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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, 08:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:22) correct
37%
(01:59)
wrong
based on 568
sessions
History
Date
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Not Attempted Yet
Let [x] represent the greatest integer less than or equal to x. If n is a positive integer such that [n/4] - [n/9] = 2, what is the minimum possible value of n?
A. 7
B. 8
C. 9
D. 12
E. 19
A. 7
B. 8
C. 9
D. 12
E. 19
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03 Jul 2025, 08:30
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Bunuel
GMAT Club Official Explanation:
Notice that as n increases, both [n/4] and [n/9] increase, but [n/4] increases faster. Every time n reaches a multiple of 4, [n/4] increases by 1. Similarly, [n/9] increases by 1 at multiples of 9. For example, for values n = 1 to 3, both n/4 and n/9 are less than 1, so [n/4] and [n/9] are both 0. When n reaches 4, [n/4] becomes 1 while [n/9] remains 0, giving a difference of 1.
Now, for a difference of 2, we need a value of n for which [n/4] is 2 while [n/9] is still 0. Checking the next multiple of 4, which is 8, we get [8/4] = 2 and [8/9] = 0, giving the required difference of 2. So the minimum value of n is 8.
Answer: B.
General Discussion
03 Jul 2025, 08:13
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The key here is to remember that 0 is also an integer.
Thus, through trial and error:
A: 7/4 - 7/9 -> 1 - 0 = not 2, incorrect
B: 8/4 - 8/9 -> 2 - 0 = 2, correct
Answer: B) 8
Thus, through trial and error:
A: 7/4 - 7/9 -> 1 - 0 = not 2, incorrect
B: 8/4 - 8/9 -> 2 - 0 = 2, correct
Answer: B) 8
