It is currently 19 Oct 2017, 04:53

### 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

# m is a three-digit integer such that when it is divided by

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 2105
Followers: 29

Kudos [?]: 308 [0], given: 1260

m is a three-digit integer such that when it is divided by [#permalink]  12 Aug 2017, 10:13
Expert's post
00:00

Difficulty:

5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

m is a three-digit integer such that when it is divided by 5, the remainder is y, and when it is divided by 7, the remainder is also y. If y is a positive integer, what is the smallest possible value of m?

[Reveal] Spoiler: OA
106

_________________
GRE Instructor
Joined: 10 Apr 2015
Posts: 638
Followers: 29

Kudos [?]: 450 [1] , given: 3

Re: m is a three-digit integer such that when it is divided by [#permalink]  12 Aug 2017, 13:44
1
KUDOS
Expert's post
Carcass wrote:
m is a three-digit integer such that when it is divided by 5, the remainder is y, and when it is divided by 7, the remainder is also y. If y is a positive integer, what is the smallest possible value of m?

[Reveal] Spoiler: OA
106

There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

When m is divided by 5, the remainder is y
So, m = 5k + y for some integer k

When m is divided by 7, the remainder is y
So, m = 7j + y for some integer j

Since both equations are set to equal m, we can write: 5k + y = 7j + y
Subtract y from both sides to get: 5k = 7j
Well, 5k represents a multiple of 5, and 7j represents a multiple of 7
So, what's the smallest 3-digit number that is a multiple of 5 AND a multiple of 7?

The smallest 3-digit number is 100
100 is a multiple of 5, but it's NOT a multiple of 7

Next we have 105
105 is a multiple of 5, AND it's a multiple of 7
Now be careful. This does NOT mean that m = 105

When we divide 105 by 5 we get a remainder of 0, but we're told that the remainder (y) is a POSITIVE INTEGER.
To MINIMIZE the value of m, we need a super small remainder.
The smallest possible non-zero remainder is 1.
105 + 1 = 106

So, 106 is the smallest possible 3-digit value of m.

RELATED VIDEO

_________________

Brent Hanneson – Founder of greenlighttestprep.com

Check out the online reviews of our course

Re: m is a three-digit integer such that when it is divided by   [#permalink] 12 Aug 2017, 13:44
Display posts from previous: Sort by