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Data Sufficiency - CAT 2008
Question 4 the day:
April 22, 2002
- Mark 1
- If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.
- Mark 2
- If the question can be answered by using either statement alone.
- Mark 3
- If the question can be answered by using both statements together, but cannot be answered by using either statement alone.
- Mark 4
- If the question cannot be answered even by using both the statements together.
- Question
- Is p > q?
(A) p + 5q is positive.
(B) p + 4q is negative.
Correct Answer - (3)
Solution:
Statement A alone is not sufficient. From this statement alone we do not know if p or q which is greater of the two?
Statement B alone is not sufficient. Again this statement alone does not tell us if p is greater than q or vice versa.
Therefore, the answer is neither (1) nor (2). It has to be either (3) or (4).
Let us try and use the information given and statement A and statement B together.
Statement A - p + 5q is positive.
Statement B - p + 4q is negative.
p + 4q which is a negative number becomes positive when another q is added to it (as p + 5q is positive). Hence, we can conclude that q is a positive number. Otherwise, p + 4q will not become positive when a q is added to it.
If q is positive, then p + 4q will be negative only if p happened to be negative. Therefore, if p is negative and q is positive, then we can conclude that q > p or that p is not greater than q. As statement (A) and statement (B) together have conclusively determined that q > p, the correct answer is (3)
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