7 different numbers selected

Expert replies

money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Tue Feb 09, 2010 1:36 am

Hello... I'm having some difficulty with this question... hope you can help:

Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?

(1) The range of the seven remainders is 6.
(2) The seven numbers selected are consecutive integers.

Standard Data Sufficiency Answer Choices.

OA B

My goal is to make MBA applicants take onus over their process.

My story from Pre-MBA to Cornell MBA - New Post in Pre-MBA blog

Me featured on Poets & Quants

Free Book for MBA Applicants

Like this post

Source: Beat The GMAT — Data Sufficiency | Tue Feb 09, 2010 1:36 am

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Tue Feb 09, 2010 1:49 am

You just need to remember that when a number is divided by 'n', the maximum remainder that you could get is (n-1). Basically, remainders range from 0 to (n-1).

Here, the question asks for the sum of remainders. The seven integers could be any integer.

A. Range of seven remainders is 6.

Firstly, we don't know the seven integers. With this info, we could try some numbers.

Let's say the set of remainders are 0, 0, 0, 0, 0, 0, 6. Range is 6. Sum of Remainders is 6
Let's consider this set (0,1,2,3,4,5,6). Range is again 6. Sum of Remainders is 21

Insufficient.

B. Seven numbers are consecutive.

The remainders are going to be the same whatever consecutive numbers you are dividing by n (here 7). Let's try some numbers,

1,2,3,4,5,6,7 - Remainders when divided by 7 gives the same set of remainders (0 to 6). Sum of remainders is 21.
23,24,25,26,27,28,29 - Remainders when divided by 7 gives (2,3,4,5,6,0,1) respectively. Sum of remainders is 21.

Sufficient.

Like this post

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Tue Feb 09, 2010 2:09 am

money9111 wrote:Hello... I'm having some difficulty with this question... hope you can help:

Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?

(1) The range of the seven remainders is 6.
(2) The seven numbers selected are consecutive integers.

Standard Data Sufficiency Answer Choices.

OA B

s1) there can be various seven number for which sum is varying
insuff
s2)
let no be 2,3,4,5,6,7,8 rem are 2,3,4,5,6,0,1
sum=21
let another set of no's=20,21,22,23,24,25,26;rem r 6,0,1,2,3,4,5 sum=21
let another set of no's
43,44,45,46,47,48,49 rem r 1,2,3,4,5,6,0 aum=21
hence we can conclude that sum is 21
hence suff

Like this post

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 Feb 09, 2010 2:49 am

money9111 wrote:Hello... I'm having some difficulty with this question... hope you can help:

Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?

(1) The range of the seven remainders is 6.
(2) The seven numbers selected are consecutive integers.

Standard Data Sufficiency Answer Choices.

OA B

(1) There's no marvel if the range of those seven remainders is 6, when 7 is the divisor, 0 through 6 are the seven possible remainders whose range is 6. But one thing can be surely drawn out from it and that's that at least one integer is a multiple of 7 and that at least one integer is 1 less than a multiple of 7, from the seven different numbers that are to be selected from the integers 1 to 100. Other 5 remainders could take any value 0 through 6. Insufficient

(2) It works! When the seven numbers selected are consecutive integers, and then each one is divided by 7, irrespective of the fact that which one is the first, the seven remainders taken in order would include each integer 0 through 6 just once. Sufficient

[spoiler]B[/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

Like this post

MBA: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Thu May 13, 2010 3:02 am

by MBA » Sun Jul 03, 2011 4:56 am

Hi,

If we take 4,5,6,7,8,9,10(7 consecutive numbers) and divide each one by 7,we have remainders 3,2,1,0,1,2,3.The sum is not equal to 21 but is 12.Thus we can conclude that B is not sufficient.

can anyone explain,plz.

Thanks

Like this post

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 » Mon Jul 04, 2011 12:56 am

MBA wrote:Hi,

If we take 4,5,6,7,8,9,10(7 consecutive numbers) and divide each one by 7,we have remainders 3,2,1,0,1,2,3.The sum is not equal to 21 but is 12.Thus we can conclude that B is not sufficient.

can anyone explain,plz.

Thanks

But I believe that when 4,5,6,7,8,9,10 are divided by 7, the remainders are 4,5,6,0,1,2,3 respectively NOT 3,2,1,0,1,2,3, so please re-examine your work.

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 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