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

Question

A. 2x + 2
B. 4x + 3
C. 12x-6
D. 13x
E. 14x

BrentGMATPrepNow · Answer

Let's test a nice easy value of x. 
How about x =  0

We get...
A. 2( 0 ) + 2 = 2, which is EVEN
B. 4( 0 ) + 3 = 3, which is   ODD  
C. 12( 0 ) - 6 = 12, which is EVEN
D. 13( 0 ) = 0, which is EVEN
E. 14( 0 ) = 0, which is EVEN

Answer: B

Cheers, 
Brent

Abhishek009 · Answer

(A) If x is Odd 2x is even & 2x + 2 will hence be Even ; If x is even then 2x is even & 2x + 2 will hence be Even.
(B) If x is Odd 4x is even & 4x + 3 will hence be Odd ; If x is even then 4x is even & 4x + 3 will hence be Odd.
(C) If x is Odd 12x is even & 12x - 6 will hence be Even ; If x is even then 12x is even & 12x - 6 will hence be Even.
(D) If x is Odd 13x is Odd ; If x is even then 13 x is even
(E) If x is Odd 14x is Even ; If x is even then 14 x is even

Hence , Answer must be (B) as for either odd/even value of x the result is always Odd.

MHIKER · Answer

Multiple of an EVEN number is always even and if an odd number is added with an even number then the result is must be odd.

The answer is B

MathRevolution · Answer

A. 2x + 2 : even(2x) + even(2) = even

B. 4x + 3 : even(2x) + even(2x) + odd = odd

C. 12x - 6: even(12x) - even(6) = even

D. 13x: 13 * 1 = odd; 13 * 2 = even

E. 14x: even(14) * x = even

Answer B

ScottTargetTestPrep · Answer

Solution:
 
Since 4x is even regardless of what integer x is and 3 is odd, 4x + 3 = even + odd = odd.

Answer: B

egmat · Answer

The question asks which expression MUST be odd for every integer x. The  key principle  here is:

Even + Odd = Always Odd 
 Even + Even = Always Even 
 Odd × Anything = Could be either

Let's test each choice:

A)   2 x +  2  =  2 (x +  1 ) — This has a factor of  2 , so it's ALWAYS EVEN. Eliminate.

B)   4 x +  3  — Since  4  times any integer is always even,  4 x is even. Adding  3  (an odd number) to an even number ALWAYS gives an odd number. This MUST be odd.  This is our answer!

But let's confirm by eliminating the rest:

C)   12 x -  6  =  6 ( 2 x -  1 ) — This has a factor of  6 , so it's ALWAYS EVEN. Eliminate.

D)   13 x — If x =  1 , this is  13  (odd). If x =  2 , this is  26  (even). So it's  NOT always odd . Eliminate.

E)   14 x =  2 ( 7 x) — This has a factor of  2 , so it's ALWAYS EVEN. Eliminate.

Answer: B

Key Insight:   The general principle to remember:  Even number + Odd number = ALWAYS Odd . In  4 x +  3 , the  4 x part is always even (any number multiplied by an even number is even), and  3  is always odd. So the result must always be odd.

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

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GMAT Problem Solving (PS) Questions

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

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