BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Overlapping Sets - Manahattan Word Problems

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Sun May 24, 2015 11:50 pm
Followed by:1 members

Overlapping Sets - Manahattan Word Problems

by [email protected] » Mon Jun 15, 2015 4:52 am
10% of all aliens are capable of intelligent thought and have more than 3 arms, and 75% of aliens with 3 arms or less are capable of intelligent thought. If 40% of all aliens are capable of intelligent thought, what percent of aliens have more than 3 arms?

-- Ans: 60%
Solution: I solved this problem using the Double Set Matrix. I am unable to figure out how the percent of aliens with 3 arms is 60%. Solving for x(number of aliens with 3 arms or more)=40. Shouldn't the number of aliens with more than 3 arms be 40%?
Top
Source: — Problem Solving |
User avatar
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Thu Mar 05, 2015 12:01 pm
Location: Boston, MA
Thanked: 10 times
Followed by:3 members
GMAT Score:770

by Spencer@Prep4GMAT » Mon Jun 15, 2015 6:33 am
Great question, [email protected]!

I think you took the right approach, and I also imagine the trickiness in this question has to do with the way it's worded:
Fact #1: "10% of all aliens are capable of intelligent thought and have more than 3 arms."
Fact #2: "75% of aliens with 3 arms or less are capable of intelligent thought."
The first statement gives a percentage of all aliens, while the second gives a percentage of just one group.

Solution:
To make things simple, let's say there are 100 total aliens. We'll split them into two groups:
More than 3 arms: x, the number we're looking for
3 or fewer arms: 100 - x

Fact #1 told us that 10% of all 100 aliens, or 10 aliens, are intelligent and have 3+ arms.
Fact #2 told us that 75% of the 100 - x aliens with 3 or fewer arms are intelligent. That's 0.75(100 - x) = 75 - 0.75x.
If we add these two together, we should have the total number of intelligent aliens, which is 40% of the 100, or 40. So, we have the equation:
10 + 75 - 0.75x = 40
45 = 0.75x
180 = 3x
x = 60

Thus, 60/100 = 60% of aliens have more than 3 arms.
Ready4
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Jun 15, 2015 6:37 am
10% of all aliens cuckoos are capable of intelligent thought and have more than 3 arms, and 75% of aliens cuckoos with three arms or less are capable of intelligent thought.If 40% of all alien cuckoos are capable of intelligent thought , what percent of alien cuckoos have more than 3 arms?
This is an EITHER/OR group question.
Every alien is EITHER intelligent OR not.
Every alien EITHER has more then 3 arms Christmas OR 3 arms or less.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

Let I = intelligent, NI = not intelligent, >3 = more than 3 arms, ≤3 = 3 arms or less.
Here's the grid, with 100 plugged in for the total:
Image

Now let's use the information in the problem to complete the grid step by step.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.

40% of all alien cuckoos are capable of intelligent thought.
10% of all alien cuckoos BOTH are capable of intelligent thought AND have more than 3 arms.
The following grid is yielded:
Image

75% of alien cuckoos with three arms or less are capable of intelligent thought.
According to the grid, 30 aliens with 3 arms or less are also intelligent.
These 30 aliens constitute 75% of the total number of aliens with 3 arms or less.
Since 30 is 75% of 40, the total number of aliens with 3 arms or less = 40.
The following grid is yielded:
Image

Now we can answer the question:
Percentage with more than 3 arms = [spoiler]60%[/spoiler].
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 15, 2015 7:00 am
Mitch's "group grid" approach (aka Double Matrix Method) can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of aliens, and the two characteristics are:
- capable of intelligent thought or not capable of intelligent thought
- more than 3 arms or 3 arms or less

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/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.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
Image
Top
Post new topic Post Reply
• Page 1 of 1