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If for positive integer x, y the sum of all the digit of x i

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If for positive integer x, y the sum of all the digit of x i

by Max@Math Revolution » Wed Apr 20, 2016 4:41 am
For positive integer x, if the sum of all the digit of x is 170 where x and y are positive integers and x=1020-y, which of the following can be the value of y?

A. 41
B. 47
C. 50
D. 55
E. 60


*A solution will be posted in two days.
Last edited by Max@Math Revolution on Thu Apr 21, 2016 4:38 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Wed Apr 20, 2016 5:55 am
Max@Math Revolution wrote:If for positive integer x, y the sum of all the digit of x is 170 and x=1020-y, which of the following can be the value of y?

A. 41
B. 47
C. 50
D. 55
E. 60
What does this mean: y the sum of all the digit of x is 170
It sounds like you're saying that y is the sum of x's digits AND y is 170. Of course that makes no sense, since the objective is to find the value of y.

Please clarify.

Cheers,
Brent
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by Max@Math Revolution » Thu Apr 21, 2016 4:38 pm
Brent@GMATPrepNow wrote:
Max@Math Revolution wrote:If for positive integer x, y the sum of all the digit of x is 170 and x=1020-y, which of the following can be the value of y?

A. 41
B. 47
C. 50
D. 55
E. 60
What does this mean: y the sum of all the digit of x is 170
It sounds like you're saying that y is the sum of x's digits AND y is 170. Of course that makes no sense, since the objective is to find the value of y.

Please clarify.

Cheers,
Brent

Sorry for the incorrectness. I have modified the question.
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by Max@Math Revolution » Wed Apr 27, 2016 12:38 am
For positive integer x, if the sum of all the digit of x is 170 where x and y are positive integers and x=1020-y, which of the following can be the value of y?

A. 41
B. 47
C. 50
D. 55
E. 60


->10^20-y=99999....9( )[ ] is derived.
In this case, the number of the first digits of 9 is 18, which is 9*18=162.
Also, the sum of all digits is 170.
That is, it should be ( )+[ ]=170-162=8.
Then, one should be selected amongst y=29,38,47,56,6,5,74,83,92.
Since 47 is in the option, the answer is B.
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