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In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates. (2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

Practice Questions Question: 44 Page: 278 Difficulty: 600

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates. Say the number of college graduates is \(x\), then the number of not college graduates is \(3x\). Thus, \(x+3x=80\). We can find \(x\). Sufficient.

(2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates. Say the number of college graduates is \(x\), then the number of not college graduates is \(x+(x+40)\). Thus, \(x+(x+40)=80\). We can find \(x\). Sufficient.

Re: In a random sample of 80 adults, how many are college [#permalink]

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18 Sep 2012, 06:39

Bunuel wrote:

In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates. (2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

Since there are 80 adults we don't need to consider non-adults number here. Otherwise, we would have to solve this by 2X2 matrix. Either adults are college graduates (X) or not (Y) Stmt 1) X + Y = 80 Y = 3X these 2 eq can be solved to get the value of X

Stmt 2) Similar way X + Y = 80 Y = 40 + X these 2 eqns can also be solved for value of X

Both statements are sufficient, Hence D
_________________

In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates. (2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

Practice Questions Question: 44 Page: 278 Difficulty: 600

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Lets say college going graduate is X and college not going graduate is Y

form question X + Y = 80. Option 1: Y = 3X so, X + 3X = 80 leads to X = 20. Therefore option 1 is sufficient to answer the question. Option 2: Y - X = 40. so, 2Y = 120, leads to Y = 60 and X = 20. therefore option 2 is sufficient to anser the question.

Therefor from above both the options are individually sufficient to answer the question => "D" is the correct choice.

In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates. Say the number of college graduates is \(x\), then the number of not college graduates is \(3x\). Thus, \(x+3x=80\). We can find \(x\). Sufficient.

(2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates. Say the number of college graduates is \(x\), then the number of not college graduates is \(x+(x+40)\). Thus, \(x+(x+40)=80\). We can find \(x\). Sufficient.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________

In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates. (2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

Practice Questions Question: 44 Page: 278 Difficulty: 600

Basically, we need to solve for x + y = 80, so we need to solve for 2 unknowns, either by solving for one of them or for both at the same time.

1) This statement tells us that x + 3x = 80, we have one equation and one unknown, so it's sufficient. 2) This tells us that (y + 40) + y = 80, so again we have 1 unknown and 1 equation, so we can solve it. Sufficient.

In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates. (2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

We need to determine the number of college graduates in a sample of 80 adults. Because some of the 80 adults are college graduates, while others are not, let’s define two variables:

c = the number of adults who are college graduates

n = the number of adults who are not college graduates

Since there are 80 adults in the random sample, we can create the following equation:

c + n = 80

Statement One Alone:

In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates.

From statement one we can say:

n = 3c

Since n = 3c, we can plug 3c for n into the equation c + n = 80.

c + 3c = 80

4c = 80

c = 20

Thus, there are 20 college graduates. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

From statement two, we can say:

n = 40 + c

Since 40 + c = n, we can substitute 40 + c for n into the equation c + n = 80.

c + 40 + c = 80

2c = 40

c = 20

There are 20 college graduates.

Statement two is also sufficient to answer the question.

The answer is D.
_________________

Scott Woodbury-Stewart Founder and CEO

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