BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Properties of Numbers - OG (2nd edition)

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 110
Joined: Thu Apr 05, 2012 8:48 am
Thanked: 3 times
Followed by:1 members

Properties of Numbers - OG (2nd edition)

by shanice » Fri Apr 06, 2012 6:26 pm
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

(A)3 (B)4 (c)12 (D)32 (E)35

The answer is B.

I understand the 1st and 2nd sentence of the question but having problem understanding the 3rd sentence - "What is the smallest positive integer k such that k+n is a multiple of 35?". What does the question mean?

Thank you in advance.
Top
Source: — Quantitative Reasoning |
User avatar
GMAT Instructor
Posts: 1248
Joined: Thu Mar 29, 2012 2:57 pm
Location: Everywhere
Thanked: 503 times
Followed by:192 members
GMAT Score:780

by Bill@VeritasPrep » Fri Apr 06, 2012 6:30 pm
The sum of k and n must be a multiple of 35, i.e. 35, 70, etc. Since we're looking for k, we need to solve for the value of n, then see what we must add to that value to make the sum a multiple of 35.
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test
Top
Master | Next Rank: 500 Posts
Posts: 110
Joined: Thu Apr 05, 2012 8:48 am
Thanked: 3 times
Followed by:1 members

by shanice » Fri Apr 06, 2012 6:57 pm
Thank you, Bill.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 435
Joined: Mon Mar 15, 2010 6:15 am
Thanked: 32 times
Followed by:1 members

by eaakbari » Thu Nov 08, 2012 10:40 pm
Solution please?
Whether you think you can or can't, you're right.
- Henry Ford
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Fri Nov 09, 2012 7:38 am
eaakbari wrote:Solution please?
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

(A)3
(B)4
(C)12
(D)32
(E)35

Here's one approach:

There's a nice rule that says, If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

First we're told that when n is divided by 5, the remainder is 1.
So, possible values of n are 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, etc.

Next we're told that when n is divided by 7, the remainder is 3.
So, possible values of n are 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, etc.

So, we can see that n could equal 31, or 66, or an infinite number of other values.

Important: Since the Least Common Multiple of 7 and 5 is 35, we can conclude that if we list the possible values of n, each value will be 35 greater than the last value.

So, n could equal 31, 66, 101, 136, and so on.

Notice that, if we take any of these values, we need to add 4 to it so that the sum will be a multiple of 35. So, the smallest value of k is 4 such that k+n is a multiple of 35.

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1