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Data Sufficiency - CAT 2013
Question 4 the day:
April 26, 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 x an even number if ‘a’ and ‘b’ are integers?
(A) x =  , where the term leaves no reminder and b is even.
(B) x = , where the term leaves no reminder and both ‘a’ and ‘b’ are odd.
Correct Answer - (1)
Solution:
We need to conclusively know if x is an even number or not. Remember, even if we can conclusively know that x is not even, we have found the answer.
Statement A is: x = , where the term leaves no reminder and b is even. If there is no reminder when b divides a and b is even, then a has to be an even number too. When an even number divides another even number, the quotient (x in this case) can be either odd or even. For eg. 6/2 = 3 (odd) or 8/2 (even). In both cases, 2 which is an even number divides another even number (6 or 8). Therefore, from statement A, we will not know conclusively if x is odd or even. It could be either.
Statement B is x = , where the term leaves no reminder and both ‘a’ and ‘b’ are odd.
If a and b are both odd and when b divides a there is no reminder. When an odd number divides another odd number and there is no reminder, then the quotient has to be odd. Therefore, the quotient ‘x’ in this case is conclusively odd.
Hence Statement B alone answers the question while statement A alone does not.
Therefore, the answer is (1).
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