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

Redeem

OG Quant PS Question Answer Explanation

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Thu Jul 01, 2010 8:40 am
Location: London

OG Quant PS Question Answer Explanation

by kourousafama » Mon Sep 06, 2010 2:14 am
Hi,

Does anybody have a clear and simple answer for the following problem? The answer given is the OG quant review seems to me very complicated.

Many thanks,

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
kourousafama
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 324
Joined: Mon Jul 05, 2010 6:44 am
Location: London
Thanked: 70 times
Followed by:3 members

by kmittal82 » Mon Sep 06, 2010 2:49 am
There are 2 ways of doing this:

1) Hard way (Using algebra)

n= 5p + 1
n= 7q + 3

n+k = 5p + (1+k)
n+k = 7q + (3+k)

if k = 4
n+4 = 5p + 5 = 5(p+1)
n+4 = 7q + 7 = 7(q+1)

Thus, 4 is the smallest number which gives us no remainder for each case, since any number divisible by 35 must be divisible by both 7 and 5.

2) Easy way (picking numbers)

31 is a good number which satisfies this criteria, and you can see adding 4 to 31 will make it divisible by 35

Hence, (B)
Top
Senior | Next Rank: 100 Posts
Posts: 84
Joined: Mon Apr 26, 2010 2:51 am
Thanked: 6 times
Followed by:1 members

by brijesh » Mon Sep 06, 2010 2:52 am
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[/quote]

I tried as follows:

K+n may be one of the 35, 70, 105, 140....etc

last digit of n may be = 1 or 6

here the k+n= 105 satisfying the above condition , considering the k=4 (smallest +ve integer)

ans: B
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 98
Joined: Thu Aug 19, 2010 10:00 am
Thanked: 7 times
Followed by:1 members
GMAT Score:760

by scorpionz » Mon Sep 06, 2010 5:00 am
kourousafama wrote:Hi,

Does anybody have a clear and simple answer for the following problem? The answer given is the OG quant review seems to me very complicated.

Many thanks,

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 simplest way in my opinion is as follows -

n = 5p + 1 ==> This means that for n to be exactly divisible by 5, we must add 4 or subtract 1
n = 7q + 3 ==> This means that for n to be exactly divisible by 7, we must add 4 or subtract 3

The question asks us what no. "k" should be added to make the no. k+n divisible by 35. If a no. has to be divisible by 35, clearly it must be divisible by both 5 and 7. Looking at the above two equations for n, it is obvious that the least value that must be added to make the no. divisible by both 5 and 7 is 4. Hence B is the answer.

This method works for me. Hopefully it will work for you too!!

Cheers!
Top
Post new topic Post Reply
• Page 1 of 1