Data Sufficiency Ex-1

Directions : For questions in this section mark

(a) If condition (i) alone is sufficient
(b) If condition (ii) alone is sufficient
(c) If both conditions together are sufficient
(d) If condition (i) alone & (ii) alone are sufficient
(e) information not sufficient

1. Is x < 4?
1) x = 9
2) x =25

A) if statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not;
B) if statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not;
C) if statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient;
D) If either statement by itself is sufficient to answer the question;
E) If statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

Solution:
(1) implies that x = +/- 3 (+/- means positive or negative). Both +3 and -3 are less than 4, so the answer is “NO” and (1) is sufficient, that is NO, x is not greater than 4. A “NO” answer is equally acceptable as a “YES” answer. It is only necessary that there is sufficient information to answer the question. (2) implies x = positive or negative 5. -5 is less than 4 and + 5 is greater than 4, so the question cannot be answered with the information given in (2). The correct response is A.

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2. What is x - y?
1) x + y = 8
2) x - 2y = 2

A) if statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not;
B) if statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not;
C) if statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient;
D) If either statement by itself is sufficient to answer the question;
E) If statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

Solution:
(1) is not sufficient since (x - y) is the quantity desired. Likewise, (2) is not sufficient. But (1) and (2) together provide us with 2 equations and two unknowns from which x - y can be determined. The correct response is C. (We may solve the problem by subtracting (2) from (1): 3y = 6, therefore y = 2 and x = 6, so that x - y = 6 - 2 = 4. This calculation is, however, unnecessary.)

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3. How old is Gloria?
1) Gloria’s age is four times Alex’s age plus Becky’s age.
2) Becky was Alex’s age fifteen years ago.

A) if statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not;
B) if statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not;
C) if statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient;
D) If either statement by itself is sufficient to answer the question;
E) If statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

Solution:
(1) is obviously not sufficient as is (2). Can the question be answered with (1) and (2)? Let x be Gloria’s age, y be Alex’s age, and z be Becky’s age. (1) states that x = 4y + z. (2) states that z - 15 = y. These two equations contain three unknowns; consequently, we cannot determine x. More information is needed and the correct response is E.

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4. A student group sold only donuts and GMAT books to raise funds. How many GMAT books were sold?
1) 30% of the 90 items sold were GMAT books.
2) 63 donuts were sold.

A) if statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not;
B) if statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not;
C) if statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient;
D) If either statement by itself is sufficient to answer the question;
E) If statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

Solution:
(1) is sufficient since 30% of 90 is 0.3 x 90 = 27. (2) is not sufficient since we do not know the total number of items sold. So the correct response is A. A note of caution: Never let information in (1) influence your decision regarding the information in (2). In this example we cannot assume that 90 items were sold when deciding if (2) provides sufficient information. This is the Amnesia trick that undisciplined test takers will always fall into. Remember to look at each statement individually before comparing the two.

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5. From a group of 10 teachers, a committee of N teachers has to be formed. What is the value of N?
(1) There are 120 ways to form the required committee
(2) If the group had 2 more teachers, there would be 220 ways to form the required committee

A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient
B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient

Solution:
(C) Either statement alone is not sufficient to answer the question. This is because equation 10CN = 120 as well as equation 12CN = 220 has two roots: formula for combinations is such that 10CN = 10C(10 – N) and 12CN = 12C(12 – N).

However, if we combine the two statements, we will be able to answer the question. From Statement 1 it follows that N is either 7 or 3. From Statement 2 it follows that N is either 9 or 3. From Statement 1 + Statement 2 it follows that N is 3. Therefore, both statements are needed.

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