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Is b an even integer?

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by VJesus12 » Fri Apr 27, 2018 12:51 am

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Difficulty—

Is b an even integer?

(1) The product of b and integer c is even.
(2) b is divisible by 4.

The OA is the option B.

Why is not sufficient the first statement? May anyone clarifies this for me?
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Source: — Data Sufficiency |
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by GMATinsight » Fri Apr 27, 2018 12:55 am
VJesus12 wrote:Is b an even integer?

(1) The product of b and integer c is even.
(2) b is divisible by 4.

The OA is the option B.

Why is not sufficient the first statement? May anyone clarifies this for me?
Question: Is b an Even Integer?

Statement 1: The product of b and integer c is even.

Case 1: One of the Integers b and c is definitely Even
Case 2: Both integers are even
Case 3: One of the number is (2/3 ) and other Number is 3

NOT SUFFICIENT

Statement 2: b is divisible by 4.

i.e. b is Definitely EVEN Hence

SUFFICIENT

Answer: Option B
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by Vincen » Fri Apr 27, 2018 3:03 am
VJesus12 wrote:Is b an even integer?

(1) The product of b and integer c is even.
(2) b is divisible by 4.

The OA is the option B.

Why is not sufficient the first statement? May anyone clarifies this for me?
Hi vjesus12.

(1) The product of b and integer c is even.

This statement is not sufficient because if c=2 then b*c will be even, but it doesn't tell us anything about b.

(2) b is divisible by 4.

Now, since b is divisible by 4, then $$b=4\cdot k=2\cdot\left(2k\right)\ \ \Rightarrow\ \ b\ is\ even.$$ SUFFICIENT.

Therefore, the correct answer is the option B.
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by Brent@GMATPrepNow » Fri Apr 27, 2018 5:34 am
VJesus12 wrote:Is b an even integer?

(1) The product of b and integer c is even.
(2) b is divisible by 4.
Target question: Is b an even integer?

Statement 1: The product of b and integer c is even.
Let's TEST some values.
There are several values of b and c that satisfy statement 1. Here are two:
Case a: b = 2 and c = 3. Here, the product bc = (2)(3) = 6, which is even. In this case, b = 2, so the answer to the target question is YES, b IS even
Case b: b = 3 and c = 2. Here, the product bc = (3)(2) = 6, which is even. In this case, b = 3, so the answer to the target question is NOT, b is NOT even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b is divisible by 4.
By definition, this means we can write: b = 4k for some integer k
We can rewrite this as: b = (2)(2)(k) for some integer k
This means b is a multiple of 2, which also tells us that b is EVEN
So the answer to the target question is YES, b IS even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Brent
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by Jeff@TargetTestPrep » Tue May 01, 2018 9:22 am
VJesus12 wrote:Is b an even integer?

(1) The product of b and integer c is even.
(2) b is divisible by 4.
We need to determine whether be is an even integer.

Statement One Alone:

The product of b and integer c is even.

Statement one alone is not sufficient to answer the question. For example,

If b = 2 and c = 4, the answer is yes. If b = 1 and c = 4, the answer is no.

Statement Two Alone:

b is divisible by 4.

Since b is divisible by 4, b must be an even integer.

Answer: B

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