GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 07 Dec 2019, 12:12

### 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

# Integer d is the product of the integers a, b, and c and 1 < a < b < c

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59588
Integer d is the product of the integers a, b, and c and 1 < a < b < c  [#permalink]

### Show Tags

13 Sep 2017, 03:42
1
5
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:28) correct 26% (02:59) wrong based on 96 sessions

### HideShow timer Statistics

Integer d is the product of the integers a, b, and c and 1 < a < b < c. If the remainder when 233 is divided by d is 79, what is the value of a+c?

A. 7
B. 9
C. 13
D. 14
E. 18

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: Integer d is the product of the integers a, b, and c and 1 < a < b < c  [#permalink]

### Show Tags

13 Sep 2017, 03:52
1
Bunuel wrote:
Integer d is the product of the integers a, b, and c and 1 < a < b < c. If the remainder when 233 is divided by d is 79, what is the value of a+c?

A. 7
B. 9
C. 13
D. 14
E. 18

d=a*b*c.....
If 233 lives a Remainder 79 when div by d, 233-79 or 154 should be div by d...

154=1*2*7*11..
Now 1<a<b<c and a*b*c=2*7*11, a+c=2+11=13
C
_________________
Current Student
Joined: 02 Jul 2017
Posts: 280
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
Re: Integer d is the product of the integers a, b, and c and 1 < a < b < c  [#permalink]

### Show Tags

13 Sep 2017, 03:59
given d= a*b*c
1<a<b<c
find: a+c

by equation 233 = d*x +79
d*x = 233-79 = 154.
if x=1 => d= 154

so a*b*c = 154 = 2*7*11
=> a=2 and c=11 => a+c = 2+11 =13

Intern
Joined: 19 Sep 2016
Posts: 33
Re: Integer d is the product of the integers a, b, and c and 1 < a < b < c  [#permalink]

### Show Tags

13 Sep 2017, 18:38
233=dx+79 which is the equation of the remainder. Simplifying the equation becomes - dx=154 and it is given that d=a*b*c so substituting the value of d in above equation we get (abc)*x=154. Now prime factorization of 154 is 2*7*11 and assuming the quotient i.e. x=1 and considering the condition given ie. 1<a<b<c. This states that a=2, b=7 & c=11. So a+c=2+11=13, hence the answer is C.

Sent from my SM-N920G using GMAT Club Forum mobile app
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3300
Location: India
GPA: 3.12
Re: Integer d is the product of the integers a, b, and c and 1 < a < b < c  [#permalink]

### Show Tags

13 Sep 2017, 20:47
Bunuel wrote:
Integer d is the product of the integers a, b, and c and 1 < a < b < c. If the remainder when 233 is divided by d is 79, what is the value of a+c?

A. 7
B. 9
C. 13
D. 14
E. 18

233 can be divided by 79 or 158 to give us a remainder of 79

When divided by 158, the difference is 75(3*5^2) but a < b < c
But, when divided by 79, the difference is 154(2*7*11).
Here 1 < a=2 < b=7 < c=11!

Therefore, a+c = 2+11 = 13(Option C)
_________________
You've got what it takes, but it will take everything you've got
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: Integer d is the product of the integers a, b, and c and 1 < a < b < c  [#permalink]

### Show Tags

11 Aug 2019, 19:16
Bunuel wrote:
Integer d is the product of the integers a, b, and c and 1 < a < b < c. If the remainder when 233 is divided by d is 79, what is the value of a+c?

A. 7
B. 9
C. 13
D. 14
E. 18

We see that 233 = dq + 79 where q is a positive integer. Simplifying, we have dq = 154. Since 154 = 14 x 11 = 2 x 7 x 11 and d is a product of 3 distinct positive integers greater than 1, we see that q must be 1 and d must be 154, and hence a = 2, b = 7 and c = 11. So a + c = 2 + 11 = 13.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Integer d is the product of the integers a, b, and c and 1 < a < b < c   [#permalink] 11 Aug 2019, 19:16
Display posts from previous: Sort by

# Integer d is the product of the integers a, b, and c and 1 < a < b < c

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne