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If a certain toy store's revenue in November was 2/5 of its

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If a certain toy store's revenue in November was 2/5 of its [#permalink] New post 30 Jun 2010, 16:26
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If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

(A) 1/4
(B) 1/2
(C) 2/3
(D) 2
(E) 4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-certain-toy-store-s-revenue-in-november-was-2-5-of-its-134892.html
[Reveal] Spoiler: OA
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Re: pleas help [#permalink] New post 30 Jun 2010, 18:23
the answer is 4.

E

N=(2/5)D & J= (1/4)N


D=X(N+J)/2=(1/2)D(2/5)[1+1/4]=(1/5)D(5/4)=(1/4)D

Therefore =D/[(N+J)/2] = 4
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Re: pleas help [#permalink] New post 30 Jun 2010, 18:34
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Hi xmagedo,

susana's algebraic solution is spot on. But most people (including me, incidentally) will be able to solve this question more quickly by picking numbers.

When you have a word problem involving fractions, you should start out by picking the lowest common denominator.

So, because the denominators in the question are 4 and 5, we should start with 20.

Let December's revenues be 20.
November's revenue is simply (2/5)*20 = 8.
So, January's revenue is (1/4)*8 = 2.

What is the average of 8 and 2?...(8+2)/2 = 5.

20 is how many times 5?...20/5 = 4.

Thus, the correct answer is 4.

Choose E.
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Re: If a certain toy store's revenue in november was 2/5... [#permalink] New post 12 Jul 2013, 08:57
ANSWER: E

If a certain toy store's revenue in November was \frac{2}{5} of its revenue in December and its revenue in January was \frac{1}{4} of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

A) \frac{1}{4}
B) \frac{1}{2}
C) \frac{2}{3}
D) 2
E) 4

Explanation:
let December's revenue be 100 dollars. Therefore November's is 40 dollars and Jan's 10 dollars.
The q is 100 dollars is what of 40+10/2.Therefore 4 times.
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Re: If a certain toy store's revenue in november was 2/5... [#permalink] New post 12 Jul 2013, 09:01
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If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

(A) 1/4
(B) 1/2
(C) 2/3
(D) 2
(E) 4

Probably, for most people it would be easier to solve such kind of questions by picking numbers.

Notice that January is linked with November and November is linked with December. So, we should pick some smart number for December's revenue. Since the denominators in the question are 5 and 4, the let say December's revenue was 20 (the least common multiple of 4 and 5). So, we have that:

Revenue in December = 20;
Revenue in November = 20*2/5 = 8;
Revenue in January = 8*1/4 = 2;

The average of 8 and 2 is 5, so the store's revenue in December was 20/5=4 times that value.

Answer: E.

All OG13 questions are here: the-official-guide-quantitative-question-directory-143450.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-certain-toy-store-s-revenue-in-november-was-2-5-of-its-134892.html
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Re: If a certain toy store's revenue in november was 2/5...   [#permalink] 12 Jul 2013, 09:01
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