Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 16 Jul 2019, 13:39

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

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

Show Tags

New post 05 Jul 2018, 21:45
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

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

HideShow timer Statistics


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

Show Tags

New post 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
_________________
VP
VP
User avatar
D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: If a is a positive even integer, and ab is a negative even integer, th  [#permalink]

Show Tags

New post 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)
_________________
Regards,

PKN

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

Show Tags

New post 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
VP
VP
User avatar
D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: If a is a positive even integer, and ab is a negative even integer, th  [#permalink]

Show Tags

New post 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
GMAT Club Bot
Re: If a is a positive even integer, and ab is a negative even integer, th   [#permalink] 06 Jul 2018, 03:38
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne