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- Joined: Sun Jul 24, 2011 10:36 am
Hello Sandeep,
Here is my attempt:
Question rephrasing-
a + b + c = 100
Is a > 24?
If b + c > 76, then a < 24.
If b + c = 76, then a = 24.
If b + c < 76, then a > 24.
STATEMENT 1-
a <= b and b <=c
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| a | 1 | 25 |
| b | 9 | 26 |
| c | 90 | 49 |
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| ? | N | Y |
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If b is 9 and c is 90, then a is 1. Is a > 24? NO.
If b is 26 and c is 49, then a is 25. Is a > 24? YES.
Statement 1 is insufficient.
STATEMENT 2-
3a > 2b
a > 2b / 3
If b = 60, then 2b = 120, and 120/3 = 40. In this case, a would be 40. Is a > 24? YES.
If b = 30, then 2b = 60, and 60/3 = 20. Is a > 24? NO.
Statement 2 is insufficient.
STATEMENTS 1 & 2-
If b = 6, then 2b = 12, and 12/3 = 4. 4 + 6 = 10. c would be 90. In this case, is a > 24? NO.
If a = 25, 3a = 75, and 75/2 = 37.5. a + b = 25 + 37.5 = 62.5. c would be 100 - 62.5 = 37.5, which satisfies b <=c. In this case, is a > 24? YES.
I would choose answer choice E, as neither are sufficient, by themselves or together.
Please note that the question stem says that the numbers are positive. It doesn't say that they have to be integers. If there were an integer constraint placed in the question, then the following would take place:
a = 24, b = 36, c = 40; in which is a > 24? NO.
We would then try:
a = 26, b = 39, c = 35; in which is a > 24? YES --- BUT it doesn't hold because b > c, whereas b should be <= c.
Is what I typed out clear? :-/
Hope it helps!
--Rishi
