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![GMAT Club Olympics 2025 (Day 4): Let [x] represent the greatest intege](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "GMAT Club Olympics 2025 (Day 4): Let [x] represent the greatest intege"){kind=icon}
03 Jul 2025, 10:36
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Better to plug in answer choices an see:
1. n=7
[7/4]=1, [7/9]=0, 1-0=1
2. n=8
[8/4]=2, [8/9]=0, 2-0 =2 Answer
1. n=7
[7/4]=1, [7/9]=0, 1-0=1
2. n=8
[8/4]=2, [8/9]=0, 2-0 =2 Answer
03 Jul 2025, 10:36
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For this one, I used the answer choices to find the best fit. If someone has a better approach, please let me know.
Here it goes,
So, we are given that [x] is the greatest integer that is less than or equal to x. For example, if x is 3.6, then [x] is going to be 3
With this info let's see the expression, [n/4]-[n/9] = 2, and use answer choices:
A. 7
If n=7, then,
n/4=~1.7 ----> [n/4] is 1
n/9 = ~0.7 -----> [n/9] is 0
1-0 = 1 ---> since it's not 2, this choice is incorrect
B. 8
If n=8, then
n/4=2 -----> [n/4] is 2
n/9=~0.8 -----> [n/9] is 0
2-0 = 2 ---> This matches our prompt, hence the correct choice.
Answer B.
Here it goes,
So, we are given that [x] is the greatest integer that is less than or equal to x. For example, if x is 3.6, then [x] is going to be 3
With this info let's see the expression, [n/4]-[n/9] = 2, and use answer choices:
A. 7
If n=7, then,
n/4=~1.7 ----> [n/4] is 1
n/9 = ~0.7 -----> [n/9] is 0
1-0 = 1 ---> since it's not 2, this choice is incorrect
B. 8
If n=8, then
n/4=2 -----> [n/4] is 2
n/9=~0.8 -----> [n/9] is 0
2-0 = 2 ---> This matches our prompt, hence the correct choice.
Answer B.
MBAChaser123
Joined: 19 Nov 2024
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03 Jul 2025, 10:37
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We want the minimum possible for n, so we start trying numbers from 1 up.
If n is a positive integer, for any \( n<9 \), the amount of [n/9] is equal to 0.
So, if there is any n in this range ( \( 1<=n<9 \) ), that the value for [n/4] could be 2, we have our number.
For [n/4] to be 2, the range for n is ( \( 8<=n<12 \) )
So, considering the range for [n/9]=0, and [n/4]=2, the only mutual integer is n=8.
Option B is correct.
If n is a positive integer, for any \( n<9 \), the amount of [n/9] is equal to 0.
So, if there is any n in this range ( \( 1<=n<9 \) ), that the value for [n/4] could be 2, we have our number.
For [n/4] to be 2, the range for n is ( \( 8<=n<12 \) )
So, considering the range for [n/9]=0, and [n/4]=2, the only mutual integer is n=8.
Option B is correct.
Bunuel
