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21 Oct 2021, 03:15
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
68% (02:48) correct
32%
(02:47)
wrong
based on 315
sessions
History
Date
Time
Result
Not Attempted Yet
If \(a\) and \(b\) are integers such that \(a\) is the product of \(m × \sqrt{60}\) and \(b\) is the product of \(n × \sqrt{75}\), which of the following must be a factor of \(ab\) ?
A. 90
B. 105
C. 275
D. 900
E. 4,500
A. 90
B. 105
C. 275
D. 900
E. 4,500
02 Nov 2021, 22:59
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Bunuel
\(a = m*\sqrt{60} = m * 2*\sqrt{15}\)
For 'a' to be an integer, 'm' must have another sqrt(15) in it at least.
So 'a' is at least 30.
\(b = n * \sqrt{75}\)
\(b = n * 5*\sqrt{3}\)
For 'b' to be an integer, 'n' must have another sqrt(3) in it at least.
So 'b' is at least 15.
Hence 'ab' is at least 30*15 = 450
So 90 is certainly a factor of 'ab'.
Answer (A)
General Discussion
11 Feb 2026, 11:53
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