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Intern  Joined: 03 Dec 2010
Posts: 35
If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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1 00:00

Difficulty:   35% (medium)

Question Stats: 63% (01:07) correct 37% (01:02) wrong based on 100 sessions

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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
Retired Moderator Joined: 20 Dec 2010
Posts: 1779
Re: If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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1
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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Intern  Joined: 03 Dec 2010
Posts: 35
Re: If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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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.
Retired Moderator Joined: 20 Dec 2010
Posts: 1779
Re: If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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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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Intern  Joined: 03 Dec 2010
Posts: 35
Re: If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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Thank you so much Director  Joined: 01 Feb 2011
Posts: 646
Re: If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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10y+x = 9+10x+y
=> y = 1+x

Answer E.
Retired Moderator B
Joined: 16 Nov 2010
Posts: 1391
Location: United States (IN)
Concentration: Strategy, Technology
Re: If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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10y + x = 10x + y + 9

=> 9y - 9x = 9

=> y = x + 1

Answer - E
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Manager  Joined: 11 Dec 2010
Posts: 106
WE: Consulting (Consulting)
Re: If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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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
Non-Human User Joined: 09 Sep 2013
Posts: 10949
Re: If the tens digit x and the units digit y of a positive integer n are  [#permalink]

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_________________ Re: If the tens digit x and the units digit y of a positive integer n are   [#permalink] 09 Aug 2017, 12:37
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# If the tens digit x and the units digit y of a positive integer n are

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