If b, c and d are even integers, and Y is an odd integer,

Brent@GMATPrepNow wrote: ↑

Tue Mar 10, 2020 5:34 am

If b, c and d are even integers, and Y is an odd integer, which of the following CANNOT be true?

A) b/(cd) = Y
B) (b/c)(d) = Y
C) (b + c)/d = Y
D) (Y – b)/c = d
E) (b + c + d)/2 = Y

Answer: D
Source: www.gmatprepnow.com

Let's eliminate answer choices that COULD be true.

A) 12/(2)(2)=3. ELIMINATE A
B) (2/4)(6)=3. ELIMINATE B
C) (2+4)/2=3. ELIMINATE C
D) (Y – b)/c = d
E) (2+2+2)/2=3. ELIMINATE E

By the process of elimination, the correct answer must be D

ASIDE: Here's why answer choice D is correct
If Y is ODD and b is EVEN, then Y - b = ODD - EVEN = ODD
So, (Y – b)/c = d becomes ODD/c = d
Multiply both sides by c to get: ODD = cd
Since c and d are both EVEN, we get: ODD = (EVEN)(EVEN), which can never be true
Answer: D

Cheers,
Brent

Brent@GMATPrepNow wrote: ↑

Tue Mar 10, 2020 5:34 am

If b, c and d are even integers, and Y is an odd integer, which of the following CANNOT be true?

A) b/(cd) = Y
B) (b/c)(d) = Y
C) (b + c)/d = Y
D) (Y – b)/c = d
E) (b + c + d)/2 = Y

Answer: D
Source: www.gmatprepnow.com

Looking at the choices, we see that the expression on the left hand side of the equation in choice D is (odd - even)/even = odd/even, which is not even an integer; it can’t be equal to an even integer.

Answer: D