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Thirty five percent of the portfolios managed by the Crocodile Brokers

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Thirty five percent of the portfolios managed by the Crocodile Brokers  [#permalink]

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New post 23 Oct 2016, 09:24
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Difficulty:

  55% (hard)

Question Stats:

62% (02:12) correct 38% (02:39) wrong based on 154 sessions

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Thirty five percent of the portfolios managed by the Crocodile Brokers company (C.B.C.) hold Hatsopoulos stocks. Forty percent of the portfolios managed by C.B.C. hold McQuarrie stocks and do not hold Hatsopoulos stocks. Fifteen percent of the portfolios managed by C.B.C. hold Hatsopoulos stocks and do not hold McQuarrie stocks. What percent of the portfolios managed by C.B.C. do NOT hold McQuarrie stocks?

A. 20
B. 25
C. 40
D. 60
E. 65

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Re: Thirty five percent of the portfolios managed by the Crocodile Brokers  [#permalink]

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New post 23 Oct 2016, 18:46
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This can be approached using Venn diagram.

H represent those portfolios holding Hatsopoulos stocks
M represent those portfolios holding McQuarrie stocks

35% hold H => \(z+x = 35\)
40% hold M and do not hold H => y = 40
15% hold H and not M => z = 15
We have , x = 20
\(x+y+z = 20 + 40 + 15 = 75\)
There are 25% portfolios holding neither H nor M.

Portfolios that do not hold M = \(z + (neither H nor M)\)
= \(15 + 25\)
= 40
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Re: Thirty five percent of the portfolios managed by the Crocodile Brokers  [#permalink]

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New post 24 Oct 2018, 15:52
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Bunuel wrote:
Thirty five percent of the portfolios managed by the Crocodile Brokers company (C.B.C.) hold Hatsopoulos stocks. Forty percent of the portfolios managed by C.B.C. hold McQuarrie stocks and do not hold Hatsopoulos stocks. Fifteen percent of the portfolios managed by C.B.C. hold Hatsopoulos stocks and do not hold McQuarrie stocks. What percent of the portfolios managed by C.B.C. do NOT hold McQuarrie stocks?

A. 20
B. 25
C. 40
D. 60
E. 65


We can use an approach 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 portfolios, and the two characteristics are:
- hold Hatsopoulos stocks or do not hold Hatsopoulos stocks
- hold McQuarrie stocks or do not hold McQuarrie stocks

Since we're looking for a PERCENTAGE, let's say there are 100 portfolios in TOTAL.

We get:
Image

Thirty five percent of the portfolios hold Hatsopoulos stocks.
So, 35 portfolios hold Hatsopoulos stocks
Also, if 35 of the 100 portfolios hold Hatsopoulos stocks, then the remaining 65 portfolios DO NOT hold Hatsopoulos stocks.
Add this to our matrix:
Image

Forty percent of the portfolios hold McQuarrie stocks and do not hold Hatsopoulos stocks. Fifteen percent of the portfolios hold Hatsopoulos stocks and do not hold McQuarrie stocks.
Add this to diagram:
Image

At this point, we know that the bottom-right box must have 25 portfolios (since the two bottom boxes must add to 65)
Image

What percent of the portfolios do NOT hold McQuarrie stocks?
When we add the two right-hand boxes, we get a sum of 40
Image
This means 40 of the 100 portfolios do NOT hold McQuarrie stocks

40/100 = 40%

Answer: C

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:


1 practice question:

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Re: Thirty five percent of the portfolios managed by the Crocodile Brokers   [#permalink] 24 Oct 2018, 15:52
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Thirty five percent of the portfolios managed by the Crocodile Brokers

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