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
OG Certain toy store's revenue in November
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Say the revenues in November, December and January are N, D, and J, respectively.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
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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We can let n = revenue in November, d = revenue in December, and j = revenue in January. We can create the following equations: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
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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