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

Redeem

Unemployed

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Apr 26, 2014 10:53 am
Thanked: 16 times
Followed by:4 members
GMAT Score:780

by 800_or_bust » Thu May 12, 2016 4:42 am
eitijan wrote:OA B
(1) is insufficient because it tells us nothing about the employment status of those persons over the age of 65.

(2) is sufficient because if 10 percent of women and 20 percent of men over the age of 65 are employed, then it must be the case that at least 10 percent of the overall population of those over the age of 65. As a mathematical proof, consider these equations where W = number of women & M = number of men.

Then, the total population, P = W + M. The number of employed women is 0.1W and the number of employed men is 0.2M. We need to prove that the sum of these two quantities is greater than or equal to 0.1(W + M).

0.1W + 0.2M > 0.1(W + M)

To prove this factor out 0.1 from the left side of the equation...

0.1(W + 2M) > 0.1(W + M)

Then divide both sides by 0.1...

W + 2M > W + M

This statement must be true because both W and M must be positive integers, since we are dealing with people. Note that neither W nor M can be zero, because otherwise it would have been impossible to calculate the percentages given.
800 or bust!
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 » Thu May 12, 2016 9:40 am
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

1) In Country X, 11.3 percent of the population is 65 years old or older.

2) In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed
Let's use the term seniors, to refer to those who are 65 years old or older.

Target question: Are at least 10 percent of Country X's seniors employed?

Statement 1: In Country X, 11.3 percent of the population is 65 years old or older.
Okay, so we know that a certain percent of the population are seniors, but we aren't told anything about their employment rates.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Among Country X's seniors, 20 percent of the men and 10 percent of the women are employed
To get a feel for what this tells us, let's examine the two EXTREMES:
Extreme #1 - among the seniors, there are ZERO women. This means all of the seniors are men, which means 20% of the seniors are employed
Extreme #2 - among the seniors, there are ZERO men. This means all of the seniors are women, which means 10% of the seniors are employed
Now that we have examined the extremes, we have a range of values that represent the employment rate among Country X's seniors.
We can conclude: 10% < senior employment rate < 20%
In other words, at least 10 percent of Country X's seniors are employed
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

By the way, this concept (and others) is covered in our video on weighted averages: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu May 12, 2016 10:08 am
Hi eitijan,

While this IS a weighted average question, you don't actually have to do ANY calculations to solve it. In that way, it's a great "concept" question - if you recognize (and understand) the concept, then you can quickly answer the question (you do have to pay careful attention to all of the details though).

We're asked if AT LEAST 10% of the people who are 65 or older are employed. This is a YES/NO question.

Fact 1: 11.3% of the population is 65 or older.

This tells us NOTHING about whether these people are employed or not.
If 100% of them are employed, then the answer is YES.
If 0% of them are employed, then the answer is NO.
Fact 1 is INSUFFICIENT

Fact 2: Of those 65 years or older, 20% of the men and 10% of the women are employed.

Take a moment to think about the question that was asked. Are AT LEAST 10% of the people aged 65 or older employed? From this Fact, we know that there are some men and some women in this group. With 20% of the men and 10% of the women from this group employed, the weighted average MUST be between 10% and 20%, which means that the answer to the question is ALWAYS YES. The group is AT LEAST 10% employed; you don't have to do any math to prove it.
Fact 2 is SUFFICIENT.

Final Answer: B

It's worth noting that most DS questions require a lot more work than this question required, so you won't be able to "talk" your way past too many of them. If you really know your math rules/concepts/patterns though, you will be able to answer a few DS prompts on Test Day with a minimal amount of work.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1