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Arithmetic

This topic has 2 expert replies and 0 member replies

Arithmetic

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After eating half of the chocolate mini bars in a can, Clayton gave one fourth of the remaining mini bar chocolates to his buddy and realized that he only had 6 chocolate mini bars left. How many mini bar chocolates did he originally have?

(A) 2
(B) 4
(C) 8
(D) 16
(E) 18

OA is D

pls, I need an Expert to give me a perfect interpretation of this question.Thanks

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GMAT/MBA Expert

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Quote:
After eating half of the chocolate mini bars in a can, Clayton gave one fourth of the remaining mini bar chocolates to his buddy and realized that he only had 6 chocolate mini bars left. How many mini bar chocolates did he originally have?

(A) 2
(B) 4
(C) 8
(D) 16
(E) 18

OA is D

pls, I need an Expert to give me a perfect interpretation of this question.Thanks
Hi Roland2rule,
Let's take a look at your question.

Let 'x' be the total chocolates in the can.
After eating half of the chocolate mini bars in a can, remaining chocolates will be:
$$x-\frac{1}{2}x=\frac{1}{2}x$$

Clayton gave one fourth of the remaining mini bar chocolates to his buddy.
$$=\left(\frac{1}{4}\right)\frac{1}{2}x=\frac{1}{8}x$$

After giving chocolates to his buddy, only 6 chocolate mini bars left. We can write it as:
$$\frac{1}{2}x-\frac{1}{8}x=6$$
$$x\left(\frac{1}{2}-\frac{1}{8}\right)=6$$
$$x\left(\frac{4-1}{8}\right)=6$$
$$x\left(\frac{3}{8}\right)=6$$
$$x=6\times\frac{8}{3}$$
$$x=2\times8=16$$

Hence, there were 16 chocolates in the can originally.

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
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Hi Roland2rule,

We're told that Clayton eats HALF of the chocolate mini bars in a can, then gives 1/4 of the remaining mini bar chocolates to his buddy and is left with 6 chocolate mini bars. We're asked for the number of mini bar chocolates originally in the can. This question can be solved by TESTing THE ANSWERS.

Since Clayton ended up with 6 bars after eating HALF and giving away some of the others, he clearly had MORE than 12 chocolate bars, so the correct answer is either D or E.

Let's TEST Answer D: 16 bars

IF....
Original number = 16
Clayton eats HALF = 8.... leaving 8 remaining
1/4 given to a buddy = (1/4)(8) = 2 given away
Bars remaining = 8 - 2 = 6
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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