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

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Current Student
Joined: 27 May 2014
Posts: 525
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
1
00:00

Difficulty:

5% (low)

Question Stats:

96% (00:59) correct 4% (01:27) wrong based on 46 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

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Math Expert
Joined: 02 Sep 2009
Posts: 52152
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.

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Math Expert
Joined: 02 Aug 2009
Posts: 7200
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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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 &nbs [#permalink] 28 Dec 2017, 18:41
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