Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 22 Jul 2014
Posts: 124
Concentration: General Management, Finance
WE: Engineering (Energy and Utilities)

When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 09:36
Question Stats:
75% (01:33) correct 25% (01:57) wrong based on 179 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? 98 99 100 101 102 Source: 4gmat
Official Answer and Stats are available only to registered users. Register/ Login.



Tutor
Joined: 20 Apr 2012
Posts: 99
Location: Ukraine
GMAT 1: 690 Q51 V31 GMAT 2: 730 Q51 V38
WE: Education (Education)

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 11:02
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=14446=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=14446=98.
_________________
I'm happy, if I make math for you slightly clearer And yes, I like kudos:)



Manager
Joined: 18 Jul 2013
Posts: 69
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 11:40
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=14446=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=14446=98. I'm sorry smyarga, i don't get the red part. Could you explain please?



Tutor
Joined: 20 Apr 2012
Posts: 99
Location: Ukraine
GMAT 1: 690 Q51 V31 GMAT 2: 730 Q51 V38
WE: Education (Education)

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 11:53
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=14446=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=14446=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:)



Manager
Joined: 18 Jul 2013
Posts: 69
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 13:16
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=14446=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=14446=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=14446=98 ?



Tutor
Joined: 20 Apr 2012
Posts: 99
Location: Ukraine
GMAT 1: 690 Q51 V31 GMAT 2: 730 Q51 V38
WE: Education (Education)

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 13:29
oss198 wrote: Thank you! but how can you then conclude d=14446=98 ?
We know that 144 when divided by \(d\) has a remainder 46. Hence, \(144=d*a+46\), where \(a\) is quotient. So, \(d*a=14446=98\). 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:)



Manager
Joined: 18 Jul 2013
Posts: 69
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 14:05
smyarga wrote: oss198 wrote: Thank you! but how can you then conclude d=14446=98 ?
We know that 144 when divided by \(d\) has a remainder 46. Hence, \(144=d*a+46\), where \(a\) is quotient. So, \(d*a=14446=98\). 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..



Manager
Joined: 11 Jun 2014
Posts: 56
Concentration: Technology, Marketing
WE: Information Technology (Consulting)

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 22:23
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 14446 = 98.
Option 1



Current Student
Joined: 22 Jul 2014
Posts: 124
Concentration: General Management, Finance
WE: Engineering (Energy and Utilities)

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
05 Aug 2014, 23:08
smyarga wrote: oss198 wrote: Thank you! but how can you then conclude d=14446=98 ?
We know that 144 when divided by \(d\) has a remainder 46. Hence, \(144=d*a+46\), where \(a\) is quotient. So, \(d*a=14446=98\). 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?



Manager
Joined: 18 Jul 2013
Posts: 69
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
06 Aug 2014, 00:07
alphonsa wrote: smyarga wrote: oss198 wrote: Thank you! but how can you then conclude d=14446=98 ?
We know that 144 when divided by \(d\) has a remainder 46. Hence, \(144=d*a+46\), where \(a\) is quotient. So, \(d*a=14446=98\). 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, \(d*a=14446=98\) so \(d*a=98\). That means that d is a factor of 98. It also means that 98 is a multiple of d.



Current Student
Joined: 22 Jul 2014
Posts: 124
Concentration: General Management, Finance
WE: Engineering (Energy and Utilities)

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
06 Aug 2014, 00:34
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?[/quote] hi Alphonsa, \(d*a=14446=98\) so \(d*a=98\). That means that d is a factor of 98. It also means that 98 is a multiple of d.[/quote]  Terribly sorry, for the foolish questions I may be raising



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
06 Aug 2014, 01:13
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 Quotient = 144  46 = 98 Answer = A
_________________
Kindly press "+1 Kudos" to appreciate



NonHuman User
Joined: 09 Sep 2013
Posts: 7349

Re: When a number is divided by a divisor it leaves a remainder
[#permalink]
Show Tags
01 Oct 2017, 07:05
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: When a number is divided by a divisor it leaves a remainder &nbs
[#permalink]
01 Oct 2017, 07:05






