If a is greater than 3/4 of b, is a less than 40?

[Mo2men]

If a is greater than 3/4 of b, is a less than 40?

(1) b < 50
(2) a is a prime number.

[GMATGuruNY]

If a is greater than 3/4 of b, is a less than 40?

(1) b < 50
(2) a is a prime number.

Statement 1:
Let b=4.

Substituting b=4 into a>(3/4)b, we get:
a > (3/4)(4)
a > 3.
Case 1: a=5, in which case a<40.
Case 2: a=41, in which case a>40.

Cases 1 and 2 satisfy both statements.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.

[Jay@ManhattanReview]

If a is greater than 3/4 of b, is a less than 40?

(1) b < 50
(2) a is a prime number.

Hi Mo2men,

We are given that a > (3/4)*b. We have to see whether a < 40.

Let's take each statement one by one.

S1: b < 50

Say b = 48

(3/4)*b = (3/4)*48 = 36

=> a > 36.

If a = 37, the answer is Yes; however, if a = 40 or more, the answer is No. Insufficient.

S2: a is a prime number.

Clearly, not sufficient.

Let's combine them.

S1 and S2:

Since we derived above that a > 36, 'a' can be any prime number such as 37, 41, etc.

If a = 37, the answer is Yes, else No. Insufficient.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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Hi Mo2men,

What is the source of this question? I ask because even though it includes a variety of different math concepts, the work required to answer this question barely requires knowledge of those concepts.

We're told that A is GREATER then 3/4 of B. We're asked if A is LESS than 40. This is a YES/NO question - and the answer is ultimately based on the value of B. IF B is greater than 160/3, then the answer to the question is automatically YES. Otherwise, the answer is almost certainly inconsistent.

1) B < 50

IF B = 0....
and A = 2, then the answer to the question is YES.
and A = 41, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) A is a PRIME number

IF... A = 2, then the answer to the question is YES.
IF... A = 41, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we have two 'overlapping' answers (one YES and one NO), so there's no more work required.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

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