Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 15:15 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6

Author Message
TAGS:

### Hide Tags

Director  Joined: 29 Nov 2012
Posts: 731
Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6  [#permalink]

### Show Tags

4
14 00:00

Difficulty:   75% (hard)

Question Stats: 63% (02:29) correct 37% (02:08) wrong based on 202 sessions

### HideShow timer Statistics Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6 − c)(6 − d)(6 − e) = 45. What is a + b + c + d + e?

(A) 5
(B) 17
(C) 25
(D) 27
(E) 30

Originally posted by fozzzy on 04 Oct 2013, 00:39.
Last edited by Bunuel on 14 Mar 2019, 02:58, edited 2 times in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 56257
Re: Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6  [#permalink]

### Show Tags

5
3
fozzzy wrote:
Let a, b, c, d and e be distinct integers such that (6-a)(6-b)(6-c)(6-d)(6-e) = 45. What is a+b+c+d+e?

A) 5
B) 17
C) 25
D) 27
E) 30

45=3*3*5

Since a, b, c, d and e are distinct integers, then (6-a), (6-b), (6-c), (6-d), and (6-e) must also be distinct integers, thus (6-a), (6-b), (6-c), (6-d), and (6-e) must be -1, 1, -3, 3, and 5.

(6-a) + (6-b) + (6-c) + (6-d) + (6-e) = 30- (a+b+c+d+e) = -1+1-3+3+5 = 5
a+b+c+d+e = 30 - 5 = 25.

_________________
##### General Discussion
Manager  Joined: 10 Jan 2011
Posts: 123
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)
Re: Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6  [#permalink]

### Show Tags

1
Since 45 = 3 * 3* 5. The whole product should result into 3, 3, and 5. as 6-1= 5 we assume that a=1, also 6-3 = 3 so let say b=3, now we need one more 3 which can be 6-9 = -3 (as a, b,c,d,e are distinct we can not have c = 3), so c= 9. the whole product is now negative, so we have to balance it, so we say d= 7 (resulting into 6-7 = -1) and last must be 5 so that we stick to our product. so e= 5 (6-5 =1).

The total = 1+3+9+7+5= 25. Answer is c
_________________
-------Analyze why option A in SC wrong-------
Director  Joined: 29 Nov 2012
Posts: 731
Re: Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6  [#permalink]

### Show Tags

Since the prime factorization is 3*3*5

The constraint in the question is that they are distinct so the only possible way is 3,-3,5,1,-1

6-a = 3 => a=3
6-b = -3 => b=9
6-c = 5 => c=1
6-d = 1 => c=5
6-e = -1 => e = 7

Intern  B
Joined: 20 Jan 2017
Posts: 5
Schools: Mannheim"19
Re: Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6  [#permalink]

### Show Tags

The question is exclusively asking for value of a+b+c+d+e so that should be 5.
why are we subtracting it from 30.
Math Expert V
Joined: 02 Sep 2009
Posts: 56257
Re: Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6  [#permalink]

### Show Tags

rghvaggarwal wrote:
The question is exclusively asking for value of a+b+c+d+e so that should be 5.
why are we subtracting it from 30.

Check here: https://gmatclub.com/forum/let-a-b-c-d- ... l#p1274086
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 11702
Re: Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6   [#permalink] 24 Dec 2018, 04:14
Display posts from previous: Sort by

# Let a, b, c, d, and e be distinct integers such that (6 − a)(6 − b)(6  