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# If a and b are two-digit numbers that share the same digits,

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Joined: 12 May 2005
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If a and b are two-digit numbers that share the same digits,  [#permalink]

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25 May 2010, 06:47
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Difficulty:

55% (hard)

Question Stats:

64% (02:05) correct 36% (02:02) wrong based on 276 sessions

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If a and b are two-digit numbers that share the same digits, except in reverse order, then what is the sum of a and b?

(1) a-b=45
(2) The difference between the two digits in each number is 5.
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Joined: 02 Sep 2009
Posts: 55266
Re: Number Properties - DS  [#permalink]

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25 May 2010, 07:04
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srichaks wrote:
Q:If a and b are two-digit numbers that share the same digits, except in reverse order, then what is the sum of a and b?
(1) a-b=45
(2) The difference between the two digits in each number is 5.

OA:E

Any two digit integer $$n$$ can be expressed as $$n=10x+y$$, where $$x$$ and $$y$$ are digits, $$x>0$$.

Given: $$a=10x+y$$ and $$b=10y+x$$. Q: $$a+b=11(x+y)=?$$

(1) $$a-b=10x+y-10y-x=45$$ --> $$x-y=5$$. Multiple choices for x and y: (9,4), (8, 3), (7, 2), (6, 1). Not sufficient.

(2) $$x-y=5$$. Same info as above. Not sufficient.

(1)+(2) No new info. Not sufficient.

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Re: Number Properties - DS  [#permalink]

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25 May 2010, 18:42
Thanks Bunuel!. Great explanation.
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Re: Number Properties - DS  [#permalink]

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29 May 2010, 07:09
I dont understand the "except in reverse order" part???????
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Re: Number Properties - DS  [#permalink]

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29 May 2010, 07:20
hardnstrong wrote:
I dont understand the "except in reverse order" part???????

It means that if digits in $$a$$ are $$xy$$, then in $$b$$ the digits are $$yx$$ (in reverse order).

According to the solution above there are 5 pairs of $$a$$ and $$b$$ possible satisfying both statements (94 and 49, 83 and 38, 72 and 27, 61 and 16). So multiple answer to $$a+b$$. Not sufficient.

Hope it's clear.
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Re: Number Properties - DS  [#permalink]

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30 May 2010, 06:27
Bunuel wrote:
hardnstrong wrote:
I dont understand the "except in reverse order" part???????

It means that if digits in $$a$$ are $$xy$$, then in $$b$$ the digits are $$yx$$ (in reverse order).

According to the solution above there are 5 pairs of $$a$$ and $$b$$ possible satisfying both statements (94 and 49, 83 and 38, 72 and 27, 61 and 16). So multiple answer to $$a+b$$. Not sufficient.

Hope it's clear.

This is the confusing part in this question............ except in reverse order means they cannot be in reverse order (so if a = xy then b cannot be yx)

Dont you think "except in reverse order" takes question is completely different direction, or should it be "in reverse order"
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Re: Number Properties - DS  [#permalink]

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30 May 2010, 06:40
hardnstrong wrote:
Bunuel wrote:
hardnstrong wrote:
I dont understand the "except in reverse order" part???????

It means that if digits in $$a$$ are $$xy$$, then in $$b$$ the digits are $$yx$$ (in reverse order).

According to the solution above there are 5 pairs of $$a$$ and $$b$$ possible satisfying both statements (94 and 49, 83 and 38, 72 and 27, 61 and 16). So multiple answer to $$a+b$$. Not sufficient.

Hope it's clear.

This is the confusing part in this question............ except in reverse order means they cannot be in reverse order (so if a = xy then b cannot be yx)

Dont you think "except in reverse order" takes question is completely different direction, or should it be "in reverse order"

Not a perfect wording - agree. "except in reverse order" here means "but in reverse order".
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Re: If a and b are two-digit numbers that share the same digits,  [#permalink]

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15 Sep 2018, 10:32
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Re: If a and b are two-digit numbers that share the same digits,   [#permalink] 15 Sep 2018, 10:32
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