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# If for positive integer x, y the sum of all the digit of x is 170 and

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Math Revolution GMAT Instructor
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If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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Updated on: 21 Apr 2016, 17:36
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Difficulty:

65% (hard)

Question Stats:

37% (01:52) correct 63% (02:50) wrong based on 28 sessions

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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.

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Originally posted by MathRevolution on 20 Apr 2016, 05:40.
Last edited by MathRevolution on 21 Apr 2016, 17:36, edited 1 time in total.
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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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20 Apr 2016, 05:50
MathRevolution 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

*A solution will be posted in two days.

Hi,
is the Q even possible!

sum of digit of x is 170, even if I take all digits to be 9, x will have atleast 170/9 = 19 digits...
now x and y are positive, so you mean -- a 19 digit number 9999999.. = 1020 - y, which will make y as -ive..
Please relook into all the Q and amend accordingly..

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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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20 Apr 2016, 06:56
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.

Cheers,
Brent
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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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21 Apr 2016, 17:37
GMATPrepNow wrote:
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.

Cheers,
Brent

Sorry for the incorrectness. I have modified the question.
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If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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Updated on: 21 Apr 2016, 19:06
I assumed the extra added 0 to 170 was erroneous.

Correction : I also assumed, in my deep slumber, that the equation looks like this
x = 1120- y

So now,Considering the equation given to us is x = 1120 - y and the options for value of y are also positive 2-digit numbers,
we can safely say that the sum of all the digit of x is 17

using the options provided,
A. 41 x=1120 - 41 = 1079 adds up to 17
B. 47 x=1120 - 47 = 1073 adds up to 11
C. 50 x=1120 - 50 = 1070 adds up to 8
D. 55 x=1120 - 55 = 1065 adds up to 12
E. 60 x=1120 - 60 = 1060 adds up to 7

Correct Option : Unbelievably, it still gave unique answer, A

Originally posted by ronny123 on 21 Apr 2016, 18:37.
Last edited by ronny123 on 21 Apr 2016, 19:06, edited 1 time in total.
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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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21 Apr 2016, 18:57
How do you solve this??
It reads to me like ... X = 1020 - Y
The sum of the digits of X equals 170
The possible values of Y are: 41,47,50,55,60
Therefore, X equals: 979,973,970,965,960

None of these numbers equal 170.
Am I missing something?
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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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25 Apr 2016, 10:23
MathRevolution wrote:
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.

Can you please post OE to this question
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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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25 Apr 2016, 22:33
Can somebody please shed some light on the solution.
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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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25 Apr 2016, 22:41
1
praveen7728 wrote:
Can somebody please shed some light on the solution.

Hi,
Light can be shed ONLY if the Q can have a solution
The Q is of very poor quality OR I would say, it is not a Q at all..
No use wasting even seconds on it
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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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25 Apr 2016, 23:15
1
praveen7728 wrote:
Can somebody please shed some light on the solution.

But let me tell you what could be a Q in this format and what could we make out of it..
x=1020-y..
so x+y = 1020..
now sum of digits of 1020 = 3, so 1020 is div by 3 and therefore x+y also should be div by 3..
1) It is given that sum of digits of x is 170- ofcourse not possible in given scenario, but I take it for oonce- so x when div by 3 will give us a remainder of 2 -- 170 = 1+7+0=8.. 8/3: R =2..
2) that tells us that y as a number and also its sum of digits should give us 1 as a remainder when div by 3..

so the choices should have ONLY one choice where the number is of type 3k+1..
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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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27 Apr 2016, 01:35
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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Re: If for positive integer x, y the sum of all the digit of x is 170 and  [#permalink]

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22 Jul 2017, 13:50
Hi,

Is this 10 to the power of 20 or 1020?

Thanks
Re: If for positive integer x, y the sum of all the digit of x is 170 and   [#permalink] 22 Jul 2017, 13:50
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