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xy is a 2 digit number whose reverse, yx, is x less than twice xy.

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xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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New post 09 Jul 2017, 21:37
8
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A
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D
E

Difficulty:

  55% (hard)

Question Stats:

65% (02:26) correct 35% (02:36) wrong based on 109 sessions

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xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

A. 8
B. 9
C. 11
D. 12
E. 13

(source:self)
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Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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New post 09 Jul 2017, 22:20
3
It can be written:
xy = 10x+y ; yx = 10y+x.

Also given,

10y+x = 2(10x+y) - x
=> 4y = 9x
x: y = 4:9
So, x+y will be a multiple of 13. Hence, E.
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Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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New post 09 Jul 2017, 23:07
3
gracie wrote:
xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

A. 8
B. 9
C. 11
D. 12
E. 13

(source:self)


gracie this is a very good question. Thanks for posting it.

Integer xy = 10x+y
Integer yx = 10y+x

Now Integer yx = 2 * Integer xy - x
10y + x = 2*(10x+y) - x
8y = 18x
4y = 9x
x/y = 4/9

So sum x+y must be a multiple of 4+9 = 13...

Answer E.
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Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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New post 12 Jul 2017, 17:04
gracie wrote:
xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

A. 8
B. 9
C. 11
D. 12
E. 13


We use the concept that the number 46, for example, can be expressed as (4)(10) + (6)(1) = 46. Thus, we see that the number “xy” = (10)(x) + (y)(1) = 10x + y.

Since the number “xy” = 10x + y, then its reverse “yx” = 10y + x.

Since “yx” is x less than twice “xy”:

2(10x + y) - x = 10y + x

20x + 2y - x = 10y + x

19x + 2y = 10y + x

18x - 8y = 0

9x - 4y = 0

Since x and y are single digits, the only way 9x - 4y = 0 is if x = 4 and y = 9. Thus, x + y = 4 + 9 = 13.

Answer: E
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Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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New post 04 Jan 2019, 02:13
Made a mistake here: yx is x less than twice xy means that

\(yx=2(xy)-x\)
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Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.   [#permalink] 04 Jan 2019, 02:13
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