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![If [x] is the greatest integer less than or equal to x, then how many](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If [x] is the greatest integer less than or equal to x, then how many"){kind=icon}
14 Apr 2020, 09:37
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D
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Difficulty:
95%
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Question Stats:
40% (02:52) correct
60%
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wrong
based on 101
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If [x] is the greatest integer less than or equal to x, then how many positive integers n satisfy \([\frac{n}{11}] = [\frac{n}{13}]\) ?
A. 25
B. 31
C. 32
D. 35
E. 40
Are You Up For the Challenge: 700 Level Questions
A. 25
B. 31
C. 32
D. 35
E. 40
Are You Up For the Challenge: 700 Level Questions
14 Apr 2020, 09:47
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When n = 1, 2, 3....10, both values will be equal to 0. 10 possibilities
When n = 13, 14, ....21, both values will be equal to 1. 9 possibilities
When n = 26, 27, ....32, both values will be equal to 2. 7 possibilities
When n = 39, 27, ....43, both values will be equal to 3. 5 possibilities
When n = 52, 53, 54, both values will be equal to 4. 3 possibilities
when n = 65, both will be equal to 5. 1 possibility
So, totally there are 1 + 3 + 5 + 7 + 9 + 10 = 35 possibilities.
The question is Find the number of positive integers n such that [n/11] = [n/13].
Hence the answer is "35 possibilities"
Choice D is the correct answer.
When n = 13, 14, ....21, both values will be equal to 1. 9 possibilities
When n = 26, 27, ....32, both values will be equal to 2. 7 possibilities
When n = 39, 27, ....43, both values will be equal to 3. 5 possibilities
When n = 52, 53, 54, both values will be equal to 4. 3 possibilities
when n = 65, both will be equal to 5. 1 possibility
So, totally there are 1 + 3 + 5 + 7 + 9 + 10 = 35 possibilities.
The question is Find the number of positive integers n such that [n/11] = [n/13].
Hence the answer is "35 possibilities"
Choice D is the correct answer.
14 Apr 2020, 11:38
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Bunuel
Asked: If [x] is the greatest integer less than or equal to x, then how many positive integers n satisfy \([\frac{n}{11}] = [\frac{n}{13}]\) ?
n = 1 to 10 = 10 values satisfy [n/11] = [n/13] = 0
n = 13 to 21= 9 values satisfy [n/11] = [n/13] = 1
n = 26 to 32= 7 values satisfy [n/11] = [n/13] = 2
n = 39 to 43= 5 values satisfy [n/11] = [n/13] = 3
n = 52 to 54= 3 values satisfy [n/11] = [n/13] = 4
n = 65 = 1 values satisfy [n/11] = [n/13] = 5
Total values of n = 10 + 9 + 7 + 5 + 3 + 1 = 35
IMO D
