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OG Certain toy store's revenue in November

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG Certain toy store's revenue in November

Post Tue Jul 25, 2017 8:11 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post 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

    x = 4.

    The correct answer: E

    Hope this helps!

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    Post 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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    Post 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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