If a is a positive even integer, and ab is a negative even integer, th

Question

If a is a positive even integer, and ab is a negative even integer, then b must be which of the following?

A. A negative number
B. A negative even integer
C. A negative integer
D. A positive even integer
E. A positive integer

chetan2u · Answer

let a = 4 ... take a as a multiple of 4 so that 'b' can be tested as a fraction
so 4b = -x where x is even integer..
if x = 2
 4b=-x=-2..........b=\frac{-2}{4}=-\frac{1}{2}  ..... b is a negative fraction
if x=4
 4b=-x=-4..........b=\frac{-4}{4}=-1  ..... b is a negative integer

A

even the choices give the answer away.. 
if a is positive and ab is negative.......b has to be negative
eliminate D and E

now negative numbers = ( negative fractions, negative integers, negative even integers, negative odd integers, )
so A consists of B and C as B and C are subset
so A itself would mean D and e

ans A

PKN · Answer

Given a=positive even 
 ab=negative even

For ab to be negative even , there are 3 cases of b:-
When a=18 
1. b=-2, so ab=18*(-2)=-36 (here b is negative even integer)--------option D & E eliminated.
2. b=-3, so ab=18*(-3)=-54 (here b is negative odd integer)--------option B eliminated.
3. b= \frac{-1}{3} , so ab=18* \frac{-1}{3} =-6 (here b is rational number)----------------option C eliminated.
Therefore, Since a*b is negative even & a is positive even, so 'b' is always a negative number.
Caution:- This is a  MUST BE TRUE  question.

Ans. (A)

SonalSinha803 · Answer

In my opinion the answer should be C. The question asks b "must be" what ? With your example 18*(-1/3) will result in an integer but 18*(-1/4) won't be an integer.

A would have been the answer if the question would have asked "could be". But the stem asks "must be". Thus, b must be a negative integer.

I would go with C.

Posted from my mobile device

PKN · Answer

Hi,

you have to choose 'b' judiciously so that ab will yield a negative even integer as per question.
So, in your case if  b=\frac{-1}{4}  and a=18(say),  a*b=-\frac{18}{4}  which violates the data provided in question.

So, choose (a,b) accordingly.

Hope it helps.

TommasoP · Answer

Given that a is positive and ab is negative then b must be negative.
Given that a is even and ab is even, b may be even or odd.
Given that a and ab are an integer, try some cases:
a=6; b=(-1/3); ab=(-2)
a=6; b=(-3); ab=(-18)

b must be negative, but is not necessarily an integer, and parity isn't defined.

A

AkshayprasannaM · Answer

The answer seems to be incorrect for this - would like to know expert's answer on this

Bunuel · Answer

If a is a positive even integer, and ab is a negative even integer, then b must be which of the following?

A. A negative number
B. A negative even integer
C. A negative integer
D. A positive even integer
E. A positive integer

Since a > 0 and ab < 0, b must be negative, so the answer is A.

To discard other options, let a = 4. Then:

B is not necessarily true. For example, consider b = -1.
C is not necessarily true. For example, consider b = -1/2.
D and E are ruled out because b must be negative for ab to be negative.

Answer: A.

AkshayprasannaM · Answer

But the question asks which "must" be true. 
So if a = 4 and b = -1/8. In that case ab would not be a negative integer. 
So, I feel C might be correct.

Bunuel · Answer

You are missing a key point. Option A states that b must be a negative number, and this is always true given that a > 0 and ab < 0, so it must be true. Option C, however, is not always true, as shown by the examples in my solution (a = 4 and b = -1/2), so it cannot be the correct answer.

AkshayprasannaM · Answer

Oh okay. Got it! 
Thanks for clarifying!

If a is a positive even integer, and ab is a negative even integer, th

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a is a positive even integer, and ab is a negative even integer, th

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards