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A candy store

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A candy store

by LalaB » Wed Mar 07, 2012 10:48 am
A candy store attendant noticed that 45% of the kids bought coco-candy and orange-candy. However, 10% of the kids who bought coco-candy didn't order orange-candy. What is the probability that the next kid does not buy coco-candy?

(A) 35%
(B) 40%
(C) 45%
(D) 50%
(E) 55%

[spoiler]
didn't get why OE is 45+0.1x=x. could anyone show me the Venn diagram of this? [/spoiler]
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by GMATGuruNY » Wed Mar 07, 2012 11:21 am
LalaB wrote:A candy store attendant noticed that 45% of the kids bought coco-candy and orange-candy. However, 10% of the kids who bought coco-candy didn't order orange-candy. What is the probability that the next kid does not buy coco-candy?

(A) 35%
(B) 40%
(C) 45%
(D) 50%
(E) 55%

[spoiler]
didn't get why OE is 45+0.1x=x. could anyone show me the Venn diagram of this? [/spoiler]
ALWAYS LOOK AT THE ANSWER CHOICES.
The answer choices represent the percentage who DID NOT buy coco-candy.
The phrase 10% of the kids who bought coco-candy implies that the percentage who DID BUY coco-candy is a multiple of 10.
Thus, the correct answer is almost certainly either B (which implies that 60% bought coco-candy) or D (which implies that 50% bought coco-candy).

Let the total number of children = 100.

Answer choice D: 50% DID NOT buy coco-candy.
Thus, 50 kids DID BUY coco-candy.
Of these 50 kids who bought coco-candy, the 10% who DID NOT ALSO BUY orange-candy = .1(50) = 5.
Thus, the number who bought BOTH candies = 50-5 = 45.
Success! According to the problem, 45% bought both types of candy.

The correct answer is D.
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by Neo Anderson » Wed Mar 07, 2012 10:05 pm
Image
the catch is the statement :
10% of the kids who bought coco-candy didn't order orange-candy
from figure above c = 10% of C -45
=> C = 0.1C -45
thus C =45 / 0.9 = 50 thus O =50 and thus the probability is also 50. and answer D
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by LalaB » Thu Mar 08, 2012 1:19 am
ah I got it. we can also assume, that 0.9C=45 c=50
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by mjmehta81 » Thu Mar 08, 2012 11:38 am
LalaB wrote:ah I got it. we can also assume, that 0.9C=45 c=50
Hi,

I did not get who you derived this equation nor did I understand how the solution was arrived by others. Please help me.
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by LalaB » Thu Mar 08, 2012 11:47 am
mjmehta81 wrote:
I did not get who you derived this equation nor did I understand how the solution was arrived by others. Please help me.
imagine that we have 100 kids
A candy store attendant noticed that 45% of the kids bought coco-candy and orange-candy.
means Coco+Orange=45

However, 10% of the kids who bought coco-candy didn't order orange-candy.
if 10% of Coco didnt buy Orange ,then 90% did buy Orange too.
we also know that Coco &Orange =45
so, 0.90x=45
x=50

it means that Coco -kid and Orange-kid are equal (50:50), so the chances that the next kid does not buy coco are 1/2
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