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Intern  Joined: 08 Aug 2017
Posts: 4
Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 52% (01:59) correct 48% (01:53) wrong based on 114 sessions

### HideShow timer Statistics Each of the items in a box is either a ball or a cube and each item is either red or blue. 72% of the items are cubes and 54% of the items are blue cubes. What percent of the cubes are red?

(A) 18%
(B) 25%
(C) 46%
(D) 50%
(E) 54%

Hi! My calculation for the question before gave me 33% as a result. Obviously, there is no such result in the answer bank.
72*0,54 = 38,88 = 39% blue cubes
72-39 = 33 % red cubes
Could anyone clarify why my calculations are wrong?
Thank you very much for your help.
Math Expert V
Joined: 02 Sep 2009
Posts: 56304
Re: Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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1
Kate2017 wrote:
Each of the items in a box is either a ball or a cube and each item is either red or blue. 72% of the items are cubes and 54% of the items are blue cubes. What percent of the cubes are red?

(A) 18%
(B) 25%
(C) 46%
(D) 50%
(E) 54%

Hi! My calculation for the question before gave me 33% as a result. Obviously, there is no such result in the answer bank.
72*0,54 = 38,88 = 39% blue cubes
72-39 = 33 % red cubes
Could anyone clarify why my calculations are wrong?
Thank you very much for your help.

Check below: Say there are total of 100 items.
72 of the items are cubes and 54 of the items are blue cubes, thus 18 of the items are red cubes.

What percent of the cubes are red?

(red cubes)/(total # of cubes)*100 = 18/72*100 = 25%.

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Manager  S
Joined: 30 Mar 2017
Posts: 67
Re: Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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I think the answer should be 25% .
If we assume 100 items in the box , then 72 of them are cubes. And 54 of them are blue cubes. Which gives us 18 remaining cubes which must be red colored. And 18 is one fourth or 25% of the total no of cubes(72).

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Intern  Joined: 08 Aug 2017
Posts: 4
Re: Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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Dear Bunuel and BeingHan thanks for your help. I see your point. I got it now!
What if the task say that 72% of the items are cubes and 54% of cubes are blue? Can we apply my calculation in that case?
Manager  S
Joined: 30 Mar 2017
Posts: 67
Re: Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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Kate2017 wrote:
Dear Bunuel and BeingHan thanks for your help. I see your point. I got it now!
What if the task say that 72% of the items are cubes and 54% of cubes are blue? Can we apply my calculation in that case?

There will be no need to apply any calculation then. Because in that case 46% of cubes will be red, as 54% of the cubes are already blue.

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Current Student P
Joined: 18 Aug 2016
Posts: 617
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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Kate2017 wrote:
Each of the items in a box is either a ball or a cube and each item is either red or blue. 72% of the items are cubes and 54% of the items are blue cubes. What percent of the cubes are red?

(A) 18%
(B) 25%
(C) 46%
(D) 50%
(E) 54%

Hi! My calculation for the question before gave me 33% as a result. Obviously, there is no such result in the answer bank.
72*0,54 = 38,88 = 39% blue cubes
72-39 = 33 % red cubes
Could anyone clarify why my calculations are wrong?
Thank you very much for your help.

100 items
72 cubes
54 blue cubes
red cubes = 72-54 = 18
% of red cubes out of all cubes = (18/72) * 100 = 25%
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Luckisnoexcuse
Intern  Joined: 08 Aug 2017
Posts: 4
Re: Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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Senior Manager  G
Joined: 09 Aug 2017
Posts: 359
Re: Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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What percent of the cubes are red? and what percent are red cube? Both are different. later answers 18% but we are asked about first which is (18%/72%)*100= 25%
Senior Manager  V
Joined: 22 Feb 2018
Posts: 427
Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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Kate2017 wrote:
Each of the items in a box is either a ball or a cube and each item is either red or blue. 72% of the items are cubes and 54% of the items are blue cubes. What percent of the cubes are red?

(A) 18%
(B) 25%
(C) 46%
(D) 50%
(E) 54%

OA: B
Let Total Number of items be $$100$$
\begin{matrix}
& Ball & Cubes & Total\\
Red & & 18 & \\
Blue& & 54 & \\
Total& & 72 & 100
\end{matrix}

Percent of the cubes are red $$= \frac{Red \quad Cubes}{Total \quad Cubes}*100 =\frac{18}{72}*100 =25$$%
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Re: Each of the items in a box is either a ball or a cube and each item is  [#permalink]

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Kate2017 wrote:
Each of the items in a box is either a ball or a cube and each item is either red or blue. 72% of the items are cubes and 54% of the items are blue cubes. What percent of the cubes are red?

(A) 18%
(B) 25%
(C) 46%
(D) 50%
(E) 54%

We can assume there are 100 items in the box. Thus, 72 items are cubes and 28 items are balls. Furthermore, 54 items are blue cubes, and hence 72 - 54 = 18 cubes are red. Therefore, the percent of cubes that are red is:

18/72 x 100 = 1/4 x 100 = 25

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