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

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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
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Use plug in value.
Let Dec rev =100
Then Nov rev is 2/5 (100) => 40
Therefore Jan rev = 1/4(Nov rev) = 1/4(40) => 10

Hence Dec rev = x*( Nov rev+Jan rev)/2
100 = x* (40+10)/2
x = 100/25 => 4

Ans) E
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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
N = 2/5*D or D = 5/2N
J= 1/4*N

avg (N+J) =( N+1/4*N)/ 2 =5/8*N
so, avg(N+J)/D = 4

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

if we translate can write: N= 2/5 D and J = 1/4 N

Now observing and substituting we obtaine N = 4J .......ravenues of November and January is 4. E is the answer.
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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
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Bunuel 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

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
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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
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: $$D>2N>2*Average$$

The only option left is (E).
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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
Hi All,

This question can be solved by TESTing VALUES.

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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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
Here is a visual that should help. Notice that I simplified the equation using algebra, and then I substituted numbers once the math was simplified.

Trying to substitute numbers up-front can also work, but it often involves too much trial and error. Hence the hybrid technique.

Please note that "(2d /10)" should have been written as "(2d / 20)."
Attachments

Screen Shot 2016-03-28 at 5.57.03 PM.png [ 128.5 KiB | Viewed 87433 times ]

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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
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Nice Official Question.
Here is what i did on tis one =>

Method 1->
December = x
November =2x/5
January =x/10

Mean (J+N)= {2x/5+x/10}/2 => x/4

Hence x=p*x/4
p=4

Hence E

Method 2=> December = 10
November = 4
January => 1

Mean(J+N) = 2.5

Hence 10 = 4 times 2.5

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

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.

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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
Kind of tricky... I glanced over the question and found the average for NOV, DEC and JAN instead of just NOV and JAN. I need to read all the way through the problem instead of taking a quick glance. Other than that little issue, the problem isn't difficult at all to solve, if you pick smart numbers.
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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
Bunuel 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

Diagnostic Test
Question: 8
Page: 21
Difficulty: 600

ok I got it

revenue in december 100
revenue in november is 100

November was 2/5 of its revenue in December ---> N = 2/5*100 = 40
January was 1/4 of its revenue in November ---> J = 1/4 * 40 = 10

then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

average (arithmetic mean) of its revenues in November and January ---> $$\frac{40+10}{2}$$$$= 25$$

Average revenue 25, hence $$100/25$$$$= 4$$ finally !
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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
Bunuel 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

Diagnostic Test
Question: 8
Page: 21
Difficulty: 600

We will calculate L.C.M of the denominators =4*5=20

Let,

December revenue =20

November revenue =2/5*20=8

January revenue =1/4*8=2

Now,

Average of Nov. & Jan. =8+2/2=5

So, December revenue is 20/5=4 times.

Posted from my mobile device
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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
This is purely a reading comprehension question...
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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
Picking numbers is a good method. Another way to solve is to use the ratios.

Let November be N, December be D, and January be J. The goal is to find $$\frac{D}{mean(N+J)}=\frac{D}{(N+J)/2}=\frac{2*D}{(N+J)}$$. So, we are told that

(1) N:D = 2:5
(2) D:N = 5:2
(3) N:J = 4:1

From the above, one can see that (2) and (3) can transform into a relationship between all three terms, but (2) needs to be multiplied by 2. So, we get
(2') D:N = 10:4
(3) N:J = 4:1

In other words, we get D:N:J = 10:4:1. One can simply plug the numbers from the obtained relationship into our original formula, i.e. $$\frac{2*10}{(4+1)} = 4$$.

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Re: If a certain toy store's revenue in November was 2/5 of its [#permalink]
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As we are dealing with 2 fractions here : $$\frac{2}{5}$$ and $$\frac{1}{4}$$ let us assume that revenue in December was 20 [LCM of '4' and '5']

=> November: $$\frac{2}{5}$$ * 20 = 8 [November is $$\frac{2}{5}$$ of Decemeber]

=> January: $$\frac{1}{4}$$ * 8 = 2 [January is $$\frac{1}{4}$$ of November]

Average of revenue's in Novemebr and January: $$\frac{(8 + 2) }{ 2}$$ = $$\frac{10 }{ 2}$$ = 5

Revenue(December) was how many times the average of its revenues in November and January

Decemeber (20) = x * 5

=> x = $$\frac{20}{5}$$ = 4

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

N = 2/5D
J = N/4 = D/10

N + J / 2 = 2/5D + D/10 /2 = D/4

Then,

D / D/4 = 1/4

So D is 4x the average revenue in November and January.

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