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OG Certain toy store's revenue in November

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by AbeNeedsAnswers » Tue Jul 25, 2017 8:11 pm
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

E
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by Jay@ManhattanReview » Tue Jul 25, 2017 10:45 pm
AbeNeedsAnswers wrote: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

E
Say the revenues in November, December and January are N, D, and J, respectively.

Thus, we have,

N = 2D/5;
J = N/4 = (2D/5)/4 = D/10

Say the revenue in December was x times the average (arithmetic mean) of its revenues in November and January.

Thus, D = x*(N + J)/2

D = x*(2D/5 + D/10)/2

D = Dx*(2/5 + 1/10)/2

2 = 5x/10; D cancells

[spoiler]x = 4.[/spoiler]

The correct answer: E

Hope this helps!

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by [email protected] » Wed Jul 26, 2017 7:02 pm
Hi AbeNeedsAnswers,

This question can be solved by TESTing VALUES.

We're told two facts about a toy store's revenue:
1) The revenue in November was 2/5 of the revenue in December.
2) The revenue in January was 1/4 of the revenue in November.

We're asked to define how the revenue in December relates to the AVERAGE of the revenues in November and January.

Let's TEST the common-denominator of those two fractions: 20
IF...
December revenue = $20
November revenue = (2/5)($20) = $8
January revenue = (1/4)($8) = $2

The average of the November and January revenues is ($8+$2)/2 = $5. The December revenue ($20) is 4 times that average.

Final Answer: E

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by Scott@TargetTestPrep » Mon Aug 14, 2017 1:10 pm
AbeNeedsAnswers wrote: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

E
We can let n = revenue in November, d = revenue in December, and j = revenue in January. We can create the following equations:

n = (2/5)d

j = (1/4)n

So, j = (1/4)(2/5)d = (1/10)d

We now determine that the average revenue for November and January is:

[(2/5)d + (1/10)d]/2

[(4/10)d + (1/10)d]/2

(5/10)d/2 = (1/4)d

Thus, the revenue in December is d/[(1/4)d] = 4 times the average revenue for November and January.

Answer: E

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