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

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02 Jul 2014, 00:52

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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 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.

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

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24 Jun 2016, 18:03

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

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07 Aug 2017, 00:32

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

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

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07 Aug 2017, 06:47

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This post received KUDOS

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 .

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

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07 Aug 2017, 11:12

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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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