GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 09:21 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  A number when divided by 105 leaves 99 as remainder

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 21 Jun 2014
Posts: 3
A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

3
3 00:00

Difficulty:   5% (low)

Question Stats: 89% (01:16) correct 11% (01:31) wrong based on 242 sessions

HideShow timer Statistics

A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?

A. 9
B. 14
C. 20
D. 6
E. 15

Originally posted by Gmatkarma101 on 01 Jul 2014, 22:54.
Last edited by Gnpth on 01 Jul 2014, 22:57, edited 1 time in total.
Tweak
Senior Manager  Joined: 13 Jun 2013
Posts: 266
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

8
1
Gmatkarma101 wrote:
A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?

A. 9
B. 14
C. 20
D. 6
E. 15

let the number be x, then we have x=105k+99 , where k=0,1,2,3...

now remainder when x is divided by 21, will be
(105k+99)/21
here 105 is a multiple of 21. therefore will leave zero remainder. whereas 99 when divided by 21 will leave 15 as a remainder.

therefore overall remainder is 15
General Discussion
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

2
1
Let the number be 105+99 = 204

204 when divided by 105, give a remainder of 99

Dividing 204 by 21

Remainder =

204 - 189 = 15

_________________
Kindly press "+1 Kudos" to appreciate Manager  Joined: 25 Apr 2014
Posts: 93
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

Hi PareshGmat

Is this method shown by you going to work for all of such type of questions? Or you just did it this way for this particular question?
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

1
maggie27 wrote:
Hi PareshGmat

Is this method shown by you going to work for all of such type of questions? Or you just did it this way for this particular question?

It would work with all such type of questions _________________
Kindly press "+1 Kudos" to appreciate Senior Manager  S
Joined: 24 Jun 2016
Posts: 344
GMAT 1: 770 Q60 V60 GPA: 4
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

A = 105k + 99 = 21*5k + 21*4 + 15, so A/21 remainder 15.

_________________
Stuck in the 600's and want to score 700+ on the GMAT?
If this describes you, we should talk. I specialize in getting motivated students into the 700's.

\$90/hour as of August 2019. I am not accepting any more students for the Fall 2019 application cycle, but if you are planning to apply in 2020, feel free to reach out!

HanoiGMATTutor@gmail.com
Manager  G
Joined: 12 Jun 2016
Posts: 212
Location: India
WE: Sales (Telecommunications)
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

Hi Moderators/Math experts,

I have a question on this one. Can you please advice?

Let N be the number. So, we have

$$N = 105q + 99$$ (where q is an integer). Dividing throughout by 21 we get

$$\frac{N}{21} = 3q + \frac{99}{21}$$

From the responses given by fellow club members, I do see that we should not reduce $$\frac{99}{21}$$ to its lowest form $$\frac{33}{7}$$ for finding the reaminder. My question is - why should we not do so and then find the remainder?

I wanted to know this because the answer will be different in both cases and worry that there may be a Trap answer in real GMAT TIA for the help!
_________________
My Best is yet to come!
Intern  B
Joined: 01 Aug 2017
Posts: 8
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

1
susheelh wrote:
Hi Moderators/Math experts,

I have a question on this one. Can you please advice?

Let N be the number. So, we have

$$N = 105q + 99$$ (where q is an integer). Dividing throughout by 21 we get

$$\frac{N}{21} = 3q + \frac{99}{21}$$

From the responses given by fellow club members, I do see that we should not reduce $$\frac{99}{21}$$ to its lowest form $$\frac{33}{7}$$ for finding the reaminder. My question is - why should we not do so and then find the remainder?

I wanted to know this because the answer will be different in both cases and worry that there may be a Trap answer in real GMAT TIA for the help!

The question is asking you to divide by 21 not by 7 .. the remainder for divisor 21 will vary from 1 - 20 and for 7 will vary from 1-6 .

Always better to stick to the original divisor
Senior Manager  G
Joined: 06 Jul 2016
Posts: 358
Location: Singapore
Concentration: Strategy, Finance
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

N = 105Q + 99
Let Q = 1
=> N = 204
204 divided by 21 = 21*9 + 15
E is the answer.

Sent from my iPhone using GMAT Club Forum
_________________
Put in the work, and that dream score is yours!
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4017
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

2
Top Contributor
Gmatkarma101 wrote:
A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?

A. 9
B. 14
C. 20
D. 6
E. 15

When it comes to remainders, we have a nice rule that says:

If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

A number when divided by 105 leaves 99 as remainder.
So, the possible values of the number are: 99, 99+105, 99+(2)(105), 99+(3)(105), 99+(4)(105), etc.
Let's see what happens when test out the smallest possible value: 99

What will be the remainder if the number is divided by 21?
99 divided by 21 equals 4 with remainder 15

RELATED VIDEO

_________________
Director  V
Joined: 04 Dec 2015
Posts: 743
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

Gmatkarma101 wrote:
A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?

A. 9
B. 14
C. 20
D. 6
E. 15

Let the number be $$= n$$

Number $$n$$ is in form ; $$n = 105q + 99$$

Dividing $$n$$ by $$21$$, we get;

$$\frac{n}{21} => \frac{105q + 99}{21} => \frac{105q}{21} + \frac{99}{21}$$

$$105$$ is divisible by $$21$$ leaving remainder $$0$$. ($$21*5 = 105$$)

$$\frac{99}{21}$$ gives ; $$21* 4 = 84$$

$$99-84 = 15$$

Remainder $$= 15$$

_________________
Please Press "+1 Kudos" to appreciate. Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8125
Location: United States (CA)
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

Gmatkarma101 wrote:
A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?

A. 9
B. 14
C. 20
D. 6
E. 15

n = 105Q + 99

Thus, when that number is divided by 21, we have:

(105Q + 99)/21

5Q + 99/21

Since 5Q is an integer, the remainder will come from 99 divided by 21:

99/21 = 4 R 15

We see that the remainder is 15.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

Show Tags

Gmatkarma101 wrote:
A number when divided by 105 leaves 99 as remainder. What will be the remainder if the number is divided by 21?

A. 9
B. 14
C. 20
D. 6
E. 15

The number could be 105 + 99 = 204 since 204/105 = 1 R 99. Since 204/21 = 9 R 15, the remainder is 15.

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A number when divided by 105 leaves 99 as remainder   [#permalink] 18 Aug 2018, 20:11
Display posts from previous: Sort by

A number when divided by 105 leaves 99 as remainder

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  