love play. (Sarmassophobia)

Maniaphobia- Fear of insanity.

Mastigophobia- Fear of punishment.

Mechanophobia- Fear of machines.

Medomalacuphobia- Fear of losing an erection.

Medorthophobia- Fear of an erect penis.

Megalophobia- Fear of large things.

Melissophobia- Fear of bees.

Melanophobia- Fear of the color black.

Melophobia- Fear or hatred of music.

Meningitophobia- Fear of brain disease.

Menophobia- Fear of menstruation.

Merinthophobia- Fear of being bound or tied up.

Metallophobia- Fear of metal.

Metathesiophobia- Fear of changes.

Meteorophobia- Fear of meteors.

Methyphobia- Fear of alcohol.

Metrophobia- Fear or hatred of poetry.

Microbiophobia- Fear of microbes. (Bacillophobia)

Microphobia- Fear of small things.

Misophobia or Mysophobia- Fear of being contaminated with dirt or germs.

Mnemophobia- Fear of memories.

Molysmophobia or Molysomophobia- Fear of dirt or contamination.

Monophobia- Fear of solitude or being alone.

Monopathophobia- Fear of definite disease.

Motorphobia- Fear of automobiles.

Mottephobia- Fear of moths.

Musophobia or Muriphobia- Fear of mice.

Mycophobia- Fear or aversion to mushrooms.

Mycrophobia- Fear of small things.

Myctophobia- Fear of darkness.

Myrmecophobia- Fear of ants.

Mythophobia- Fear of myths or stories or false statements.

Myxophobia- Fear of slime. (Blennophobia)

N-

Nebulaphobia- Fear of fog. (Homichlophobia)

Necrophobia- Fear of death or dead things.

Nelophobia- Fear of glass.

Neopharmaphobia- Fear of new drugs.

Neophobia- Fear of anything new.

Nephophobia- Fear of clouds.

Noctiphobia- Fear of the night.

Nomatophobia- Fear of names.

Nosocomephobia- Fear of hospitals.

Nosophobia or Nosemaphobia- Fear of becoming ill.

Nostophobia- Fear of returning home.

Novercaphobia- Fear of your step-mother.

Nucleomituphobia- Fear of nuclear weapons.

Nudophobia- Fear of nudity.

Numerophobia- Fear of numbers.

Nyctohylophobia- Fear of dark wooded areas or of forests at night

Nyctophobia- Fear of the dark or of night.

O-

Obesophobia- Fear of gaining weight.(Pocrescophobia)

Ochlophobia- Fear of crowds or mobs.

Ochophobia- Fear of vehicles.

Octophobia - Fear of the figure 8.

Odontophobia- Fear of teeth or dental surgery.

Odynophobia or Odynephobia- Fear of pain. (Algophobia)

Oenophobia- Fear of wines.

Oikophobia- Fear of home surroundings, house.(Domatophobia, Eicophobia)

Olfactophobia- Fear of smells.

Ombrophobia- Fear of rain or of being rained on.

Ommetaphobia or Ommatophobia- Fear of eyes.

Oneirophobia- Fear of dreams.

Oneirogmophobia- Fear of wet dreams.

Onomatophobia- Fear of hearing a certain word or of names.

Ophidiophobia- Fear of snakes. (Snakephobia)

Ophthalmophobia- Fear of being stared at.

Opiophobia- Fear medical doctors experience of prescribing needed pain medications for patients.

Optophobia- Fear of opening one’s eyes.

Ornithophobia- Fear of birds.

Orthophobia- Fear of property.

Osmophobia or Osphresiophobia- Fear of smells or odors.

Ostraconophobia- Fear of shellfish.

Ouranophobia or Uranophobia- Fear of heaven.

P-

Pagophobia- Fear of ice or frost.

Panthophobia- Fear of suffering and disease.

Panophobia or Pantophobia- Fear of everything.

Papaphobia- Fear of the Pope.

Papyrophobia- Fear of paper.

Paralipophobia- Fear of neglecting duty or responsibility.

Paraphobia- Fear of sexual perversion.

Parasitophobia- Fear of parasites.

Paraskavedekatriaphobia- Fear of Friday the 13th.

Parthenophobia- Fear of virgins or young girls.

Pathophobia- Fear of disease.

Patroiophobia- Fear of heredity.

Parturiphobia- Fear of childbirth.

Peccatophobia- Fear of sinning or imaginary crimes.

Pediculophobia- Fear of lice.

Pediophobia- Fear of dolls.

Pedophobia- Fear of children.

Peladophobia- Fear of bald people.

Pellagrophobia- Fear of pellagra.

Peniaphobia- Fear of poverty.

Pentheraphobia- Fear of mother-in-law. (Novercaphobia)

Phagophobia- Fear of swallowing or of eating or of being eaten.

Phalacrophobia- Fear of becoming bald.

Phallophobia- Fear of a penis, esp erect.

Pharmacophobia- Fear of taking medicine.

Phasmophobia- Fear of ghosts.

Phengophobia- Fear of daylight or sunshine.

Philemaphobia or Philematophobia- Fear of kissing.

Philophobia- Fear of falling in love or being in love.

Philosophobia- Fear of philosophy.

Phobophobia- Fear of phobias.

Photoaugliaphobia- Fear of glaring lights.

Photophobia- Fear of light.

Phonophobia- Fear of noises or voices or one’s own voice; of telephones.

Phronemophobia- Fear of thinking.

Phthiriophobia- Fear of lice. (Pediculophobia)

Phthisiophobia- Fear of tuberculosis.

Placophobia- Fear of tombstones.

Plutophobia- Fear of wealth.

Pluviophobia- Fear of rain or of being rained on.

Pneumatiphobia- Fear of spirits.

Pnigophobia or Pnigerophobia- Fear of choking of being smothered.

Pocrescophobia- Fear of gaining weight. (Obesophobia)

Pogonophobia- Fear of beards.

Poliosophobia- Fear of contracting poliomyelitis.

Politicophobia- Fear or abnormal dislike of politicians.

Polyphobia- Fear of many things.

Poinephobia- Fear of punishment.

Ponophobia- Fear of overworking or of pain.

Porphyrophobia- Fear of the color purple.

Potamophobia- Fear of rivers or running water.

Potophobia- Fear of alcohol.

Pharmacophobia- Fear of drugs.

Proctophobia- Fear of rectums.

Prosophobia- Fear of progress.

Psellismophobia- Fear of stuttering.

Psychophobia- Fear of mind.

Psychrophobia- Fear of cold.

Pteromerhanophobia- Fear of flying.

Pteronophobia- Fear of being tickled by feathers.

Pupaphobia - Fear of puppets.

Pyrexiophobia- Fear of Fever.

Pyrophobia- Fear of fire.

R-

Radiophobia- Fear of radiation, x-rays.

Ranidaphobia- Fear of frogs.

Rectophobia- Fear of rectum or rectal diseases.

Rhabdophobia- Fear of being severely punished or beaten by a rod, or of being severely criticized. Also fear of magic.(wand)

Rhypophobia- Fear of defecation.

Rhytiphobia- Fear of getting wrinkles.

Rupophobia- Fear of dirt.

Russophobia- Fear of Russians.

S-

Samhainophobia: Fear of Halloween.

Sarmassophobia- Fear of love play. (Malaxophobia)

Satanophobia- Fear of Satan.

Scabiophobia- Fear of scabies.

Scatophobia- Fear of fecal matter.

Scelerophibia- Fear of bad men, burglars.

Sciophobia Sciaphobia- Fear of shadows.

Scoleciphobia- Fear of worms.

Scolionophobia- Fear of school.

Scopophobia or Scoptophobia- Fear of being seen or stared at.

Scotomaphobia- Fear of blindness in visual field.

Scotophobia- Fear of darkness. (Achluophobia)

Scriptophobia- Fear of writing in public.

Selachophobia- Fear of sharks.

Selaphobia- Fear of light flashes.

Selenophobia- Fear of the moon.

Seplophobia- Fear of decaying matter.

Sesquipedalophobia- Fear of long words.

Sexophobia- Fear of the opposite sex. (Heterophobia)

Siderodromophobia- Fear of trains, railroads or train travel.

Siderophobia- Fear of stars.

Sinistrophobia- Fear of things to the left or left-handed.

Sinophobia- Fear of Chinese, Chinese culture.

Sitophobia or Sitiophobia- Fear of food or eating. (Cibophobia)

Snakephobia- Fear of snakes. (Ophidiophobia)

Soceraphobia- Fear of parents-in-law.

Social Phobia- Fear of being evaluated negatively in social situations.

Sociophobia- Fear of society or people in general.

Somniphobia- Fear of sleep.

Sophophobia- Fear of learning.

Soteriophobia - Fear of dependence on others.

Spacephobia- Fear of outer space.

Spectrophobia- Fear of specters or ghosts.

Spermatophobia or Spermophobia- Fear of germs.

Spheksophobia- Fear of wasps.

Stasibasiphobia or Stasiphobia- Fear of standing or walking. (Ambulophobia)

Staurophobia- Fear of crosses or the crucifix.

Stenophobia- Fear of narrow things or places.

Stygiophobia or Stigiophobia- Fear of hell.

Suriphobia- Fear of mice.

Symbolophobia- Fear of symbolism.

Symmetrophobia- Fear of symmetry.

Syngenesophobia- Fear of relatives.

Syphilophobia- Fear of syphilis.

T-

Tachophobia- Fear of speed.

Taeniophobia or Teniophobia- Fear of tapeworms.

Taphephobia Taphophobia- Fear of being buried alive or of cemeteries.

Tapinophobia- Fear of being contagious.

Taurophobia- Fear of bulls.

Technophobia- Fear of technology.

Teleophobia- 1) Fear of definite plans. 2) Religious ceremony.

Telephonophobia- Fear of telephones.

Teratophobia- Fear of bearing a deformed child or fear of monsters or deformed people.

Testophobia- Fear of taking tests.

Tetanophobia- Fear of lockjaw, tetanus.

Teutophobia- Fear of German or German things.

Textophobia- Fear of certain fabrics.

Thaasophobia- Fear of sitting.

Thalassophobia- Fear of the sea.

Thanatophobia or Thantophobia- Fear of death or dying.

Theatrophobia- Fear of theatres.

Theologicophobia- Fear of theology.

Theophobia- Fear of gods or religion.

Thermophobia- Fear of heat.

Tocophobia- Fear of pregnancy or childbirth.

Tomophobia- Fear of surgical operations.

Tonitrophobia- Fear of thunder.

Topophobia- Fear of certain places or situations, such as stage fright.

Toxiphobia or Toxophobia or Toxicophobia- Fear of poison or of being accidently poisoned.

Traumatophobia- Fear of injury.

Tremophobia- Fear of trembling.

Trichinophobia- Fear of trichinosis.

Trichopathophobia or Trichophobia- Fear of hair. (Chaetophobia, Hypertrichophobia)

Triskaidekaphobia- Fear of the number 13.

Tropophobia- Fear of moving or making changes.

Trypanophobia- Fear of injections.

Tuberculophobia- Fear of tuberculosis.

Tyrannophobia- Fear of tyrants.

U-

Uranophobia or Ouranophobia- Fear of heaven.

Urophobia- Fear of urine or urinating.

V-

Vaccinophobia- Fear of vaccination.

Venustraphobia- Fear of beautiful women.

Verbophobia- Fear of words.

Verminophobia- Fear of germs.

Vestiphobia- Fear of clothing.

Virginitiphobia- Fear of rape.

Vitricophobia- Fear of step-father.

W-

Walloonphobia- Fear of the Walloons.

Wiccaphobia: Fear of witches and witchcraft.

X-

Xanthophobia- Fear of the color yellow or the word yellow.

Xenoglossophobia- Fear of foreign languages.

Xenophobia- Fear of strangers or foreigners.

Xerophobia- Fear of dryness.

Xylophobia- 1) Fear of wooden objects. 2) Forests.

Xyrophobia-Fear of razors.

Z-

Zelophobia- Fear of jealousy.

Zeusophobia- Fear of God or gods.

Zemmiphobia- Fear of the great mole rat.

Zoophobia- Fear of animals.

May 30th, 2007 — CAT, CAT Preparation, Entrance Exams, MBA, MBA Study Material, Prep Material

•Whenever there appears any term of the type a3 + b3 + c3, do check for a + b + c being equal to zero. If a + b + c is indeed zero, then a3 + b3 + c3 = 3abc.

•The series 1, 3, 6, 10, 15 should immediately be recognized as series of sum of first n natural numbers.

•To form all natural numbers from 1 to N by adding any natural numbers, one would just need 1, 2, 4, 8, 16, 32, 64…..2n, where 2n is the largest power of 2 smaller than or equal to N. E.g. What is the minimum number of weights needed to be able to measure all natural numbers weights till 80, if weights can be kept only on one pan of the balance. One would need weights 1, 2, 4, 8, …64

•To form all natural numbers from 1 to N by adding or subtracting any natural numbers, one would just need 1, 3, 9, 27, 81, …..3n. Be careful of the largest number needed in this case. E.g. What is the minimum number of weights needed to be able to measure all natural numbers weights till 80, if weights can be kept on both pans of the balance. One would need weights 1, 3, 9, 27, 81.

•In questions of the type where certain flowers/sweets/points etc gets diminished and then increases and again diminishes and again increases……rather than forming an equation, see if one can work backwards if final quantity is given or else work with options. Also in such cases, if 1/3rd the objects are given away, work on the objects that are remaining i.e. 2/3rd to save time.

If working with options, select options intelligently e.g. I pick 1/3rd of the chocolates in a bowl and then return 3, next I pick 1/5th of the chocolates and then return five, next ……What is the number of chocolates in the bowl initially? The initial number of chocolates has to be a multiple of 3. Also 2/3rd of the initial number of chocolates plus 3 should be divisible by 5. This should be enough to reduce the possible options to just about 2.

•Remember that a2, b2, c2 or |a|, |b|, |c| are either zero or positive quantity. Thus solution to a2 + b2 + c2 = 0 or |a| + |b| + |c| = 0 is a = b = c =0

May 30th, 2007 — CAT, CAT Preparation, Entrance Exams, MBA, MBA Study Material, Prep Material

**Integer solutions to equations of the type** **Ax ± By = C**:

• If A, B and C have a common factor divide the entire equation by this common factor. The following matter considers that you have done this step and A and B are considered after the division.

• Now if A and B are not co-prime, the equation will not have any integer solution. Think why!!!

• Consecutive integer solutions to the equation will have x values differing by B and y values differing by A. **For equation of type Ax + By = C,** a increase (decrease) in x will cause a decrease (increase) in y and vice-versa. For equation of type Ax – By = C, a increase (decrease) in x will cause a increase (decrease) in y and vice-versa.

• Thus in any set of A consecutive integers, y can assume one and only one value for which it will be a integer solution to the equation. And in any set of B consecutive integers, x can assume one and one one value for which it will be a integer solution to the eqn. (To understand this point, i.e. if you have’nt, refer to the concept explained in this article under the heading of LCM and HCF)

• **E.g. For the equation 17x + 5y = 513**:

There has to be a value of x from 1 to 5 (or from 0 to 4) that will satisfy this equation. For an integral solution 513 – 17x has to be divisible by 5 i.e. 513 – 17x has to end with a 0 or 5. Thus from 0 to 4, x can only take a value 4. Thus one can easily find that (4, 97) is a solution to this equation.

Further if the total number of natural number solution is asked, as x increases in steps of 5 starting with 4 (there is no question of x decreasing as it will not be a natural number then), y will decrease in steps of 17, starting from 97. Since 17 × 5 = 85, there can be 5 such steps of decrease and the number of natural number solutions is 6

If the question was asked as to how many integer solutions exists for the equation such that -43 = x = 67, from -43 to 67 there exists a total of 110 integers. Since x can take one and only one value in any given 5 consecutive integers, the number of solutions will be 22.

If the question was asked as to **how many integer solutions exists for the equation** such that 0 < x < 168, from 1 to 165 there exists a total of 165 integers. Since x can take one and only one value in any given 5 consecutive integers, the number of solutions will be for 0 < x = 165 will be 33. For x = 166 and 167 would not be a solution as x has to be of the type 5n – 1 to be a solution.

• Consider this question, how many non-negative integral solution exists for the equation 17x – 4y = 1 such that y = 1000.

y can take one and only one value out of 17 consecutive integers to be a solution to the equation. 17 × 60 = 1020. Thus 17 × 58 = 986. Thus from 1 to 986, y will take 58 values. Now all that remains to be checked is that from 987 to 1000 will there be a value that y can take to be a solution to the equation. One solution x = 1 and y = 4 is evident. Thus if we consider sets of 17 consecutive integers as 1 to 17, 18 to 34, 35 to 51, the fourth number in the set will be a solution. Thus from 987 to 1003, y = 991 will be the 59th solution.

May 30th, 2007 — CAT, CAT Preparation, Entrance Exams, GRE, GRE Preparation, MBA, MBA Study Material, Prep Material

**Exercise1 + Answers + Explanations**

Question:

The sum of the first 100 numbers, 1 to 100 is divisible by

(1) 2, 4 and 8

(2) 2 and 4

(3) 2 only

(4) None of these

Correct Answer - (3)

Explanation:

The sum of the first 100 natural numbers is given by (n(n + 1))/2 = (100(101))/2 = 50(101).

101 is an odd number and 50 is divisible by 2. Hence, 50 (101) will be divisible by 2.

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Question:

What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?

(1) 176

(2) 187

(3) 54043

(4) 748

Correct Answer - (2)

Explanation:

The marbles used to tile the floor are square marbles. Therefore, the length of the marble = width of the marble.As we have to use whole number of marbles, the side of the square should a factor of both 5 m 78 cm and 3m 74. And it should be the highest factor of 5 m 78 cm and 3m 74. 5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm.

The HCF of 578 and 374 = 34.

Hence, the side of the square is 34.

The number of such square marbles required = = 187 marbles.

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What is the remainder when 9^1 + 9^2 + 9^3 + …. + 9^8 is divided by 6?

(1) 3

(2) 2

(3) 0

(4) 5

Correct Answer - (3)

Explanation:

6 is an even multiple of 3. When any even multiple of 3 is divided by 6, it will leave a remainder of 0. Or in other words it is perfectly divisible by 6.

On the contrary, when any odd multiple of 3 is divided by 6, it will leave a remainder of 3. For e.g when 9 an odd multiple of 3 is divided by 6, you will get a remainder of 3.

9 is an odd multiple of 3. And all powers of 9 are odd multiples of 3. Therefore, when each of the 8 powers of 9 listed above are divided by 6, each of them will leave a remainder of 3.

The total value of the remainder = 3 + 3 + …. + 3 (8 remainders) = 24. 24 is divisible by 6. Hence, it will leave no remainder.

Hence the final remainder when the expression 9^1 + 9^2 + 9^3 + ….. + 9^8 is divided by 6 will be equal to ‘0′.

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Question:

What is the reminder when 91 + 92 + 93 + …… + 99 is divided by 6?

(1) 0

(2) 3

(3) 4

(4) None of these

Correct Answer - (2)

Explanation:

Any number that is divisible by ‘6′ will be a number that is divisible by both ‘2′ and ‘3′. i.e. the number should an even number and should be divisible by three (sum of its digits should add to a multiple of ‘3′). Any number that is divisible by ‘9′ is also divisible by ‘3′ but unless it is an even number it will not be divisibly by ‘6′. In the above case, ‘9′ is an odd number. Any power of ‘9′ which is an odd number will be an odd number which is divisible by ‘9′.

Therefore, each of the terms 91, 92 etc are all divisibly by ‘9′ and hence by ‘3′ but are odd numbers.

Any multiple of ‘3′ which is odd when divided by ‘6′ will leave a reminder of ‘3′. For example 27 is a multiple of ‘3′ which is odd. 27/6 will leave a reminder of ‘3′. Or take 45 which again is a multiple of ‘3′ which is odd. 45/6 will also leave a reminder of ‘3′.

Each of the individual terms of the given expression 91 + 92 + 93 + …… + 99 when divided by 6 will leave a reminder of ‘3′. There are 9 such terms. The sum of all the reminders will therefore be equal to 9*3 = 27.

27/6 will leave a reminder of ‘3′.

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Question:

Find the value of 1.1! + 2.2! + 3.3! + ……+n.n!

(1) n! +1

(2) (n+1)!

(3) (n+1)!-1

(4) (n+1)!+1

Correct Answer - (3)

Explanation:

1.1! can be written as (2!-1!), likewise 2.2! = (3!-2!) , 3.3! = (4!-3!) and n.n! = (n+1)!-n!.

Thus by summing it up we get the result as given below.

1.1! + 2.2! + 3.3! + ……+n.n! = (2!-1!) + (3!-2!) + (4!-3!) +……+ (n+1)!-n! = (n+1)!-1.

May 30th, 2007 — CAT Preparation, Entrance Exams, GRE Preparation, MBA Study Material, Prep Material

**Exercise2 + Answers + Explanations**

Question:

‘a’ and ‘b’ are the lengths of the base and height of a right angled triangle whose hypotenuse is ‘h’. If the values of ‘a’ and ‘b’ are positive integers, which of the following cannot be a value of the square of the hypotenuse?

(1) 13

(2) 23

(3) 37

(4) 41

Correct Answer - (2)

Explanation:

The value of the square of the hypotenuse = h2 = a2 + b2

As the problem states that ‘a’ and ‘b’ are positive integers, the values of a2 and b2 will have to be perfect squares. Hence we need to find out that value amongst the four answer choices which cannot be expressed as the sum of two perfect squares.

Choice 1 is 13. 13 = 9 + 4 = 32 + 22. Therefore, Choice 1 is not the answer as it is a possible value of h2

Choice 2 is 23. 23 cannot be expressed as the sum two numbers, each of which in turn happen to be perfect squares. Therefore, Choice 2 is the answer.

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Question:

Two numbers when divided by a certain divisor leave remainders of 431 and 379 respectively. When the sum of these two numbers is divided by the same divisor, the remainder is 211. What is the divisor?

(1) 599

(2) 1021

(3) 263

(4) Cannot be determined

Correct Answer - (1)

Explanation:

Two numbers when divided by a common divisor, if they leave remainders of x and y and when their sum is divided by the same divisor leaves a remainder of z, the divisor is given by x + y - z.

In this case, x and y are 431 and 379 and z = 211. Hence the divisor is 431 + 379 - 211 = 599.

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Question:

What is the least number that should be multiplied to 100! to make it perfectly divisible by 350?

(1) 144

(2) 72

(3) 108

(4) 216

Correct Answer - (2)

Explanation:

100! has 348 as the greatest power of 3 that can divide it. Similarly, the greatest power of 2 that can divide 100! is 297. 297 = 448 * 21.

Therefore, the largest power of 12 that can divide 100! is 48.

Therefore, for 350 to be included in 100!, 100! needs to be multiplied by 32 * 23 = 9 * 8 = 72.

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Question:

A certain number when successfully divided by 8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder when the number is divided by the product of 8 and 11, viz 88?

(1) 3

(2) 21

(3) 59

(4) 68

Correct Answer - (3)

Explanation:

When a number is successfully divided by two divisors d1 and d2 and two remainders r1 and r2 are obtained, the remainder that will be obtained by the product of d1 and d2 is given by the relation d1r2 + r1.

Where d1 and d2 are in ascending order respectively and r1 and r2 are their respective remainders when they divide the number.

In this case, the d1 = 8 and d2 = 11. And r1 = 3 and r2 = 7.

Therefore, d1r2 + r1 = 8*7 + 3 = 59.

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Question:

What is the total number of different divisors including 1 and the number that can divide the number 6400?

(1) 24

(2) 27

(3) 27

(4) 68

Correct Answer - (2)

Explanation:

To find the number of divisors for a number, express then number as the product of the prime numbers like ax * by * cz .

In this case, 6400 can be expressed as 64*100 = 26 * 4 * 25 = 28 * 52.

Having done that, the way to find the number of divisors is by multiplying the indices of each of the prime numbers after incrementing the indices by 1.

i.e. the number of divisors = (x+1)(y+1)(z+1).

In this case, (8 + 1)(2 + 1) = 9*3 = 27.

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May 30th, 2007 — CAT Preparation, Entrance Exams, GRE Preparation, MBA Study Material, Prep Material

**Exercise3 + Answers + Explanations**

Question:

When 26854 and 27584 are divided by a certain two digit prime number, the remainder obtained is 47. Which of the following choices is a possible value of the divisor?

(1) 61

(2) 71

(3) 73

(4) 89

Correct Answer - (3)

Explanation:

When both 26854 and 27584 are divided by a divisor, the remainder obtained happens to be the same value 47.

Which means that the difference between 26854 and 27584 is a multiple of the divisor. Else the remainders would have been different.

=> 27584 - 26854 = 730

Now we need to find out a two digit prime number, whose multiple will be 730. 730 can be written as 73 * 10, where 73 is a prime number and greater than 47.

Hence, the two digit prime divisor is 73.

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Question:

How many times will the digit ‘0′ appear between 1 and 10,000?

(1) 4000

(2) 4003

(3) 2893

(4) 3892

Correct Answer - (3)

Explanation:

In two digit numbers, ‘0′ appears 9 times.

In 3-digit numbers, either 1 ‘0′ or 2 ‘0s’ can appear.

When one ‘0′ appears: The first digit of a 3-digit number can be any of the 9 digits other than ‘0′. The second digit can be any of the ‘9′ digits and the third digit be ‘0′.Hence there will 9*9 = 81 such combinations. The ‘0′ can either be the 2nd digit or the third digit, hence there are 2 arrangements possible.Therefore, there are a total of 81 * 2 = 162 three digit numbers with ‘0′ as one of the digits.

When two ‘0s’ appear: The first digit of the number can be any of the 9 digits. The second and third digit are 0s.

Hence there are 9 such numbers and 0 appears 9*2 = 18 times. Hence, ‘0′ appears 18 + 162 = 180 times in three digit numbers. In 4-digit numbers, 0 might be either 1 or 2 or 3 of the digits.

When one ‘0′ appears: The remaining three digits can be any of the 9 digits.i.e. 93 combinations = 729. The ‘0′ can either be the second or third or fourth digit. Hence 3*729 numbers = 2187.

When two 0s appear: The remaining two digits can be any of the 9 digits.Hence 92 = 81 possible combinations. The two 0s can be in two of the three positions = 3*81 = 243 such numbers and 2*243 = 486 number of times 0 will be appear.

When three 0s appear: There are 9 such numbers and 0 appears thrice in each. Hence 9*3 = 27 times.

Hence the number of 0s in 4-digit numbers = 2187 + 486 + 27 = 2700 times.

There is one 5-digit number - 10,000 and 0 appears four times in this number.

Hence the total number of times 0 appears between 1 and 10,000 = 9 + 180 + 2700 + 4 = 2893.

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Question:

What number should be subtracted from x^3 + 4x^2 – 7x + 12 if it is to be perfectly divisible by x + 3?

(1) 42

(2) 39

(3) 13

(4) None of these

Correct Answer - (1)

Explanation:

According to remainder theorem when, then the remainder is f(-a). In this case, as x + 3 divides x3 + 4×2 – 7x + 12 – k perfectly (k being the number to be subtracted), the remainder is 0 when the value of x is substituted by –3.

=> (-3)3 + 4(-3)2 – 7(-3) + 12 – k = 0

=> -27 + 36 + 21 + 12 = k

=> k = 42

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Question:

What is the value of M and N respectively? If M39048458N is divisible by 8 and 11; Where M and N are single digit integers?

(1) 7, 8

(2) 8, 6

(3) 6, 4

(4) 5, 4

Correct Answer - (3)

Explanation:

If the last three digits of a number is divisible by 8, then the number is divisible by 8 (test of divisibility by 8).

Here, last three digits 58N is divisible by 8 if N = 4. (Since 584 is divisible by 8.)

For divisibility by 11. If the digits at odd and even places of a given number are equal or differ by a number divisible by 11, then the given number is divisible by 11.

Therefore, (M+9+4+4+8)-(3+0+8+5+N)=(M+5) should be divisible by 11 => when M = 6.

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Question:

How many zeros contained in 100!?

(1) 100

(2) 24

(3) 97

(4) Cannot be determined

Correct Answer - (2)

Explanation:

If the number N = 2×1.3×2.5×3 ….. pxq. It is clear that each pair of prime factors 2 and 5 will generate one zero in the number N, because 10 = 2X5.

For finding out the number of zeros in the number it is sufficient to find out how many two’s and five’s appear in the expansion of each product N.

No. of five’s = No. of two’s = Hence it is evident that there are only 24 pairs of primes 2 and 5 and therefore 100! ends in 24 zeros.

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May 30th, 2007 — CAT Preparation, Entrance Exams, GRE Preparation, MBA Study Material, Prep Material

**Exercise4 + Answers + Explanation**

Question:

When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?

(1) 11

(2) 17

(3) 13

(4) 23

Correct Answer - (3)

Explanation:

Let the divisor be d.

When 242 is divided by the divisor, let the quotient be ‘x’ and we know that the remainder is 8. Therefore, 242 = xd + 8

Similarly, let y be the quotient when 698 is divided by d.

Then, 698 = yd + 9.

242 + 698 = 940 = xd + yd + 8 + 9

940 = xd + yd + 17

As xd and yd are divisible by d, the remainder when 940 is divided by d should have been 17.

However, as the question states that the remainder is 4, it would be possible only when leaves a remainder of 4.

If the remainder obtained is 4 when 17 is divided by d, then d has to be 13.

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Question:

What is the total number of different divisors of the number 7200?

(1) 20

(2) 4

(3) 54

(4) 32

Correct Answer - (3)

Explanation:

Express 7200 as a product of prime numbers. We get 7200 = 25 * 32 * 52.

The number of different divisors of 7200 including 1 and 7200 are (5 + 1)(2 + 1)(2 + 1) = 6 * 3 * 3 = 54

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Question:

When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?

(1) 10

(2) 7

(3) 192

(4) None of these

Correct Answer - (2)

Explanation:

Let the number be ‘a’.

When ‘a’ is divided by 36, let the quotient be ‘q’ and we know the remainder is 19

=> and remainder is 19

=> a = 36q + 19

now, a is divided by 12

=> 36q is perfectly divided by 12

Therefore, remainder = 7

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Question:

A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before the will have result that will end with 3 zeroes?

(1) 11

(2) 10

(3) 6

(4) 5

Correct Answer - (3)

Explanation:

A number will end in 3 zeroes when it is multiplied by 3 10s. To get a 10, one needs a 5 and a 2.

Therefore, this person should multiply till he encounters three 5s and three 2s.

20 has one 5 (5 * 4) and 25 has two 5s (5 * 5).

20 has two 2s (5 * 2 * 2) and 22 has one 2 (11 * 2).

Therefore, he has to multiply till 25 to get three 5s and three 2s, that will make three 10s. So, he has to multiply from 20 to 25 i.e. 6 numbers.

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Question:

How many four digit numbers exist which can be formed by using the digits 2, 3, 5 and 7 once only such that they are divisible by 25?

(1) 4! - 3!

(2) 4

(3) 8

(4) 6

Correct Answer - (2)

Explanation:

The numbers that are divisible by 25 are the numbers whose last two digits are ‘00′, ‘25′, ‘50′ and ‘75′.

However as ‘0′ is not one of the four digits given in the problem, only numbers ending in ‘25′ and ‘75′ need to be considered.

Four digit number whose last two digits are ‘25′ using 3 and 7 as the other two digits are 3725 and 7325.

Similarly, four digit numbers whose last two digits are ‘75′ using 2 and 3 as the other two digits are 2375 and 3275.

Hence there are four 4-digit numbers that exist.

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May 30th, 2007 — CAT, CAT Preparation, Entrance Exams, MBA, MBA Study Material, Prep Material

A collection of questions that typically appear in the Common Admission Test (CAT) from the topic Number Theory.

These questions will guide you through your CAT and other MBA entrance exam preparation.

1. When 26854 and 27584 are divided by a certain two digit prime number, the remainder obtained is 47. Which of the following choices is a possible value of the divisor?

2. If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of ‘a’?

3. What is the remainder when 9^1 + 9^2 + 9^3 + …. + 9^8 is divided by 6?

2. A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

4. ‘a’ and ‘b’ are the lengths of the base and height of a right angled triangle whose hypotenuse is ‘h’. If the values of ‘a’ and ‘b’ are positive integers, which of the following cannot be a value of the square of the hypotenuse?

5. Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?

6. What is the reminder when 91 + 92 + 93 + …… + 99 is divided by 6?

7. For what value of ‘n’ will the remainder of 351^n and 352^n be the same when divided by 7?

8. How many keystrokes are needed to type numbers from 1 to 1000?

9. When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?

10. Find the greatest number of five digits, which is exactly divisible by 7, 10, 15, 21 and 28.

11.Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

12. Find the value of 1.1! + 2.2! + 3.3! + ……+n.n!

13. Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

14. When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?

15. A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before the will have result that will end with 3 zeroes?

16. How many different factors are there for the number 48, excluding 1 and 48?

17. How many zeros contained in 100!?

18. Two numbers when divided by a certain divisor leave remainders of 431 and 379 respectively. When the sum of these two numbers is divided by the same divisor, the remainder is 211. What is the divisor?

19. What number should be subtracted from x^3 + 4x^2 – 7x + 12 if it is to be perfectly divisible by x + 3?

20. What is the least number that should be multiplied to 100! to make it perfectly divisible by 350?