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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 08:36

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

73% (01:32) correct 27% (02:03) wrong based on 158 sessions

HideShow timer Statistics

When a number is divided by a divisor it leaves a remainder 72. However, when twice the number is divided by the same divisor, the remainder obtained is 46. What is the value of the divisor?

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 10:02

2

This post received KUDOS

Suppose we have number \(n\) and it is divided by a divisor \(d\) with a quotient \(q\) and remainder 72. Then we have: \(n=d\cdot q+72\) Multiply by 2 this equation: \(2n=d\cdot 2q+ 144\) When divide \(2n\) by \(d\) again we will have remainder equal to the remainder when 144 is divided by \(d\) since \(d*2q\) is divisible by \(d\). Therefore d=144-46=98.

The correct answer is A.

Hint: If the divisor doesn't change in the problem, you can work only with remainders. We have a remainder 72. If we multiply the number by 2, it's remainder will double: 72*2=144 Then d=144-46=98.
_________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 10:40

smyarga wrote:

Suppose we have number \(n\) and it is divided by a divisor \(d\) with a quotient \(q\) and remainder 72. Then we have: \(n=d\cdot q+72\) Multiply by 2 this equation: \(2n=d\cdot 2q+ 144\) When divide \(2n\) by \(d\) again we will have remainder equal to the remainder when 144 is divided by \(d\) since \(d*2q\) is divisible by \(d\). Therefore d=144-46=98.

The correct answer is A.

Hint: If the divisor doesn't change in the problem, you can work only with remainders. We have a remainder 72. If we multiply the number by 2, it's remainder will double: 72*2=144 Then d=144-46=98.

I'm sorry smyarga, i don't get the red part. Could you explain please?

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 10:53

1

This post received KUDOS

oss198 wrote:

smyarga wrote:

Suppose we have number \(n\) and it is divided by a divisor \(d\) with a quotient \(q\) and remainder 72. Then we have: \(n=d\cdot q+72\) Multiply by 2 this equation: \(2n=d\cdot 2q+ 144\) When divide \(2n\) by \(d\) again we will have remainder equal to the remainder when 144 is divided by \(d\) since \(d*2q\) is divisible by \(d\). Therefore d=144-46=98.

The correct answer is A.

Hint: If the divisor doesn't change in the problem, you can work only with remainders. We have a remainder 72. If we multiply the number by 2, it's remainder will double: 72*2=144 Then d=144-46=98.

I'm sorry smyarga, i don't get the red part. Could you explain please?

\(2n/d=2q+ 144/d\)

So, the remainder will come only as a remainder of 144 when divided by \(d\).
_________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 12:16

smyarga wrote:

oss198 wrote:

smyarga wrote:

Suppose we have number \(n\) and it is divided by a divisor \(d\) with a quotient \(q\) and remainder 72. Then we have: \(n=d\cdot q+72\) Multiply by 2 this equation: \(2n=d\cdot 2q+ 144\) When divide \(2n\) by \(d\) again we will have remainder equal to the remainder when 144 is divided by \(d\) since \(d*2q\) is divisible by \(d\). Therefore d=144-46=98.

The correct answer is A.

Hint: If the divisor doesn't change in the problem, you can work only with remainders. We have a remainder 72. If we multiply the number by 2, it's remainder will double: 72*2=144 Then d=144-46=98.

I'm sorry smyarga, i don't get the red part. Could you explain please?

\(2n/d=2q+ 144/d\)

So, the remainder will come only as a remainder of 144 when divided by \(d\).

Thank you! but how can you then conclude d=144-46=98 ?

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 12:29

3

This post received KUDOS

oss198 wrote:

Thank you! but how can you then conclude d=144-46=98 ?

We know that 144 when divided by \(d\) has a remainder 46. Hence, \(144=d*a+46\), where \(a\) is quotient.

So, \(d*a=144-46=98\). Divisor \(d\) must be a factor of 98, and must be greater than 72, because divisor is always greater than a remainder. The only one possible such value is 98.

Sorry, for not enough detailed explanation:(
_________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 13:05

1

This post received KUDOS

smyarga wrote:

oss198 wrote:

Thank you! but how can you then conclude d=144-46=98 ?

We know that 144 when divided by \(d\) has a remainder 46. Hence, \(144=d*a+46\), where \(a\) is quotient.

So, \(d*a=144-46=98\). Divisor \(d\) must be a factor of 98, and must be greater than 72, because divisor is always greater than a remainder. The only one possible such value is 98.

Sorry, for not enough detailed explanation:(

Thank you very much ! (-: it was not a bad explanation, I only have a big weakness with remainders..

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 21:23

1

This post received KUDOS

Its as simple as multiply 72*2 and then subtract 46 = 98.

Here is why.. The original number is 72 more than a multiple of the divisor. when the number is multiplied by 2, the resulting number is 144 more than a multiple of the divisor. But its given that its also 46 more than the multiple of the divisor. SO we do 144-46 = 98.

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 22:08

smyarga wrote:

oss198 wrote:

Thank you! but how can you then conclude d=144-46=98 ?

We know that 144 when divided by \(d\) has a remainder 46. Hence, \(144=d*a+46\), where \(a\) is quotient.

So, \(d*a=144-46=98\). Divisor \(d\) must be a factor of 98, and must be greater than 72, because divisor is always greater than a remainder. The only one possible such value is 98.

Sorry, for not enough detailed explanation:(

---------------------------------

Hi sorry, even I am pretty weak with remainders.. Sorry to ask a silly question..

But you said, 98 is a factor of 'd' , the divisor.

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

05 Aug 2014, 23:07

1

This post received KUDOS

alphonsa wrote:

smyarga wrote:

oss198 wrote:

Thank you! but how can you then conclude d=144-46=98 ?

We know that 144 when divided by \(d\) has a remainder 46. Hence, \(144=d*a+46\), where \(a\) is quotient.

So, \(d*a=144-46=98\). Divisor \(d\) must be a factor of 98, and must be greater than 72, because divisor is always greater than a remainder. The only one possible such value is 98.

Sorry, for not enough detailed explanation:(

---------------------------------

Hi sorry, even I am pretty weak with remainders.. Sorry to ask a silly question..

But you said, 98 is a factor of 'd' , the divisor.

How is it so?

hi Alphonsa,

\(d*a=144-46=98\) so \(d*a=98\). That means that d is a factor of 98. It also means that 98 is a multiple of d.

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

06 Aug 2014, 00:13

1

This post received KUDOS

alphonsa wrote:

When a number is divided by a divisor it leaves a remainder 72. However, when twice the number is divided by the same divisor, the remainder obtained is 46. What is the value of the divisor?

98 99 100 101 102 Source: 4gmat

Remainder = 72 for "x"

As x doubles to 2x, remainder also doubles = 72*2 = 144

Re: When a number is divided by a divisor it leaves a remainder [#permalink]

Show Tags

01 Oct 2017, 06:05

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.
_________________