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# Which of the following is the greatest?

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Senior SC Moderator
Joined: 14 Nov 2016
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Which of the following is the greatest?  [#permalink]

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Updated on: 07 May 2017, 06:49
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Difficulty:

35% (medium)

Question Stats:

67% (01:20) correct 33% (01:34) wrong based on 159 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, 05:44.
Last edited by Bunuel on 07 May 2017, 06:49, edited 1 time in total.
Renamed the topic.
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Which of the following is the greatest?  [#permalink]

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Updated on: 21 May 2017, 02:37
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

Originally posted by Kritesh on 07 May 2017, 08:23.
Last edited by Kritesh on 21 May 2017, 02:37, edited 1 time in total.
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Re: Which of the following is the greatest?  [#permalink]

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15 May 2017, 09:12
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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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20 Feb 2020, 08:34
the top explanation on this one will get you this problem very easily

https://gmatclub.com/forum/of-the-follo ... 60693.html
Re: Which of the following is the greatest?   [#permalink] 20 Feb 2020, 08:34