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If [x(10^q)]-[y(10^r)]=10^r, where q r x and

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gmat6nplus1
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If [x(10^q)]-[y(10^r)]=10^r, where q r x and [#permalink] New post   01 Jan 2014, 10:47
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If \([x(10^q)]-[y(10^r)]=10^r\), where \(q, r, x\) and \(y\) are positive integers and \(q>r\), then what is the units digit of y?

A. 0
B. 1
C. 5
D. 7
E. 9



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E
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Re: If [x(10^q)]-[y(10^r)]=10^r, where q r x and [#permalink] New post   01 Jan 2014, 10:47
Since we are told that \(q>r\)

\(10^r[x(10^q^-^r)-y]=10^r\) and this happens when \([x(10^q^-^r)-y]=1\) They told us that q>r this conveys us that \(q-r\) is at least 10. For this reason the units digit of x will always be zero and at the same time the expression \(x(10^q^-^r)\) is greater than y, let's represent x as 10.

10-y=1 -----> y=9

the answer is E.
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Re: If [x(10^q)]-[y(10^r)]=10^r, where q r x and [#permalink] New post   01 Jan 2014, 13:56
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gmat6nplus1 wrote:
If \([x(10^q)]-[y(10^r)]=10^r\), where \(q, r, x\) and \(y\) are positive integers and \(q>r\), then what is the units digit of y?

A. 0
B. 1
C. 5
D. 7
E. 9


Perhaps I am getting use to those tricky question but now only 1:18 to do this type of question! #ThanksGmatClub !

The solution relies on two things:

A) All numbers are positive integers
B) X10 - y = 1 (you find this one by factorizing by 10^r)

Do you find the pattern? What will be the number that will allow you to have 10 - y = 1?

Well 9 of course!

Answer E!
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Re: If [x(10^q)]-[y(10^r)]=10^r, where q r x and [#permalink] New post   02 Jan 2014, 01:51
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gmat6nplus1 wrote:
If \([x(10^q)]-[y(10^r)]=10^r\), where \(q, r, x\) and \(y\) are positive integers and \(q>r\), then what is the units digit of y?

A. 0
B. 1
C. 5
D. 7
E. 9



Given question can be re-written as x*10^q= 10^r(1+y)
Therefore 10^(q-r)= (y+1)/x which should be an Integer. Given q>r and thus q-r>0.

Let q-r= 1 then 10 = (y+1)/x or 10x=y+1 -------> Take any value of x (>0) for ex
x=1 then 10=y+1 ----->y =9
x=2 then 20=y+1 ------> y =19
x=33 then 330=y+1 -----> y 329

Unit digit will be 9

Ans E



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: If [x(10^q)]-[y(10^r)]=10^r, where q r x and [#permalink]
02 Jan 2014, 01:51
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