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# The difference between a two-digit number and the number obtained by r

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Senior Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 280
The difference between a two-digit number and the number obtained by r  [#permalink]

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19 Mar 2019, 07:06
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00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:36) correct 45% (03:02) wrong based on 31 sessions

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The difference between a two-digit number and the number obtained by revers-ing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?

(A) 44

(B) 55

(C) 77

(D) 99

(E) 110
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Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: The difference between a two-digit number and the number obtained by r  [#permalink]

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19 Mar 2019, 08:18
The difference between a two-digit number and the number obtained by revers-ing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?

(A) 44

(B) 55

(C) 77

(D) 99

(E) 110

Let, Number = ab = 10a+b
Number after reversing digits = ba = 10b+a

(10a+b)-(10b+a) = 5*(a+b)

i.e. 9a - 9b = 5a + 5b

i.e. 9(a-b) = 5(a+b)

which is possible only when a+b = 9 and a-b = 5
i.e. a = 7 and b = 2

Requires sum = 72+27 = 99

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Re: The difference between a two-digit number and the number obtained by r  [#permalink]

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19 Mar 2019, 10:47
The difference between a two-digit number and the number obtained by revers-ing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?

(A) 44

(B) 55

(C) 77

(D) 99

(E) 110

we know that the difference between any two digit reversals xy and yx will be 9(x-y)
so 9(x-y)=5(x+y)→
x/y=7/2
72+27=99
D
Manager
Joined: 11 Feb 2013
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Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
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WE: Analyst (Commercial Banking)
Re: The difference between a two-digit number and the number obtained by r  [#permalink]

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19 Mar 2019, 11:16
1
The difference of the two digit number itself and it's reversal is always divisible by 9.
And the resulting number = 9(larger digit- smaller digit)
For example, difference between 18 and 81 = 9(8-1)=63.

The summation of the two digit number itself and it's reversal is always divisible by 11. And the resulting number = 11(larger digit+smaller digit)
For example, difference between 18 and 81 = 11(8+1)=99.

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Concentration: Sustainability, Marketing
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Re: The difference between a two-digit number and the number obtained by r  [#permalink]

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19 Mar 2019, 11:32
The difference between a two-digit number and the number obtained by revers-ing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?

(A) 44

(B) 55

(C) 77

(D) 99

(E) 110

given
10a+b-10b-a= 5a+5b
we get
2a=7b
a= 7 ; b = 2
so sum = 99
IMO D
Re: The difference between a two-digit number and the number obtained by r   [#permalink] 19 Mar 2019, 11:32
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