ktrout2020 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

Source: Economist GMAT Tutor

So, given the distribution of stocks, let's say

Percentage of ONLY Hatsopoulos stocks = H = 15;
Percentage of ONLY McQuarrie stocks = M = 40;

Percentage of Hatsopoulos & McQuarrie stocks = B

Thus, H + B = 35 => 15 + B = 35 => B = 20 (given)

Thus, the percentage of McQuarrie stocks = M + B = 40 + 20 = 60

Thus, the percent of the portfolios managed by C.B.C. do NOT hold McQuarrie stocks = 100 - 60 = 40%

The correct answer: C

Hope this helps!

-Jay
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ktrout2020 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

Source: Economist GMAT Tutor

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:


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:


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:


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


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

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: 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/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- 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/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- 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.gmatprepnow.com/module/gmat- ... /video/943
- 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://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

ktrout2020 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

Source: Economist GMAT Tutor

We can use the formula:

Total = H only + Q only + Both + Neither

100 = 15 + 40 + (35 - 15) + Neither

100 = 75 + Neither

25 = Neither

Since the percent of the portfolios that do not hold McQuarrie stocks is equal to "H only" plus "Neither," we see that 15 + 25 = 40 percent of the portfolios do not hold McQuarrie stocks.

Answer: C