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PyjamaScientist
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28 Aug 2021, 05:38
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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:
55%
(hard)
Question Stats:
69% (02:28) correct
31%
(02:41)
wrong
based on 538
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If M and N are two positive integers such that 7 times M is 9 times N and 1260 is the least number that is a multiple of both M and N, then which among the following is the greatest number that can divide both M and N ?
(a) 20
(b) 30
(c) 40
(d) 50
(e) 60
(a) 20
(b) 30
(c) 40
(d) 50
(e) 60
28 Aug 2021, 23:22
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7M=9N
1260 = 7 * 2^2 * 3^2 * 5
Since 1260 is the LCM of M & N and 7M=9N, M should be 2^2 * 3^2 * 5 and N should be 7 * 2^2 * 5.
So the GCF of M & N is 2^2 * 5
i.e 20 .
So Answer is A
1260 = 7 * 2^2 * 3^2 * 5
Since 1260 is the LCM of M & N and 7M=9N, M should be 2^2 * 3^2 * 5 and N should be 7 * 2^2 * 5.
So the GCF of M & N is 2^2 * 5
i.e 20 .
So Answer is A
20 Sep 2021, 04:56
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PyjamaScientist
PyjamaScientist, you are perfectly fine with your method.
If I were to do this, I would take the HCF as x.
Now 7M = 9N means M has all factors of N apart from 7, and an extra factor of 9. So M=9x
Also, 7M = 9N means N has all factors of M apart from 9, and an extra factor of 7. So M=7x
LCM(7x,9x) = 7*9*x=1260…………x=20
A
