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When you reverse the digits of the number 13, the number increases by

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Intern
Joined: 26 Dec 2018
Posts: 17
When you reverse the digits of the number 13, the number increases by  [#permalink]

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Updated on: 06 Dec 2019, 00:34
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Difficulty:

45% (medium)

Question Stats:

59% (01:44) correct 41% (01:55) wrong based on 32 sessions

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When you reverse the digits of the number 13, the number increases by 18. How many more two digit numbers increase by 18 when their digits are reversed?

A. 8
B. 5
C. 3
D. 6
E. 4

Originally posted by ab965 on 05 Dec 2019, 23:16.
Last edited by ab965 on 06 Dec 2019, 00:34, edited 1 time in total.
Intern
Joined: 14 Jul 2019
Posts: 5
Location: India
Re: When you reverse the digits of the number 13, the number increases by  [#permalink]

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06 Dec 2019, 00:09
Let original number be 10x+y ; reversed number would be 10y+x

Question states that- 10y+x= 10x+y+18
9y-9x=18
Y-x=2
We can now scroll thru such 2 digit combinations - original number : reversed number
13:31
24:42
35:53
46:64
57: 75
68: 86
79: 97

Senior Manager
Joined: 16 Feb 2015
Posts: 258
Location: United States
Concentration: Finance, Operations
Re: When you reverse the digits of the number 13, the number increases by  [#permalink]

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06 Dec 2019, 00:24
ab965 wrote:
When you reverse the digits of the number 13, the number increases by 18. How many more two digit numbers increase by 18 when their digits are reversed?

A. 8
B. 5
C. 3
D. 6
E. 4

Explanation:

Assume the number to be N= 10a + b

If the digits of the number are interchanged, then we have N' = 10b + a

It is also given that the difference between the number & reversed number is 18.

N' = N + 18

10b + a - 10a - b = 18

9b - 9a = 18

b - a = 2

Therefore, the values a & b can take are as follows.

b = 9, 8, 7, 6, 5, 4, 3, 2

a = 7, 6, 5, 4, 3, 2, 1, 0

number 02 will be 2 so cannot be considered

Therefore, the numbers are 13, 24, 35, 46, 57, 68, 79. Means 6 more numbers apart from 13

IMO-D
Re: When you reverse the digits of the number 13, the number increases by   [#permalink] 06 Dec 2019, 00:24
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