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If the two-digit integers A and B are positive and have the

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If the two-digit integers A and B are positive and have the  [#permalink]

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New post 18 Nov 2013, 12:19
2
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A
B
C
D
E

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If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B ?

(A) 108
(B) 120
(C) 132
(D) 144
(E) 156

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Re: If the two-digit integers A and B are positive and have the  [#permalink]

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New post 18 Nov 2013, 12:29
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avohden wrote:
If the two-digit integers A and B are positive and have the same digits,
but in reverse order, which of the following could be the sum of A and B ?

(A) 108
(B) 120
(C) 132
(D) 144
(E) 156


Choice C is the answer

Two two-digit positive integers have the same digits but in reverse order

So they must be in the form 10x+y and 10y+x

Adding both of them will give us 11x+11y -----------> 11(x+y) -----------> that means 11 is the factor of sum

Among the answer choices only 132(choice C) has 11 as its factor and it is the possible sum of two integers A and B

Hope that helps! :)
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Re: If the two-digit integers A and B are positive and have the  [#permalink]

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New post 19 Nov 2013, 02:34
1
1
avohden wrote:
If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B ?

(A) 108
(B) 120
(C) 132
(D) 144
(E) 156

oe to follow

Image


Similar question to practice: s-and-t-are-two-digit-positive-integers-that-have-the-same-127393.html
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Director
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Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
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Location: United States (FL)
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GPA: 3.45
WE: Accounting (Accounting)
Re: If the two-digit integers A and B are positive and have the  [#permalink]

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New post 23 Nov 2013, 14:45
Official Explanation

Answer: C - It might be tempting to try a series of numbers until you find something that works, but there must be a deeper pattern the GMAT is asking you to discover.

Let's say the tens digit of A is x and the units of A is y. So if A is 73, x = 7 and y = 3. Algebraically, A = 10x + y. If the digits are reverse to create B, x is the units digit of B and y is the tens digit of B, meaning that B = 10y + x.

We can add those together:
A + B
= (10x + y) + (10y + x)
= 11x + 11y
= 11(x + y)

Since x and y are digits, they must be integers, so the sum of x and y must be an integer. 11 times any integer is a multiple of 11, so we're looking for the choice that is a multiple of 11. You aren't expected to know multiples of 11 off the top of your head, so start with an easy one, like 110. Add 11: 121. Add 11 again: 132. That's choice (C), which is correct.
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Re: If the two-digit integers A and B are positive and have the  [#permalink]

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Re: If the two-digit integers A and B are positive and have the &nbs [#permalink] 25 Oct 2017, 06:25
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