If a b c d e and if the product abcde is negative, which of the

Question

If a > b > c >d > e and if the product abcde is negative, which of the following must be negative?

I. e - a
II. d/c
III. abe

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Ayeka · Answer

The product of abcde is negative.
(An odd number of digits are negative) 
Given: a > b > c > d > e

a,b,c,d,e

+ + + + -
+ + - - - 
- - - - -

1) e-a = -e-(a) = sum is negative. TRUE

2) d/c = 
 Either d/c or (-d/-c) 
 The negative sign gets cancelled. So, it’s always positive. FALSE

3) abe = 
 (a*b*-e) = - 
 (-a*-b*-e) = - 
 The multiplication of abe is always negative. TRUE

CORRECT ANSWER (E)

Posted from my mobile device

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/if-m-p-r-t-z ... 30820.html https://gmatclub.com/forum/if-a-b-c-d-e ... 80577.html Hope this helps.

Avinash_g · Answer

for 2, it can be -d/c as well. as d is smaller than c and one of the digits is -ve. can you please explain the logic behind your explanation. Thanks!

Happysumit007 · Answer

if a = 1 and e = -1, then it will be zero for the third possible case
. ( also not mentioned that they are integers).

Krunaal · Answer

In that case, e - a = -1 - 1 =  -2  and abe =  -b , since a > 0, b > 0 therefore abe is negative

saynchalk · Answer

Since the product is negative, either one or 3 of the numbers in ABCDE is negative. Since at least one must be negative, and because E is the smallest, E must be negative.

1) E - A = Negative - Positive = Negative
2) d/c, not necessary as either one or three numbers can be negative
3) ABE must be negative since at most 3 digits can be negative and A and B are the largest digits, so they must be positive

If a > b > c >d > e and if the product abcde is negative, 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