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A and B are two multiples of 36, and Q is the set of consecutive integ
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18 May 2021, 05:30
18 May 2021, 05:30
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Difficulty:
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Question Stats:
52% (02:52) correct
48%
(02:58)
wrong
based on 132
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A and B are two multiples of 36, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 9, how many multiples of 4 are there in Q?
A. 18
B. 19
C. 20
D. 21
E. 22
A. 18
B. 19
C. 20
D. 21
E. 22
Re: A and B are two multiples of 36, and Q is the set of consecutive integ
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18 May 2021, 06:18
18 May 2021, 06:18
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Given: A and B are two multiples of 36, and Q is the set of consecutive integers between A and B, inclusive.
Asked: If Q contains 9 multiples of 9, how many multiples of 4 are there in Q?
Let us take Q= {36,..,45,..,54,..,63,..,72,..,81,..,90,..,99,..,108}
Multiples of 4 in Q = {36,40,........,108}
Number of multiples of 4 in Q = (108-36)/4 + 1 = 72/4 + 1 = 18 + 1 = 19
IMO B
Asked: If Q contains 9 multiples of 9, how many multiples of 4 are there in Q?
Let us take Q= {36,..,45,..,54,..,63,..,72,..,81,..,90,..,99,..,108}
Multiples of 4 in Q = {36,40,........,108}
Number of multiples of 4 in Q = (108-36)/4 + 1 = 72/4 + 1 = 18 + 1 = 19
IMO B
General Discussion
Math Revolution GMAT Instructor
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Re: A and B are two multiples of 36, and Q is the set of consecutive integ
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18 May 2021, 05:52
18 May 2021, 05:52
Expert Reply
Lengthy Method:
Multiple of 36: 36, 72, 108, 144...
Q = 72 to 144 [9 multiples of 9: 72, 81, 90, 99, 108, 117, 126, 135, 144]
From 72 to 144 inclusive, multiples of 4 will be:
144 = 72 + (n-1) * 4
=> 72 = 4n - 4
=> n = 19
Answer B
Shortcut:
Between every two consecutive multiples of 36, there will be ten multiple of 4
72 = 36 + (n-1) * 4
=> 36 = 4n - 4
=> n = 10
Therefore, between two multiples of 36 (36 and 72) lies ten multiple of 4
So if there are 9 multiples of 9 in Q, the number of multiples of 4 would be = 9 + 10 = 19
Answer B
Multiple of 36: 36, 72, 108, 144...
Q = 72 to 144 [9 multiples of 9: 72, 81, 90, 99, 108, 117, 126, 135, 144]
From 72 to 144 inclusive, multiples of 4 will be:
144 = 72 + (n-1) * 4
=> 72 = 4n - 4
=> n = 19
Answer B
Shortcut:
Between every two consecutive multiples of 36, there will be ten multiple of 4
72 = 36 + (n-1) * 4
=> 36 = 4n - 4
=> n = 10
Therefore, between two multiples of 36 (36 and 72) lies ten multiple of 4
So if there are 9 multiples of 9 in Q, the number of multiples of 4 would be = 9 + 10 = 19
Answer B
