A girl scout was selling boxes of cookies. In a month, she sold both

Hi Gnpth,

When it comes to Weighted Average questions, there are several different ways to go about getting to the correct answer. This question has some rather specific patterns that you can take advantage of though... so that you can avoid doing lots of math.

First off, the answer choices are "spaced out", so we can take advantage of that spread.

Second, the average of 1 box of chocolate chip cookies and 1 box of plain cookies is ($1.25 + $0.75)/2 = $1. This is important because....

Third, there are 1585 boxes of cookies with a combined value of $1588.75.....

1588.75/1585 = Just a little bit more than $1 per box

This means that SLIGHTLY MORE than half of the boxes are chocolate chip cookies. We're asked how many boxes of PLAIN cookies were sold (thus, SLIGHTLY LESS than half of those boxes were plain cookies.

Half of 1585 is about 792. Which answer is slightly less than that....?

Final Answer:

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

First get the difference of the revenue to the number of boxes.

1588.25-1585=3.25

Now you know that the difference between plain cookies boxes and chocolate cookies boxes is small.

We now divide the revenue by two.

1588.25/2=~794

Because the difference btween the possible answers is big, this leaves us with choice E.

In this case thare is no need to make any further calculations. Glancing at the answers is very important, for it can save a lot of time. Done in under 1 minute.

Note that the options in this question are wide apart. This begs you to think of approximation. The approximate cost per box that she sold is $1. So half were choice chip and half were plain. She sold approximately 1600 cookies. Half of that is 800. The option close to 800 is 785.

Answer (E)
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1.25x + 0.75y = 1588.75 ;
5x + 3y = 6355 ...... eqn 1

x + y = 1585 ........ eqn 2

solving both eqns

x = 800, y = 785

Ans E.

1588.85/1585=1(approximately)
$1.25………$1………$0.75
…….0.25……..0.25….
1:1
1585/2=792.5
=785 approximately
ans: E

Veritas Prep Solution:
This Weighted Average problem comes with a shortcut reward for those who truly understand weighted averages. Here, with chocolate cookies costing $1.25 and plain cookies costing $0.75, the “unweighted” average is $1.00, meaning that if 1,585 boxes were sold and it was an equal amount of each type, the revenue would be exactly $1585.00. Instead, the revenue is a couple dollars more than that at $1588.75. But because the difference is only $3.75, it’s a very slight difference in the number of chocolate vs. the number of plain. And only choice E could explain that difference – that’s a total of 800 boxes of chocolate and 785 of plain – a slight advantage in the number of chocolate. Logically, this is the only correct answer, because every other choice would mean that the average would skew much, much closer to $1.25, and the actual difference is very slight.

Hi,
This seems like an ugly calculation. Was about to give up when I wondered why not use approximations?

Here we go : the boxes sold become 1600 instead of 1585
The amount of $ becomes $1600 instead of $1,588.75

a= chocolate cookies and b = plain cookies
a+b=1600 cookies
a costs 1,25$ or 5/4$ and b costs 0,75$ or 3/4$

1,25a+0,75b=1600
5/4(1600-b)+3/4b=1600
2000-5/4b+3/4b=1600
400=2/4b = 1/2b
b=800 approximately

Answer E

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