Mo2men wrote:If a is greater than 3/4 of b, is a less than 40?
(1) b < 50
(2) a is a prime number.
We are given the following:
a > (3/4)b
We need to determine whether a is less than 40.
Statement One Alone:
b < 50
Let's let b = 50 and substitute 50 for b in the given inequality.
a > (3/4)(50)
a > 75/2 = 37.5
Since b is actually less than 50, we see that a is greater than a number smaller than 37.5. However, the fact that a is greater than a number smaller than 37.5 does not mean that a is less than 40. For example, if a > 37, a can be greater than 40 (e.g., a = 41) or less than 40 (e.g., a = 39). Statement one alone is not sufficient to answer the question.
Statement Two Alone:
a is a prime number
Since there are prime numbers greater and less than 40, statement two is not sufficient to answer the question.
Statements One and Two Together:
If we let b = 48, then a could equal 37, as 37 is a prime number and 37 > 3/4 x 48 = 36. On the other hand, a could also equal 41 because 41 is also a prime number and 41 > 36 as well. Thus, we cannot definitively state that a is less than 40. The two statements together are still not sufficient to answer the question.
Answer:
E
