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28 Sep 2021, 07:09
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B
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Difficulty:
15%
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Question Stats:
85% (02:20) correct
15%
(02:36)
wrong
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A box contains 70 marbles. Some marbles are big, and the rest are small. Each marble is either blue or yellow. The number of large blue marbles is the same as the number of small yellow marbles. If there are 20 blue marbles, how many small marbles are there?
A) 10
B) 20
C) 30
D) 40
E) 50
A) 10
B) 20
C) 30
D) 40
E) 50
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28 Sep 2021, 07:54
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BrentGMATPrepNow
Another approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of marbles, and the two characteristics are:
- large or small
- blue or yellow
Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.
We can set up our matrix as follows:
Since the number of large blue marbles is the same as the number of small yellow marbles, let's let both quantities = x
Next, since the two boxes in the left column must add to 20, we can see that 20-x = the number of small blue marbles
Finally, since the sum of two boxes in the bottom row equals the total number of small boxes we can write:
Number of small boxes = (20 - x) + x = 20
Answer: B
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 this video:
EXTRA PRACTICE QUESTION
