When a number is divided by a divisor it leaves a remainder : Problem Solving (PS)

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oss198

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

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=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?

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

05 Aug 2014, 11:53

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Expert Reply

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 $d$.

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

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=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 ?

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

05 Aug 2014, 14:05

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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..

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

05 Aug 2014, 22:23

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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.

Option 1

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

05 Aug 2014, 23:08

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.

How is it so?

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

06 Aug 2014, 00:07

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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.

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

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,

$d*a=144-46=98$ so $d*a=98$. That means that d is a factor of 98. It also means that 98 is a multiple of d.[/quote]

-----------

Terribly sorry, for the foolish questions I may be raising

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

06 Aug 2014, 01:13

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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

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

07 Nov 2018, 18:48

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

because answers are so close,
say divisor, d≈100
then number, n≈100+72≈172
and 2n≈344
thus, ratio of n/d quotient to 2n/d quotient=1:3
and 3[(n-72)/d]=(2n-46)/d→
n=170
170-72=98=d
confirming, 2*170-46=3*98
A

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

01 Dec 2018, 03:43

Here is how i did it:

n = dq + 72 --> 72, d+72, 2d+72 and so on
2n=dk + 46 --> 46, d+46, 2d+46 and so on
this means:

dq + 72 = (dk + 46)/2 for some integer q and k --- (1)
49 = d(k/2 - q)

now, (k/2 -q) has to be an integer, which means d is a multiple of 49 and the only multiple of 49 is 98
Eqn (1) comes from:
n=dk + r
n=Dq + r1

then for some integers k,q and where d, D are different divisors

dk+r=Dq + r1

look up Bunuel Remainder notes

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

01 Dec 2018, 03:54

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

Dont know why this question has this much explanation thread. Its simple but.

lets say number = x and divisor is y, So x = yK + 72 . K is some constant. They said that x is doubled , remainder becomes 46, 2x = 2yK + 144, remainder here if divided with y will be 144 or 144 - y . since remainder is 46 , 144- y = 46 and y = 98.

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

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

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When a number is divided by a divisor it leaves a remainder