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05 Oct 2021, 05:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (01:28) correct
28%
(01:22)
wrong
based on 53
sessions
History
Date
Time
Result
Not Attempted Yet
If \(\frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{6} = \frac{a}{(2)(3)(5)(6)}\), which of the following options are factors of \(a\)?
I. 3
II. 4
III. 6
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
I. 3
II. 4
III. 6
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
05 Oct 2021, 05:21
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Explanation:
1/2 + 1/3 + 1/5 + 1/6 =
90+60+36+30/2.3.5.6
216/2.3.5.6
a = 216
216 is factors of 3,4 & 6
IMO-E
Posted from my mobile device
1/2 + 1/3 + 1/5 + 1/6 =
90+60+36+30/2.3.5.6
216/2.3.5.6
a = 216
216 is factors of 3,4 & 6
IMO-E
Posted from my mobile device
05 Oct 2021, 07:01
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Bunuel
Note each fraction on the left is a product of the three numbers, out of the 4 discluding the denominator. Hence \(a = 3*5*6 + 2*5*6 + 2*3*6 + 2*3*5\).
We can conclude each term has a multiple of 6. We may combine the first and last term to get \(a = 3*5*8 + 2*5*6 + 2*3*6\), then each term is a multiple of 4 as well. Thus all options listed above are factors of \(a\).
Ans: E
