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For the equation 3 - 2 [ x ] = 3 [ x ] - 12, x satisfies p â

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by Max@Math Revolution » Fri Nov 29, 2019 12:16 am
[GMAT math practice question]

For the equation 3 - 2 [ x ] = 3 [ x ] - 12, x satisfies p ≤ x < q. What is the value of p + q? ( [ x ] denotes the greatest integer less than or equal to x.)

A. 6
B. 7
C. 8
D. 9
E. 10
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by deloitte247 » Sat Nov 30, 2019 12:54 pm
3 - 2 (x) = 3 (x) -12
3 + 12 = 3x + 2x
15 = 5x
x =15/5 = 3
$$Given\ that\ p\le x<q\ =\ p\le3<q$$
p can be 3, 2, 1, 0, -1, ---, infinix
Therefore, the maximum value of p = 3
q can be 4, 5, 6, 7, 8, ---, infinix
Hence, the maximum value of q = 4
$$Therefore,3\le3<4$$
Tthe value if p+q = 3+4 = 7

Answer = option B
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by Max@Math Revolution » Sun Dec 01, 2019 7:42 pm
=>

Since [ x] is the greatest integer less than or equal to x, if we have n ≤ x < n + 1, where n is an integer, we define [x] = n.

3 - 2[ x ] = 3[ x ] - 12
=> 15 = 5[ x ]
=> [ x ] = 3
=> 3 ≤ x < 4
Then we have p = 3 and q = 4.
So p + q = 7.

Therefore, B is the answer.
Answer: B
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