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Numbers and Divisiblity

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Numbers and Divisiblity [#permalink]

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New post 19 Aug 2017, 12:41
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Let N be the greatest number that will divide 1305,4665 and 6905, leaving the same reminder in each case.Then sum of digits in N is :

A. 4
B. 5
C. 6
D. 7
E. 8

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Numbers and Divisiblity [#permalink]

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New post 19 Aug 2017, 22:35
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\(\)Hi sarth123,

Welcome to GMATClub!

In order to solve the question, you must be aware of the following rule
If the remainder is same in each case and remainder is not given,
HCF of the differences of the numbers is the required greatest number


The three numbers \(1305, 4665\) and \(6905\) will have differences \((4665 - 1305 = 3360),(6905 - 4665 = 2240),\) and \((6905 - 1305 = 5600)\)

In order to find the greatest number which divides each of these differences,
we prime factorize the differences
\(3360 = 2^5 * 3 * 5 * 7\)
\(2240 = 2^6 * 5 * 7\)
\(5600 = 2^5 * 5^2 * 7\)

The HCF of these numbers is N - 1120(2^5 * 5 * 7) and is the greatest number leaving the same remainder.

Since we have been asked to find the sum of digits in N, it must be 1+1+2+0 = 4(Option A)
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Re: Numbers and Divisiblity [#permalink]

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New post 20 Aug 2017, 03:15

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Re: Numbers and Divisiblity   [#permalink] 20 Aug 2017, 03:15
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