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A number when divided by 342 gives a remainder 47. When the

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A number when divided by 342 gives a remainder 47. When the [#permalink] New post 20 Oct 2010, 04:24
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A number when divided by 342 gives a remainder 47. When the same number divided by 19, what would be the remainder ?
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Re: Good Question ...Number system [#permalink] New post 20 Oct 2010, 04:28
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ankitranjan wrote:
A number when divided by 342 gives a remainder 47. When the same number divided by 19, what would be the remainder ?


KUDO it if u find it interesting.


Given: \(n=342q+47\) --> \(n=342q+47=19*18q+19*2+9=19(18q+2)+9\) --> so remainder upon division \(n\) by 19 is 9.
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Re: Good Question ...Number system [#permalink] New post 21 Oct 2010, 03:53
It also can be done in a "dumb" way.
let's take 342*2+47 = 731
now 731/19 = 38, remainder 19.
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Re: Good Question ...Number system [#permalink] New post 21 Oct 2010, 04:58
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Using the concept of division works really well in such questions. It is good to remember that division is nothing but grouping. So when I say that a number is divided by 342, it means I split that number into groups of 342 and 47 was leftover.
342 is divisible by 19 so when you divide the same number by 19, every group of 342 will be cleanly split in groups of 19 and nothing will be left over. (This is what happens in most such cases.)
We only need to worry about the leftover 47. You can split 47 in two groups of 19 and then 9 will be leftover. Hence your remainder here will be 9.

(Note: For further clarity, refer to the theory of division.)
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Re: Good Question ...Number system [#permalink] New post 21 Oct 2010, 05:31
u cld also try this solution:

n= 32q + 47
when n is divided by 19 means divide the expression 32q+47 by 19:

324q/ 19+ 47/19= remainder (r)
18q + 47/19 = remainder

From this, the remainder will only result from dividing 47 by 19; this leaves a remainder of 9
Ans= 9
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Re: Good Question ...Number system [#permalink] New post 05 Dec 2010, 01:11
i tried it in da foll way..
x=342q + 47
taking least possible way suppose q=1 ,then x is 347+47 =389
hence x = 19p + z
try dividing 389 by 9 ,u get remainder 9.. :)
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Re: Good Question ...Number system [#permalink] New post 05 Dec 2010, 05:17
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bhushan288 wrote:
i tried it in da foll way..
x=342q + 47
taking least possible way suppose q=1 ,then x is 347+47 =389
hence x = 19p + z
try dividing 389 by 9 ,u get remainder 9.. :)


This approach is fine though the least possible such number is 47 (q = 0). To understand how to figure it out orally, check out the blog post:

http://gmatquant.blogspot.com/2010/11/divisibility-and-remainders-if-you.html
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Re: Good Question ...Number system [#permalink] New post 05 Dec 2010, 22:31
9.

Is this an actual gmat problem?
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Re: Good Question ...Number system [#permalink] New post 06 Dec 2010, 04:44
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USCTrojan2006 wrote:
9.

Is this an actual gmat problem?


The topic 'Remainders' is tested often in GMAT. You could definitely see something similar to this in the actual test.
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Re: A number when divided by 342 gives a remainder 47. When the [#permalink] New post 13 Oct 2013, 02:54
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Re: A number when divided by 342 gives a remainder 47. When the [#permalink] New post 17 Jul 2015, 19:06
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Re: A number when divided by 342 gives a remainder 47. When the [#permalink] New post 18 Jul 2015, 03:51
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ankitranjan wrote:
A number when divided by 342 gives a remainder 47. When the same number divided by 19, what would be the remainder ?


There are generally one common thing among almost all such questions i.e. First Divisor (342 in this case) will be a Multiple of Second Divisor (19 in this case). i.e. Remainder with first divisor will always be the remainder with second divisor

Since 342 is a multiple of 19 therefore
If Remainder when Number divided by 343 is 47
then, Remainder when Number divided by 19 will be 47 (which can further be divided to finally calculation the final remainder) = Remainder (47/19)=9

Another method is to find a number that satisfies the first condition and calculate the remiainder with second divisor

i.e. Number when divided by 342 gives remainder 47
i.e. one of the numbers of such tyoe can be 342+47 = 389
now divide 389 by 19 and see the remainder
Remainder (47/19)=9 Final Remainder
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Re: A number when divided by 342 gives a remainder 47. When the   [#permalink] 18 Jul 2015, 03:51
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