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

Question

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

A)  \frac{b}{cd} = Y

B)  (\frac{b}{c})(d) = Y

C)  \frac{b + c}{d} = Y

D)  \frac{Y – b}{c} = d

E)  \frac{b + c + d}{2} = Y

Gknight5603 · Answer

answer D... Y = cd+b... 
c,d,b all are even...by this way Y will become even, buy in stem Y is given Odd.

Posted from my mobile device

shameekv1989 · Answer

\frac{Y – b}{c}  will be  \frac{O-E}{E}  =  \frac{O}{E}  which will not be an integer. But as given "d" is an integer hence this scenario is not possible.

Answer - D

ArnoldPushkin · Answer

Can you please provide me with an example when B is true?

Posted from my mobile device

shameekv1989 · Answer

\frac{2*6}{4}

BrentGMATPrepNow · Answer

Let's eliminate answer choices that COULD be true.

A)  \frac{12}{(2)(2)} = 3 . ELIMINATE A

B)  (\frac{2}{4})(6) = 3 . ELIMINATE B

C)  \frac{2 + 4}{2} = 3 . ELIMINATE C

D)  \frac{Y – b}{c} = d

E)  \frac{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

ScottTargetTestPrep · Answer

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

aashishagarwal2 · Answer

How can we avoid error in such type of questions? Do we have to by heart (mug-up) to always check 2/4 as substitution in such problem types?

RahulJain293 · Answer

It would be D

For each, you can create cases and start eliminating..

A & B are same and we can use 14/2 as an example which gives 7 (ODD) as output.

For C -> Numerator has sum of 2 Even which gives Even. And even by even can given us ODD as we saw with A & B

For D -> Odd - Even gives Odd  (Note that +/- Even to any expression DOES NOT change even/odd nature of it) 
Odd by Even cannot be Even as there would be a single (an extra 1) left. Imagine ODD and EVEN number of marbles and start cancelling them. You will be left with 1 marble in the numerator.   Hence this CANNOT BE TRUE

For E -> Even + Even + Even gives even and that divided by 2 again can give ODD. Same as A & B
To make it easier, take an even number which is an odd multiple of 2 and break it down into 3 even numbers
Say 14 (2+4+8) and this divided by 2 CAN give us ODD which is 7

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

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 b, c and d are even integers, and Y is an odd integer, which of the

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