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If the tens digit x and the units digit y of a positive integer n are

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Intern
Joined: 03 Dec 2010
Posts: 43

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If the tens digit x and the units digit y of a positive integer n are [#permalink]

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05 Apr 2011, 15:46
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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
[Reveal] Spoiler: OA

Kudos [?]: 47 [0], given: 7

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1949

Kudos [?]: 2130 [0], given: 376

Re: If the tens digit x and the units digit y of a positive integer n are [#permalink]

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05 Apr 2011, 15:59
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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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Kudos [?]: 2130 [0], given: 376

Intern
Joined: 03 Dec 2010
Posts: 43

Kudos [?]: 47 [0], given: 7

Re: If the tens digit x and the units digit y of a positive integer n are [#permalink]

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05 Apr 2011, 16:05
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.

Kudos [?]: 47 [0], given: 7

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1949

Kudos [?]: 2130 [0], given: 376

Re: If the tens digit x and the units digit y of a positive integer n are [#permalink]

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05 Apr 2011, 16:09
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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Kudos [?]: 2130 [0], given: 376

Intern
Joined: 03 Dec 2010
Posts: 43

Kudos [?]: 47 [0], given: 7

Re: If the tens digit x and the units digit y of a positive integer n are [#permalink]

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05 Apr 2011, 16:17
Thank you so much

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Director
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Re: If the tens digit x and the units digit y of a positive integer n are [#permalink]

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05 Apr 2011, 17:55
10y+x = 9+10x+y
=> y = 1+x

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TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1586

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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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05 Apr 2011, 18:21
10y + x = 10x + y + 9

=> 9y - 9x = 9

=> y = x + 1

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Manager
Joined: 11 Dec 2010
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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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05 Apr 2011, 18:26
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

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Re: If the tens digit x and the units digit y of a positive integer n are [#permalink]

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09 Aug 2017, 12:37
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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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