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Unit digits

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Unit digits [#permalink] New post 05 Apr 2011, 14:46
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A
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E

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Question Stats:

90% (01:52) correct 10% (00:28) wrong based on 21 sessions
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
[Reveal] Spoiler: OA
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Re: Unit digits [#permalink] New post 05 Apr 2011, 14:59
Acer86 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


Original Digits=xy i.e. Number=10x+y

After reversing the digits:
Digits=yx i.e. Number=10y+x

10y+x is 9 more than 10x+y

10x+y+9=10y+x
10x-x+9=10y-y
9x+9=9y
x+1=y
OR
y=x+1

Ans: "E"
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Re: Unit digits [#permalink] New post 05 Apr 2011, 15:05
fluke wrote:
Acer86 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


Original Digits=xy i.e. Number=10x+y

After reversing the digits:
Digits=yx i.e. Number=10y+x

10y+x is 9 more than 10x+y

10x+y+9=10y+x
10x-x+9=10y-y
9x+9=9y
x+1=y
OR
y=x+1

Ans: "E"




hey can u explain the concept behind this. As in how do the digits become 10y+x from yx when switched over. Thanks.
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Re: Unit digits [#permalink] New post 05 Apr 2011, 15:09
Acer86 wrote:
hey can u explain the concept behind this. As in how do the digits become 10y+x from yx when switched over. Thanks.


It is a way to represent a number when digits are known:

38=3*10+8
4567=4*1000+5*100+6*10+7

Thus, every digit will be multiplied by its place value.

xy
Here x is at Ten's place and y is at units place:
Number = 10*x+y

yx
Here y is at Ten's place and x is at units place:
Number = 10*y+x

Like:
89
Number = 8*10+9

98
Number = 9*10+8
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Re: Unit digits [#permalink] New post 05 Apr 2011, 15:17
Thank you so much :)
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Re: Unit digits [#permalink] New post 05 Apr 2011, 16:55
10y+x = 9+10x+y
=> y = 1+x

Answer E.
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Re: Unit digits [#permalink] New post 05 Apr 2011, 17:21
10y + x = 10x + y + 9

=> 9y - 9x = 9

=> y = x + 1

Answer - E
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Re: Unit digits [#permalink] New post 05 Apr 2011, 17:26
Whenever the digits of two digit numbers are reversed, the difference between the digits of the number is mod(tens-units digits)*9... Check the multiplication table of 9...

So if the number increases by 9, then difference between them is 1... check 45...54-45=9

So y=x+1
Re: Unit digits   [#permalink] 05 Apr 2011, 17:26
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