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If a and b are two-digit numbers that share the same digits, 25 May 2010, 06:47
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45% (medium)

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64% (02:05) correct 36% (01:59) wrong based on 463 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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E
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Bunuel
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If a and b are two-digit numbers that share the same digits, 25 May 2010, 07:04
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srichaks
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.

Please explain your answer in detail including why each choice is right or wrong?

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OA:E
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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.

Answer: E.
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If a and b are two-digit numbers that share the same digits, 25 May 2010, 18:42
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Thanks Bunuel!. Great explanation.
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If a and b are two-digit numbers that share the same digits, 29 May 2010, 07:09
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I dont understand the "except in reverse order" part???????
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If a and b are two-digit numbers that share the same digits, 29 May 2010, 07:20
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I dont understand the "except in reverse order" part???????
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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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hardnstrong
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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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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If a and b are two-digit numbers that share the same digits, 30 May 2010, 06:40
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Bunuel
hardnstrong
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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Not a perfect wording - agree. "except in reverse order" here means "but in reverse order".
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