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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

Diagnostic Test Question: 8 Page: 21 Difficulty: 600

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.

Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]

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25 Jun 2012, 04:29

2

This post received KUDOS

Hi,

Lets say, revenue in November = N was 2/5 of its revenue in December = D revenue in January = J As per given data, N = (2/5)D J = (1/4)N = 1/4 * 2/5 *D = (1/10)D

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, then 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.

Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]

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16 Jul 2014, 19:48

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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]

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06 Aug 2015, 06:24

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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

Diagnostic Test Question: 8 Page: 21 Difficulty: 600

If N = 2/5 D and J = 1/4N, we should put all expressions into a common variable. Let's use D. D =D; N =2/5D; and J = 1/10D. Assuming D =10, we now have N = 4 and J = 1. The average of 4 and 1 is 2.5 10 is 4 times greater than 2.5 Answer E is correct
_________________

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

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20 Nov 2015, 06:19

This can be solved even faster:

The revenue in November (N) is less than half the revenue in December (D). Therefore, December revenue is more than twice the November revenue: \(D>2N\)

The revenue in January (J) is even smaller than revenue in November. Consequently, the average of the two will be less than N: \(Average = (J+N)/2 < N\)

Therefore, December revenue will be far more than twice the average: \(D>2N>2*Average\)

We're given information comparing revenue for 3 months: 1) November revenue = 2/5 of December revenue 2) January revenue = 1/4 of November revenue

We're asked to compare the December revenue to the AVERAGE of November's and January's revenues (and we're asked how many times greater the December revenue is).

With the two fractions involved, the common denominator is 20, but you can use any number you like. For example...

December revenue = $100 November revenue = (2/5)(100) = $40 January revenue = (1/4)(40) = $10

The average of November and January is (40+10)/2 = 25

Since December revenue is 100, that is 4 TIMES the average of the other two months.

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