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

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4 00:00

Difficulty:   5% (low)

Question Stats: 87% (01:15) correct 13% (01:42) wrong based on 215 sessions

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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, 21:54.
Last edited by Gnpth on 01 Jul 2014, 21:57, edited 1 time in total.
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Manager  Joined: 13 Jun 2013
Posts: 246
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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8
2
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
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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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5
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

Manager  Joined: 25 Apr 2014
Posts: 90
Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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1
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?
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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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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 Senior Manager  S
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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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

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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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Hi Moderators/Math experts,

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!
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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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susheelh wrote:
Hi Moderators/Math experts,

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
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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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N = 105Q + 99
Let Q = 1
=> N = 204
204 divided by 21 = 21*9 + 15

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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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3
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

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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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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 $$= 15$$

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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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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.

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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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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.

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Re: A number when divided by 105 leaves 99 as remainder  [#permalink]

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_________________ Re: A number when divided by 105 leaves 99 as remainder   [#permalink] 07 Nov 2019, 11:07

# A number when divided by 105 leaves 99 as remainder  