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

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VP
Joined: 07 Dec 2014
Posts: 1152
xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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09 Jul 2017, 20:37
8
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:24) correct 40% (02:25) wrong based on 97 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)
Intern
Joined: 14 Sep 2014
Posts: 10
Location: India
GPA: 3.36
WE: Programming (Consulting)
Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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09 Jul 2017, 21:20
2
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.
Director
Joined: 13 Mar 2017
Posts: 700
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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09 Jul 2017, 22:07
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...

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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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12 Jul 2017, 16:04
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.

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Intern
Joined: 03 Sep 2018
Posts: 44
Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

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04 Jan 2019, 01:13
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. &nbs [#permalink] 04 Jan 2019, 01:13
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