Problem Solving

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.

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!!!

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

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

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

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 ...

plugin 0 and 2, you'll get E