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A certain cake has two layers - Gmat Prep

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by lazarogb » Sat Dec 01, 2012 3:55 am
A certain cake has two layers with pieces of fruit on top of each layer. Of all the pieces of fruit on the cake, 25 percent are strawberies. How many pieces of fruit are on the first layer of the cake?

1) Of the pieces of fruit on the first layer, 6 are strawberries.

2) 20 percent of the 20 pieces of fruit on the second layer are strawberries.

OA: C

The explanation from the gmat prep is a bit confusing, can anyone make a more direct user-friendly solution??
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sat Dec 01, 2012 5:37 am
lazarogb wrote:A certain cake has two layers with pieces of fruit on top of each layer. Of all the pieces of fruit on the cake, 25 percent are strawberies. How many pieces of fruit are on the first layer of the cake?

1) Of the pieces of fruit on the first layer, 6 are strawberries.

2) 20 percent of the 20 pieces of fruit on the second layer are strawberries.

OA: C

The explanation from the gmat prep is a bit confusing, can anyone make a more direct user-friendly solution??
Let us assume that all the fruits in both layers = T
Then strawberries = 25% of T = 0.25T
Also, 0.25T = strawberries in layer 1 + strawberries in layer 2

(1) Of the pieces of fruit on the first layer, 6 are strawberries.
0.25T = 6 + strawberries in layer 2, but we do not know number of strawberries in layer 2; NOT sufficient.

(2) 20 percent of the 20 pieces of fruit on the second layer are strawberries implies 20% of 20 pieces of fruit or 0.20 * 20 = 4 fruit pieces on the second layer are strawberries.
So, 0.25T = strawberries in layer 1 + 4; NOT sufficient.

Combining (1) and (2), strawberries on first layer = 6 and strawberries on 2nd layer = 4; SUFFICIENT to answer the question.

The correct answer is C.
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by mcdesty » Fri Aug 01, 2014 2:11 am
Here is how I would set this one up.
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Last edited by mcdesty on Thu Aug 21, 2014 9:54 am, edited 2 times in total.
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I am experienced - I have tutored calculus and linear algebra for over two years.
For a very modest fee, I will ensure that your GMAT journey is a smooth one: Daily assignments and careful micro management.
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by Brent@GMATPrepNow » Fri Aug 01, 2014 6:23 am
I'd like to point out that mcdesty's approach is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of fruit pieces, and the two characteristics are:
- strawberry or not a strawberry
- on the 1st layer or on the 2nd layer

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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