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SC Moderator V
Joined: 23 Sep 2015
Posts: 1716
A grocery store sells boxes of two kinds of cereals, wheat-based and r  [#permalink]

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Difficulty:   15% (low)

Question Stats: 81% (01:23) correct 19% (02:02) wrong based on 42 sessions

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A grocery store sells boxes of two kinds of cereals, wheat-based and rice-based. In this store, the average weight of a box of rice-based cereal is 60 ounces, the average weight of a box of wheat-based cereal is 48 ounces, and the average weight of all the boxes of cereal is 50 ounces. What is the ratio in this store of boxes of rice-based cereals to wheat-based cereals?

A. $$\frac{1}{12}$$
B. $$\frac{1}{6}$$
C. $$\frac{1}{5}$$
D. $$\frac{1}{4}$$
E. $$\frac{1}{3}$$

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Re: A grocery store sells boxes of two kinds of cereals, wheat-based and r  [#permalink]

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aragonn wrote:
A grocery store sells boxes of two kinds of cereals, wheat-based and rice-based. In this store, the average weight of a box of rice-based cereal is 60 ounces, the average weight of a box of wheat-based cereal is 48 ounces, and the average weight of all the boxes of cereal is 50 ounces. What is the ratio in this store of boxes of rice-based cereals to wheat-based cereals?

A. 1/12
B. 1/6
C. 1/5
D. 1/4
E. 1/3

One approach is to use weighted averages
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let R = number of boxes of rice-based cereal
Let W = number of boxes of wheat-based cereal

So, R+W = TOTAL number of boxes of cereal
Also, R/(R + W) = proportion of cereal boxes that are rice-based
And W/(R + W) = proportion of cereal boxes that are wheat-based

Plug all values into the above formula. . .
We get: 50 = [R/(R + W)](60) + [W/(R + W)](48)
Multiply both sides by (R+W) to get: 50(R + W) = 60R + 48W
Expand to get: 50R + 50W = 60R + 48W
Rearrange: 2W = 10R
Rearrange more: 2/10 = R/W
Simplify: R/W = 1/5

What is the ratio in this store of boxes of rice-based cereals to wheat-based cereals?
R/W = 1/5

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Re: A grocery store sells boxes of two kinds of cereals, wheat-based and r  [#permalink]

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Avg. Wheat = 48 Ounc , Avg. Rice = 60 Ounc , Avg. Total = 50 Ounc

So , W48+R60 = T50

==> if we see all the options , in all the R/W ratio given R = 1 always
==> W48+(1)60 = (1+W)50
==> 60-50 = 2W
==> W = 5,
R/W = 1/5 ==> Option C
SC Moderator V
Joined: 23 Sep 2015
Posts: 1716
Re: A grocery store sells boxes of two kinds of cereals, wheat-based and r  [#permalink]

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Official Explanation:

Method One: Algebraic Approach

This approach is longer, more time-consuming, but easier to understand.

We can set up a weighted average. Let W be the number of boxes of wheat-based cereals, and R be the number of boxes of rice-based cereals. Here’s the weighted average formula:

$$\frac{(60R+48W)}{(R+W)​​}$$= 50

Multiply both sides by (R + W)

60R + 48W = 50R + 50W

10R + 48W = 50W

10R = 2W

5R = W

$$\frac{R}{W}$$ = $$\frac{1}{5}$$

Method Two: Intuitive Geometric Approach

This approach is lightning fast but harder to understand.

Look at the the two distance of the individual averages from the weighted average. Wheat-based cereals are at 60, 10 units away from 50. Rice-based cereals are at 48, just 2 units from 50. The ratio of the distances is 10 to 2, or 5:1, so the ratio of the group sizes must be the reciprocal, 1:5.

_________________
Thanks!
Do give some kudos.

Simple strategy:
“Once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth.”

GMAT Ninja YouTube! Series 1| GMAT Ninja YouTube! Series 2 | How to Improve GMAT Quant from Q49 to a Perfect Q51 | Time management

My Notes:
Reading comprehension | Critical Reasoning | Absolute Phrases | Subjunctive Mood
Intern  Joined: 04 Mar 2019
Posts: 1
Re: A grocery store sells boxes of two kinds of cereals, wheat-based and r  [#permalink]

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Can you solve it as follows? If we're trying to determine the ratio of Rice:Wheat

R:W
60/50R=48/50W
Cross multiply
60*50R=48*50W
3000R=2400W
R/W=2400/3000
1-4/5= 1/5 Re: A grocery store sells boxes of two kinds of cereals, wheat-based and r   [#permalink] 04 Mar 2019, 16:01
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