If a and b are distinct positive integers, and a is even, then which

Question

If a and b are distinct positive integers, and a is even, then which of the following must also be even?

A. 2(a + b) – 3
B. (a – b) + 2
C. a + b – 1
D. a – b
E. ab – 2

Basavaraju · Answer

Consider a=2 and b=1

This will eliminate options A,B,D

Now consider a=2, b=2
This will eliminate C

Posted from my mobile device

mokarios · Answer

Product of a and b will always be even if they are both integers, and if a is even.

Subtracting 2 from an even sum (as in option E) leaves you with an even number.

Posted from my mobile device

Archit3110 · Answer

a=e and b= e/o

A. 2(a + b) – 3 ; always odd
B. (a – b) + 2; can be both o/e
C. a + b – 1; can be both o/e
D. a – b; can be both o/e
E. ab – 2;; always even
IMO E

btrg · Answer

IMO E. let a =2k b= 2k+1 .

ab -2 = 2k(2k+1) - 2 =  2 (k(2k+1)-1))) always even

DrDilipkumar · Answer

If a=2 and b=1 then E will be zero! (0 is neither odd nor even)
Why is everyone saying e is the right option??
I think it should be C. Please correct me if i'm wrong?

DrDilipkumar · Answer

if a=2 b=1 then ab-2 should be zero. Am i missing something?

Bunuel · Answer

0 is an even integer.

ZERO:

1. Zero is an  INTEGER .

2. Zero is an  EVEN  integer.

3. Zero is  neither positive nor negative  (the only one of this kind)

4. Zero is  divisible by EVERY integer except 0 itself  ( \frac{0}{x} = 0 , so 0 is a divisible by every number, x).

5. Zero is a  multiple of EVERY integer  ( x*0 = 0 , so 0 is a multiple of any number, x)

6. Zero is  NOT a prime number  (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed:  anything/0 is undefined .

8. Any non-zero number  to the power of 0 equals 1  ( x^0 = 1 )

9.  0^0  case is  NOT tested on the GMAT .

10. If the exponent n is positive (n > 0),  0^n = 0 .

11. If the exponent n is negative (n < 0),  0^n  is undefined, because  0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0} , which is undefined.  You CANNOT take 0 to the negative power .

12.  0! = 1! = 1 .

If a and b are distinct positive integers, and a is even, then which

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a and b are distinct positive integers, and a is even, then which

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards