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If 1/2 + 1/3 + 1/5 + 1/6 = a/(2)(3)(5)(6), which of the following opti 05 Oct 2021, 05:15
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E
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25% (medium)

Question Stats:

72% (01:28) correct 28% (01:22) wrong based on 53 sessions

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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
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E
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If 1/2 + 1/3 + 1/5 + 1/6 = a/(2)(3)(5)(6), which of the following opti 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

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If 1/2 + 1/3 + 1/5 + 1/6 = a/(2)(3)(5)(6), which of the following opti 05 Oct 2021, 07:01
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Bunuel
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
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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
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If 1/2 + 1/3 + 1/5 + 1/6 = a/(2)(3)(5)(6), which of the following opti 05 Oct 2021, 07:14
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Correct Option E

LCM of 2,3,5,6 = 60

I - 60/3 = 30 - (yes)
II - 60/4 = 15 - (yes)
III - 60/6 = 15 - (yes)

Option E,
satisfy the option factor for (a)

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If 1/2 + 1/3 + 1/5 + 1/6 = a/(2)(3)(5)(6), which of the following opti 05 Oct 2021, 12:00
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Bunuel
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
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\(\frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{6} = \frac{a}{(2)(3)(5)(6)}\)

Or, \(\frac{15+10+6+5}{30} = \frac{a}{(2)(3)(5)(6)}\)

Or, \(\frac{36}{30} = \frac{a}{30}\)

\(a = 36 = 2^2*3^2\)

So, All the options , 3 , 4 & 6 are factors of 36 , Answer must be (E)



100mitra
Correct Option E

LCM of 2,3,5,6 = 60

I - 60/3 = 30 - (yes)
II - 60/4 = 15 - (yes)
III - 60/6 = 15 - (yes)

Option E,
satisfy the option factor for (a)

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LCM will be 30, rest is perfect, though 30 or 60 makes no difference as 60 is a multiple of 30.
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