# Question: Cashews

## Comment on Cashews

### How can we solve this

How can we solve this question?

Q.N. Each new car produced in a certain factory includes at least one of the following three options: Bluetooth, navigation system, and sunroof. Of the cars that came off the production line yesterday, 25 had Bluetooth, 13 had a navigation system, and 30 had a sunroof. Yesterday, 50 cars were completed. Which of the following could be true about the cars that came off the production line yesterday?

-There were 2 cars that had exactly two of the options and there were 8 cars that had all three options.
-There were 3 cars that had exactly two of the options and there were 7 cars that had all three options.
-There were 4 cars that had exactly two of the options and there were 7 cars that had all three options.
-There were 6 cars that had exactly two of the options and there were 6 cars that had all three options.
-There were 7 cars that had exactly two of the options and there were 5 cars that had all three options.
-There were 8 cars that had exactly two of the options and there were 4 cars that had all three options. ### This question is very hard to

This question is very hard to provide a solution using text only, since the best explanation involves a 3-circle Venn diagram.
Can you please watch https://www.greenlighttestprep.com/module/gre-word-problems/video/924 (all about 3-circle Venn diagrams) and see if you can apply the strategy in that video.

If that doesn't help, I'll find a way to post some graphics.

### Unless I don't quite figure

Unless I don't quite figure it out, it appears we are not given any information on the number of cars that have all the 3 options. If we don't have this information, how can we work from the innermost region outwards? If this information in the problem description, can you please help identify it? ### Great question!

Great question!
We'll have to check each answer choice.

A) There were 2 cars that had exactly two of the options and there were 8 cars that had all three options

We can test this answer choice by drawing the diagram and placing 8 cars in the middle (cars that have all 3 features) and 2 cars in one of the intersections denoting 2 features. Then plug in the remaining values to see whether we can account for all 5 cars.

And so on.

### Hi Brent,

Hi Brent,

Have you got any solutions to this question posted in first comment?
I found this one particularly challenging. ### Would this equation work as

Would this equation work as well?
0.05(75-x)+0.8x=15 ### That's a perfectly valid

That's a perfectly valid solution - nice work.

You are letting x = the weight of the Brand X nut mix needed, which means 0.8x = the weight of the CASHEWS in the Brand X nut mix.

Since the total weight of the resulting nut mix is 75 pounds, then (75-x) = the weight of the Brand W nut mix needed, which means 0.05(75-x) = the weight of the CASHEWS in the Brand W nut mix.

So, if we focus SOLELY on the weight of cashews, we get:

0.05(75-x) + 0.8x = 15

Cheers,
Brent