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A company was approved to spent a certain sum of money for an annual.

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A company was approved to spent a certain sum of money for an annual.  [#permalink]

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New post 23 Oct 2019, 01:21
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Question Stats:

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A company was approved to spent a certain sum of money for an annual. It spent (1/4)th of the sum during the first quarter of the year, and (1/6)th of the remainder was spent during the second quarter. By what percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters?

(A) 10%
(B) 22.22%
(C) 33.33%
(D) 66.66%
(E) 133.33%

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A company was approved to spent a certain sum of money for an annual.  [#permalink]

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New post Updated on: 23 Oct 2019, 08:39
Bunuel wrote:
A company was approved to spent a certain sum of money for an annual. It spent (1/4)th of the sum during the first quarter of the year, and (1/6)th of the remainder was spent during the second quarter. By what percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters?

(A) 10%
(B) 22.22%
(C) 33.33%
(D) 66.66%
(E) 133.33%


1st ; x/4
2nd ; 3x/4 *1/6 ; x/8
total spent in 1st & 2nd ; 3x/8
for 3rd & 4th quarter we have ; x-(x/4+x/8) = 5x/8
total 1 &2 ; 3
%∆ ; 5x-3x/3x ; 2x/3x ; 66.66%
IMO D

Originally posted by Archit3110 on 23 Oct 2019, 02:15.
Last edited by Archit3110 on 23 Oct 2019, 08:39, edited 2 times in total.
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A company was approved to spent a certain sum of money for an annual.  [#permalink]

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New post 23 Oct 2019, 05:37

Solution



Given:
    • A company spent \((\frac{1}{4})^{th}\) of the sum during the first quarter of the year, and
    • \((\frac{1}{6})^{th}\) of the remainder was spent during the second quarter

To find:
    • What percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters

Approach and Working Out:
    • Let the amount be 100x
      o After 1st quarter, remaining amount = \(100x – \frac{100x}{4} = 75x\)
      o After 2nd quarter, the remaining amount = \(75x – \frac{75x}{6} = 62.5x\)

    • Amount remaining at the beginning of third quarter = 62.5x
    • Amount spend in first two quarters = 100x – 62.5x = 37.5x
    • Therefore, required percentage = \(\frac{(62.5 – 37.5)}{37.5} * 100 = 66.66%\)

Hence, the correct answer is Option D.

Answer: D
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A company was approved to spent a certain sum of money for an annual.  [#permalink]

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New post 23 Oct 2019, 08:03
EgmatQuantExpert please see highlighted part..

for 2nd quarter its given that money spent is (1/6)th of the remainder was spent during the second quarter.
total being 100x
the remainder in this case would be from the money spent in 1st quarter which was 75x so left with remainder 25x whose 1/6 is spent in 2nd quarter therefore money spent in 2nd quarter should be 25x/6 isnt it?

EgmatQuantExpert wrote:

Solution



Given:
    • A company spent \((\frac{1}{4})^{th}\) of the sum during the first quarter of the year, and
    • \((\frac{1}{6})^{th}\) of the remainder was spent during the second quarter

To find:
    • What percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters

Approach and Working Out:
    • Let the amount be 100x
      o After 1st quarter, remaining amount = \(100x – \frac{100x}{4} = 75x\)
      o After 2nd quarter, the remaining amount = \(75x – \frac{75x}{6} = 62.5x\)

    • Amount remaining at the beginning of third quarter = 62.5x
    • Amount spend in first two quarters = 100x – 62.5x = 37.5x
    • Therefore, required percentage = \(\frac{(62.5 – 37.5)}{37.5} * 100 = 66.66%\)

Hence, the correct answer is Option D.

Answer: D
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Re: A company was approved to spent a certain sum of money for an annual.  [#permalink]

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New post 23 Oct 2019, 08:28
Bunuel wrote:
A company was approved to spent a certain sum of money for an annual. It spent (1/4)th of the sum during the first quarter of the year, and (1/6)th of the remainder was spent during the second quarter. By what percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters?

(A) 10%
(B) 22.22%
(C) 33.33%
(D) 66.66%
(E) 133.33%


Let approval amount be 'x'

First Quarter amount = \(\frac{1*x}{4} = \frac{x}{4}\)

Remaining Amount = \(x - \frac{x}{4}\) = \(\frac{3x}{4}\)

Second Quarter Amount = \(\frac{1}{6}*\frac{3x}{4}\) = \(\frac{x}{8}\)

Remaining Amount = \(x - {\frac{x}{8}+\frac{x}{4}} = \frac{5x}{8}\)

Bunuel wrote:
what percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters


=> \([[\frac{5x}{8} - (\frac{x}{4} + \frac{x}{8})]/[(\frac{x}{4} + \frac{x}{8})]]*100\)

=> \([[\frac{5x}{8} - \frac{3x}{8}]/[\frac{3x}{8}]]*100\)

=> \([(\frac{2x}{8})/(\frac{3x}{8})]*100\)

=> \(\frac{2}{3} * 100\)

=> 66.66%

Hence D
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Re: A company was approved to spent a certain sum of money for an annual.  [#permalink]

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New post 27 Oct 2019, 19:52
Bunuel wrote:
A company was approved to spent a certain sum of money for an annual. It spent (1/4)th of the sum during the first quarter of the year, and (1/6)th of the remainder was spent during the second quarter. By what percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters?

(A) 10%
(B) 22.22%
(C) 33.33%
(D) 66.66%
(E) 133.33%


The money spent was 1/4 + 1/6 x 3/4 = 1/4 + 1/8 = 1/4 + 2/8 = 3/8, so the money left was 5/8.

We can now create the equation:

(5/8 - 3/8)/(3/8) x 100

(2/8)/(3/8) x 100

(2/3) x 100 = 66.66 percent

Answer: D
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Re: A company was approved to spent a certain sum of money for an annual.   [#permalink] 27 Oct 2019, 19:52
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