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# What is y in terms of x ?

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Director
Joined: 25 Oct 2008
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Location: Kolkata,India
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What is y in terms of x ? [#permalink]  09 Jun 2009, 19:35
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If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x ?

(A) 10 - x

(B) 9 - x

(C) x + 9

(D) x - 1

(E) x + 1
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Manager
Joined: 01 May 2009
Posts: 116
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Re: What is y in terms of x ? [#permalink]  09 Jun 2009, 21:48
tejal777 wrote:
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x ?

(A) 10 - x

(B) 9 - x

(C) x + 9

(D) x - 1

(E) x + 1

n = 10x+y -----1

now when the digits are reversed

10y+x=n+9

n=10y+x-9 -----2

1=2 implies

10x+y=10y+x-9
9x-9y=-9
y-x=9
y=x+9

SVP
Joined: 28 Dec 2005
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Re: What is y in terms of x ? [#permalink]  10 Jun 2009, 05:14
I get E. Here's how:

n=10x+y
n'=10y+x (n' denotes the integer when the digits are reversed)

We are told that n'=n+9, i.e. 10y+x=9+10x+y ... simplify this out and you end up with y=x+1
Manager
Status: Stanford GSB
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Re: What is y in terms of x ? [#permalink]  10 Jun 2009, 05:45
the difference is 9.
So the numbers will be 21/12 32/23 or 43/34 etc where the y is the bigger number.
Hence, y=x+1
Manager
Joined: 01 May 2009
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Re: What is y in terms of x ? [#permalink]  10 Jun 2009, 09:06
hasham222 wrote:
tejal777 wrote:
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x ?

(A) 10 - x

(B) 9 - x

(C) x + 9

(D) x - 1

(E) x + 1

n = 10x+y -----1

now when the digits are reversed

10y+x=n+9

n=10y+x-9 -----2

1=2 implies

10x+y=10y+x-9
9x-9y=-9
y-x=9
y=x+9

Oops!! i made a stupid mistake here 9x-9y=-9

y-x=1
y=x+1

E indeed is the right answer
Re: What is y in terms of x ?   [#permalink] 10 Jun 2009, 09:06
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