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

Question

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

(A) 1/4
(B) 1/2
(C) 2/3
(D) 2
(E) 4

Bunuel · Accepted Answer

SOLUTION

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

(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.

Answer: E.

cyberjadugar · Answer

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

D = \frac {x(N+J)}2 , we need to find x,

D = \frac {x((2/5)D+(1/10)D}2 
x = 4,

Thus, Answer is (E).

Regards,

pallavisatsangi · Answer

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

kashishh · Answer

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

carcass · Answer

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.

VeritasPrepDennis · Answer

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

ping1 · Answer

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).

EMPOWERgmatRichC · Answer

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.

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

mcelroytutoring · Answer

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)."

stonecold · Answer

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

ScottTargetTestPrep · Answer

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

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

Thus, the revenue in December is d/  = 4 times the average revenue for November and January.

Answer: E

atr0038 · Answer

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.

dave13 · Answer

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 !

shaonkarim · Answer

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.

Answer is E

Posted from my mobile device

mykrasovski · Answer

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 .

Answer E.

MathRevolution · Answer

As we are dealing with 2 fractions here :  \frac{2}{5}  and  \frac{1}{4}  let us assume that revenue in December was 20

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

=> January:  \frac{1}{4}  * 8 = 2  \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

Answer E

CEdward · Answer

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

(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.

rushimehta · Answer

Though calculation using smart numbers or algebra seems to be a straight forward and the best way of solving this problem during exam... Was just thinking of a way to solve this using logic and without any exact calculation. We have 3 months - N, D, J ... We need to check that the revenue of D is how many times the revenue of average of N and J... We are given the values of N and J in the form of revenue of December and November respectively i.e. If D is the revenue of December... N has revenue of (2/5)D, wheres J has a revenue of (1/4)N If you think logically, the revenue of N is less than that of D, and revenue of J is less than that of N, thus it is also less than that of D... using this logic we can say that the average of revenue of N and J is less than D --> thus to get the revenue of D we need to multiply the average revenue of N and J by a number greater than 1... (This helps us eliminate option A, B, C ) Now, we are left with options D and E... On thinking further, if the sum of revenue of N and J is equal to D, then average will be exactly half of D and the answer would be 2 (option D).... ... But the revenue of N is already less than half of D, and the revenue of J is even lesser than that of N, so definitely the sum of revenues of N and J will be less than revenue of D... Using this logic we can say that the average is definitely less than half of the revenue of D... thus we need to multiple the average by a number greater than 2... (This helps us eliminate option D) Only option E has such a number ... !

I do know that the thought process here is a bit heavy, and calculation might be the easier and quicker way out --> but just came across this and thought to share it here in case it helps anyone....

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards