If x is an even interger

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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Sun Jun 20, 2010 6:42 am

If x is an even interger, which of the following must be an odd integer?

a- 3x/2
b- 3x/2 + 1
c- 3x^2
d- (3(x)^2)/2
e- (3(x)^2)/2 + 1

OA e

To me, b, e were odds, so I chose one: b, wrong answer. Can anyone explain this please?

Thanks
Silvia.

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Source: Beat The GMAT — Problem Solving | Sun Jun 20, 2010 6:42 am

krazy800: Master | Next Rank: 500 Posts; Posts: 136; Joined: Sun Sep 28, 2008 8:20 pm; Location: fssf; Thanked: 17 times

by krazy800 » Sun Jun 20, 2010 7:00 am

ssuarezo wrote:If x is an even interger, which of the following must be an odd integer?

a- 3x/2
b- 3x/2 + 1
c- 3x^2
d- (3(x)^2)/2
e- (3(x)^2)/2 + 1

OA e

To me, b, e were odds, so I chose one: b, wrong answer. Can anyone explain this please?

Thanks
Silvia.

The question system says MUST BE.

Substitute X=2, in option B. you will get an even integer.

Any even integer, if substituted in option E, gives you an odd number (try out plugging in several even numbers if you want)

IMO E

HTH!!!

Aiming High

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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Sun Jun 20, 2010 7:21 am

krazy800 wrote:
ssuarezo wrote:If x is an even interger, which of the following must be an odd integer?

a- 3x/2
b- 3x/2 + 1
c- 3x^2
d- (3(x)^2)/2
e- (3(x)^2)/2 + 1

OA e

To me, b, e were odds, so I chose one: b, wrong answer. Can anyone explain this please?

Thanks
Silvia.
The question system says MUST BE.

Substitute X=2, in option B. you will get an even integer.

Any even integer, if substituted in option E, gives you an odd number (try out plugging in several even numbers if you want)

IMO E

HTH!!!

But it was soooo simply ...
I forgot division between 2 even numbers can result in an odd number too.
Thanks crazy800 ...

Silvia

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sun Jun 20, 2010 3:27 pm

This number property question can be solved either deductively (by relying on your knowledge of how numbers behave) or by plug-in. If you can, use deductive reasoning to solve number properties questions (especially DS questions) becuase plugging in values takes longer.

Why must E be odd? Well, because x is even, x*x is even*even, and x*x/2 is x(x/2) or even*(x/2). In short, 3(x*x/2) = 3*even = even. Thus [3*x*x/2]+1 is even+1 = ODD. E must be odd.

Both solutions (plug-in and deductive reasoning) are discussed in detailed, and a video solution is shown at GMATPrep question 1185. To practice similar questions, set topic='Number Properties' and difficulty='500-600' in the Drill Generator.

-Patrick

Check out my site: GMATFix.com

To prep my students I use this tool >> (screenshots, video)

Ask me about tutoring.

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vzzai: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Tue Sep 02, 2008 12:13 am; Thanked: 1 times; GMAT Score:650

by vzzai » Wed Nov 16, 2011 3:57 am

I'm sorry for digging out an old problem!.

Quick questions: If I use the following grid, proposed in one of the GMAT books, I would not get any equation that would conclusively tell me if the equation is going to be even/odd.
If we were to use the plugin, How much should we rely on plug ins?
Could you tell me when I should use and when not to?

e o Non-integer
e/e Yes Yes Yes
e/o Yes No Yes
o/e No No Yes
o/o No Yes Yes

Thank you,
Vj

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Wed Nov 16, 2011 7:08 am

ssuarezo wrote:If x is an even interger, which of the following must be an odd integer?

a- 3x/2
b- 3x/2 + 1
c- 3x^2
d- (3(x)^2)/2
e- (3(x)^2)/2 + 1

OA e

To me, b, e were odds, so I chose one: b, wrong answer. Can anyone explain this please?

Thanks
Silvia.

All even integers must be multiples of 2...

Now , out of the given options initially option a seems to be perfect , coz we can write it as -

3x/2 => 3(2a)/2 =>3a

Now here we have 2 possibilities , a can be -ve also , and in that case 3a will be -ve... So to make it +ve we can take square of x ( To make 3a part +ve )

Out of the given options only E follows ,hence E is the correct answer...

Another shortcut can be plugging in some arbitrary value of x ...

Abhishek

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Wed Nov 16, 2011 4:27 pm

plugin 0 and 2, you'll get E

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