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

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Math Expert
Joined: 02 Sep 2009
Posts: 56244
If a is a positive even integer, and ab is a negative even integer, th  [#permalink]

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05 Jul 2018, 21:45
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Question Stats:

14% (00:34) correct 86% (00:57) wrong based on 61 sessions

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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

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Math Expert
Joined: 02 Aug 2009
Posts: 7764
If a is a positive even integer, and ab is a negative even integer, th  [#permalink]

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05 Jul 2018, 23:08
Bunuel wrote:
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

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
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WE: Supply Chain Management (Energy and Utilities)
Re: If a is a positive even integer, and ab is a negative even integer, th  [#permalink]

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05 Jul 2018, 23:10
Bunuel wrote:
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

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)
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PKN

Rise above the storm, you will find the sunshine
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Joined: 14 Feb 2018
Posts: 389
Re: If a is a positive even integer, and ab is a negative even integer, th  [#permalink]

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06 Jul 2018, 03:24
1
PKN wrote:
Bunuel wrote:
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

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)

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
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Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
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Re: If a is a positive even integer, and ab is a negative even integer, th  [#permalink]

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06 Jul 2018, 03:38
SonalSinha803 wrote:
PKN wrote:
Bunuel wrote:
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

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)

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

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.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Re: If a is a positive even integer, and ab is a negative even integer, th   [#permalink] 06 Jul 2018, 03:38
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