the candies among 7 children

Expert replies

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Sep 14, 2010 4:08 am

Marge has n candies, where n is an integer such that 20 < n< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

[spoiler]Source: https://readyforgmat.com[/spoiler]

The mind is everything. What you think you become. –Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Source: Beat The GMAT — Problem Solving | Tue Sep 14, 2010 4:08 am

GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Tue Sep 14, 2010 5:23 am

When Marge divides n candies among 5 children let each child gets x candies.
Then, n = 5x + 2
When Marge divides n candies among 6 children let each child gets y candies.
Then, n = 6y + 1
So, we have 5x + 2 = 6y + 1 or 6y - 5x = 1. Now choose the values of x and y so that their difference is 1, and 20 < n< 50.
Possible integer values are:
x = 7, y = 6 implies 6(6) - 5(7) = 1
n = 5(7) + 2 = 6(6) + 1 = 37

If Marge divides 37 candies among 7 children, then 2 candies will be left.

The correct answer is [spoiler](C)[/spoiler].

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

ankur.agrawal: Master | Next Rank: 500 Posts; Posts: 261; Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members; Location: Varanasi; Thanked: 11 times

by ankur.agrawal » Tue Sep 14, 2010 5:28 am

Alternate way particularly for this question:

equally among 5 children = we can have 22,27,32,37,42,47 as possible values.

equally among 6 children = we can have 25,31,37,42,47 as possible values.

So only 37 is possible . So n =37.

Dividing by 7 we get 2 as remainder.

C

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review