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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
How many integers k greater than 100 and less than 1000 are there such
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11 Jul 2021, 23:23
11 Jul 2021, 23:23
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77% (03:37) wrong based on 9 sessions
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How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
A. 50
B. 60
C. 70
D. 80
E. 90
A. 50
B. 60
C. 70
D. 80
E. 90
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Re: How many integers k greater than 100 and less than 1000 are there such
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13 Jul 2021, 21:27
13 Jul 2021, 21:27
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GeminiHeat wrote:
How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
A. 50
B. 60
C. 70
D. 80
E. 90
A. 50
B. 60
C. 70
D. 80
E. 90
Any 3-digit integer abc can be written as 100a+10b+c
Let, k=abc
So reversed number = cba
Given, cba=abc+99
100c+10b+a=100a+10b+c+99
99c−99a=99
c−a=1
We have a total of 9 possibilities where c−a=1
(9-8), (8-7), (7-6), (6-5), (5-4), (4-3), (3-2), (2-1), (1-0)
But, (1,0) case is not feasible as k>100
So, the number of possible cases = 8
b can have 10 different values
Therefore, we can have (8)(10)=80 such numbers
Hence, option D
General Discussion
Re: How many integers k greater than 100 and less than 1000 are there such
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21 Mar 2025, 15:53
21 Mar 2025, 15:53
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