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What is the number of integers satisfying [x - 2/3] + [x + 1/3] = 5? ([x] means the greatest integer less than or equa

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What is the number of integers satisfying [x - 2/3] + [x + 1/3] = 5? ([x] means the greatest integer less than or equa

by Max@Math Revolution » Wed Feb 05, 2020 2:02 am
[GMAT math practice question]

What is the number of integers satisfying [x - 2/3] + [x + 1/3] = 5? ([x] means the greatest integer less than or equal to x.)

A. 0
B. 1
C. 2
D. 3
E. 4
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Re: What is the number of integers satisfying [x - 2/3] + [x + 1/3] = 5? ([x] means the greatest integer less than or

by Max@Math Revolution » Fri Feb 07, 2020 1:06 am
=>

Since (x + 1/3) - (x – 2/3) = x + 1/3 - x + 2/3 = 1, we have [x - 2/3] = 2 and [x + 1/3] = 3.
Since [x - 2/3] = 2, we have 2 ≤ x – 2/3 < 3 or 8/3 ≤ x < 11/3 (by adding 2/3 to all parts).
Since [x + 1/3] = 3, we have 3 ≤ x + 2/3 < 4 or 7/3 ≤ x < 10/3 (by subtracting 1/3 from all parts).

Thus, we have 7/3 ≤ x < 10/3 (because it has the smallest range), and the possible integers of x is 3 only.
The number of integers x satisfying the equation is 1.

Therefore, B is the answer.
Answer: B
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