What is the smallest positive integer that leaves a remainder of 4 on

Question

What is the smallest positive integer that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?

A. 5039
B. 2519
C. 1079
D. 979
E. 971

Are You Up For the Challenge: 700 Level Questions

GMATinsight · Accepted Answer

Remainder 4 when divided by 5 also means remainder = -1
Remainder 5 when divided by 6 also means remainder = -1
Remainder 6 when divided by 7 also means remainder = -1
Remainder 7 when divided by 8 also means remainder = -1
Remainder 8 when divided by 9 also means remainder = -1

i.e. Number = LCM {5, 6, 7, 8, 9} + Remainder = LCM {5, 6, 7, 8, 9} + (-1) = 2520 - 1 = 2519

ANswer: Option B

nick1816 · Answer

LCM(5,6,7,8,9)= 2^3*3^2*5*7 = 2520

smallest positive integer that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9 = 2520-1 = 2519

Vidhi96 · Answer

answer is B 
LCM OF (4,5,6,7,8,9) - 1

2520K - 1
K=1
2519

GaurSaini · Answer

Hi, Can you please explain this property?
"Remainder 4 when divided by 5 also means remainder = -1"

Please find my reasoning also..
let's take a number 29.

29 = 5*5 + 4...here remainder is '4'
and we can write it as...5*5 + 5 - 1, hence remainder is '-1'

Can same property be applicable to other negative remainders too ?

for eg. 28 = 5*5 + 3 = 5*5 + 5 - 2 
Hence remainder is '3' as well as '-2'

Please clarify.

Avysar · Answer

I think this problem is easier backsolved...start from the smallest choice E...it doesn't leave a remainder of 8 when divided by 9
D doesn't work because when divided by 8 the remainder is not 7 C doesn't work because when divided byb7 the remainder is not 6. B works for all the divisors 9,8,7,6&5 hence B

Posted from my mobile device

Elyazid · Answer

Hi,
Can someone please explain further the LCM method

VP1030 · Answer

When a number is divided by 8, a remainder of 7 can be thought of as a remainder of -1. This idea is very useful in a bunch of questions. So,
N = 5a - 1 or N + 1 = 5a
N = 6b - 1 or N + 1 = 6b
N = 7c - 1 or N + 1 = 7c
N = 8d - 1 or N + 1 = 8d
N = 9e - 1 or N + 1 = 9e
N + 1 can be expressed as a multiple of (5, 6, 7, 8, 9)
N + 1 = 5a×6b×7c×8d×9e
or N = (5a×6b×7c×8d×9e) - 1
Smallest value of N will be when we find the smallest common multiple of (5, 6, 7, 8, 9)
or LCM of (5, 6, 7, 8, 9)
N = LCM (5, 6, 7, 8, 9) - 1
= 2520 - 1
= 2519

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

What is the smallest positive integer that leaves a remainder of 4 on

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the smallest positive integer that leaves a remainder of 4 on

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards