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# if a two digit positive integer has its digits reversed, the sum of

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Senior Manager
Joined: 27 May 2014
Posts: 375
GMAT 1: 730 Q49 V41
if a two digit positive integer has its digits reversed, the sum of [#permalink]

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28 Dec 2017, 07:51
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Difficulty:

15% (low)

Question Stats:

96% (00:39) correct 4% (00:40) wrong based on 24 sessions

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if a two digit positive integer has its digits reversed, the sum of the resulting integer and its original integer is 110. What is the sum of the digits in the original number?

A) 7
B) 8
C) 10
D) 11
E) 12
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43378
Re: if a two digit positive integer has its digits reversed, the sum of [#permalink]

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28 Dec 2017, 07:59
saswata4s wrote:
if a two digit positive integer has its digits reversed, the sum of the resulting integer and its original integer is 110. What is the sum of the digits in the original number?

A) 7
B) 8
C) 10
D) 11
E) 12

Any two digit integer can be expressed as 10a + b, where a and b are tens and units digits, respectively. For example, 23 = 2*10 + 3.

Given that (10a + b) + (10b + a) = 110 --> 11a + 11b = 110 --> a + b = 10.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 5540
Re: if a two digit positive integer has its digits reversed, the sum of [#permalink]

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28 Dec 2017, 08:00
saswata4s wrote:
if a two digit positive integer has its digits reversed, the sum of the resulting integer and its original integer is 110. What is the sum of the digits in the original number?

A) 7
B) 8
C) 10
D) 11
E) 12

let number be ab..
so number = 10a+b and reverse = 10b +a..
sum = $$11a+11b=110...a+b=\frac{110}{11}=10$$

C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Manager
Joined: 23 Oct 2017
Posts: 63
if a two digit positive integer has its digits reversed, the sum of [#permalink]

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28 Dec 2017, 18:41
Let the original number be represented as xy, thus its value =10*x + y
The new number after the digits have been reversed would be yx, and the value = 10*y + x

Sum of values of original & new number = 10*x+y+10*y+x
= 11*x+11*y
=11*(x+y)

But we know the sum is 110
So. 11*(x+y) = 110
x+y =10 => sum of digits (x,y)
if a two digit positive integer has its digits reversed, the sum of   [#permalink] 28 Dec 2017, 18:41
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