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What is the sum of digits of smallest positive integer that can be wri

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What is the sum of digits of smallest positive integer that can be wri  [#permalink]

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New post 05 Apr 2020, 20:41
2
6
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

17% (02:33) correct 83% (02:43) wrong based on 30 sessions

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What is the sum of digits of smallest positive integer that can be written as the sum of 39 positive consecutive integers and as the sum of 41 positive consecutive integers?

A. 15
B. 18
C. 21
D. 24
E. 27
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Re: What is the sum of digits of smallest positive integer that can be wri  [#permalink]

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New post 05 Apr 2020, 21:21
2
Sum of first 39 natural numbers =780
Sum of first 41 natural numbers
=861
LCM of 780 and 861 =671580
Therefore sum of the digits = 27
Option E is the answer

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What is the sum of digits of smallest positive integer that can be wri  [#permalink]

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New post 05 Apr 2020, 21:34
1
1
Let us consider two series for this problem.
series 1: 39 consecutive integers
let the smallest positive integer of the series 1 be a
sum:
a+(a+1)+(a+2)+.......+(a+38)=39a+ 38(39)/2=39*a+741

Similarly, assume the smallest integer of the other series as b
b+(b+1)+.....+(b+40)=41*b+820

As per the question,
n=41*b+820=39*a+741 where n is the smallest positive integer.

n when divided by 41 and 39 leaves a remainder of 0

So, the smallest such number would be the L.C.M of 41 and 39 which is 1599.
sum of the digits 1+5+9+9=24

IMO D
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Re: What is the sum of digits of smallest positive integer that can be wri  [#permalink]

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New post 05 Apr 2020, 22:17
1
1
the sum of 39 positive consecutive integers
= a + (a+1) + (a+2) + ... + (a+38) = 39*[ a+ (a+38) ]/2 = 39* (a+19)
the sum of 41 positive consecutive integers
= b + (b+1) + (b+2) + ... + (b+40) = 41*[ b+ (b+40) ]/2 = 41* (b+20)
from given condition , 39* (a+19) = 41* (b+20)
since, 39 and 41 are co prime , a+19 = 41 and b+20= 39 ( we have to find the sum of digits of smallest positive integer)
therefore, sum = 39*41 =1599
the sum of digits of smallest positive integer = 1+5+9+9 = 24
correct answer is D
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Re: What is the sum of digits of smallest positive integer that can be wri   [#permalink] 05 Apr 2020, 22:17

What is the sum of digits of smallest positive integer that can be wri

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