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Which of the following is the greatest?

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Which of the following is the greatest?  [#permalink]

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New post Updated on: 07 May 2017, 07:49
5
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:01) correct 26% (00:58) wrong based on 102 sessions

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Which of the following is the greatest?

(A) \(\frac{1}{√2}+\frac{1}{√4}+\frac{1}{√6}+\frac{1}{√8}\)

(B) \(\frac{1}{{2^2}}+\frac{1}{{4^2}}+\frac{1}{{6^2}}+\frac{1}{{8^2}}\)

(C) \(\frac{1}{{2^2}}+\frac{1}{{2^4}}+\frac{1}{{2^6}}+\frac{1}{{2^8}}\)

(D) \(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{6}\)

(E) \(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\)

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Originally posted by hazelnut on 07 May 2017, 06:44.
Last edited by Bunuel on 07 May 2017, 07:49, edited 1 time in total.
Renamed the topic.
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Which of the following is the greatest?  [#permalink]

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New post Updated on: 21 May 2017, 03:37
1
We know that greater the value in the denominator compared to numerator , smaller will be the resulting number.

Based on the above statement we can eliminate options (B) and (C) when compared to other options.

For option (B) we get 1/4 + 1/16 + 1/36 + 1/64 will give you a number slightly greater than 1/4 (Between 1/4 and 1/2).

For option (C) we get 1/4+1/16+1/64+1/256 will give you a number slightly smaller than the option (B).

We are left out with three options (A) , (D) & (E).

In option (D) we are adding as well as subtracting the fractions mentioned.

(1-1/2)+(1/4-1/6) =1/2 + 1/12 which is almost equivalent to 0.6(0.5+0.1).

For answer option (E) we get

1/2+1/4+1/6+1/8 = 0.5 + 0.25 + 0.166 + 0.125 which will be greater than 1.

If your not able reduce the fraction 1/6 and 1/8 then from the first two no: itself we know that the no: is greater than 0.75 which is greater than the option (B) , (C) & (D).

Therefore currently option (E) is greatest.

Now we are left out with our final option (A) .

The option is similar to that of option (E) but the denominator is in square root form. We know that when the numerator is divided by the square root of a no: than the original no: it will yield a higher value .

For example : 1/4 = 0.25 is less than 1/[square root(4)] = 0.5 .

Considering the above analogy we can conclude that the greatest value which we can get among the options is (A).

Therefore option (A) is the answer.

Hope the explanation helps :)
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Originally posted by Kritesh on 07 May 2017, 09:23.
Last edited by Kritesh on 21 May 2017, 03:37, edited 1 time in total.
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Re: Which of the following is the greatest?  [#permalink]

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New post 15 May 2017, 10:12
Smaller the denominator larger the fraction always remember this.

√2=1.41

In all other options except A denominator is greater than 1.41

Hence largest number will be of option A
Please also note that we only have to see the first number as other numbers are smaller than first numbers and thus they don't play much role.

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Re: Which of the following is the greatest?  [#permalink]

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New post 15 Sep 2018, 08:32
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Which of the following is the greatest? &nbs [#permalink] 15 Sep 2018, 08:32
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