• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote Quant Question from Princeton Mock: tagged by: Mrrinali This topic has 1 expert reply and 1 member reply Quant Question from Princeton Mock: Hey Guys, Have posted the question, answer and solution to this DS Quant Question. I need a clarification - in light of the solution, shouldn't the answer be C and not B considering in evaluating statement (2), information from the statement (1) has been used? Would be really grateful if someone could help on this. Thank You in advance! ----------------------------------------------- Byrne and some of his friends go out to dinner and spend$111, excluding tax and tip. If the group included both men and women, how many men were in the group?

(1) There are a total of five people at the table, including Byrne.

(2) The women order meals that cost an average of $19 and the men order meals that cost and average of$27.

Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. Correct Answer
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.

Question Explanation
This is a Value Data Sufficiency question, so use the Pieces of the Puzzle approach to assess the question. Start by determining "What is known" from the question stem and "What is needed" from the statements to answer the question. Determine "What is known" from the question stem. The question stem states that the men and women together spend $111. Thus, if m represents the number of men, x represents the average amount spent by each man, w represents the number of women, and y represents the average amount spent by each woman, then together they spend x(m) + y(w) =$111. Now, determine "What is needed". To find the number of men, or m, the statements must provide the total number of people and the total number of women, or the average spent by each gender if such values lead to only one integer solution for the number of men. Evaluate the statements one at a time.

Evaluate Statement (1). It states there are a total of five people. Thus, m + w = 5. However, this statement does not provide the number of men or the number of women, Therefore, Statement (1) is insufficient. So, write down BCE.

Now, evaluate Statement (2). It states that each woman spends an average of $19 and each man spends an average of$27. Therefore, the equation indicated by the question stem is now 27(m) + 19(w) = 111. Because m represents the number of men and w represents the number of women and m and w must be integers, Plug In to determine whether there is one integer solution to the equation. The only possible values of m are 1, 2, 3, or 4. If m is 1, 3, or 4, then w is not an integer. If m = 2, then 27(2) + 19(w) = 111 which results in 54 + 19(w) = 111 or 19(w) = 57 and w = 3, which is an integer. Thus, there are 2 men in the group. Since Statement (2) provides one specific answer to the question, which is 2, the statement is sufficient. Eliminate choices C and E. The correct answer is choice B.

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10106 messages
Followed by:
494 members
2867
GMAT Score:
800
Hi Mrrinali,

To start, you would likely receive more of a response if you posted your questions in the specific forum for that category. For example, the DS forum is here:

https://www.beatthegmat.com/data-sufficiency-f7.html

We're told that Byrne and some of his friends (men and women) go out to dinner and spend $111, excluding tax and tip. We're asked for the number of men in the group. 1) There are a total of five people at the table, including Byrne. Fact 1 tells us that there are 5 total people, but we have no way of knowing how many of them are men. Fact 1 is INSUFFICIENT 2) The women order meals that cost an average of$19 and the men order meals that cost and average of $27. With a total of$111, there can't be that many ways to get to that total with meals that average either $19 each or$27 each. Since 6($19) =$114 and 5($27) =$135 - and both of those total are GREATER than $111, we know that there can be no more than 5 total meals purchased. How many different options actually add up to$111 though? You could use some brute-force Arithmetic to try out the various options, but you can also use the Units Digits to your advantage.

$111 has a unit's digit of 1 Multiples of the$19 meals: 19, 38, 57, 76, 95
Multiples of the $27 meals: 27, 54, 81, 108 Adding together a number from each row, how many options end up with a unit's digit of 1 (and a total of$111)? Only $57 +$54, so there MUST have been 3 women and 2 men in the group.
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

Junior | Next Rank: 30 Posts
Joined
19 Jun 2018
Posted:
17 messages
Thanks a lot Rich

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

Top First Responders*

1 GMATGuruNY 58 first replies
2 Jay@ManhattanReview 53 first replies
3 Brent@GMATPrepNow 47 first replies
4 Ian Stewart 23 first replies
5 ceilidh.erickson 12 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

188 posts
2 fskilnik@GMATH

GMATH Teacher

154 posts
3 Max@Math Revolution

Math Revolution

91 posts
4 GMATGuruNY

The Princeton Review Teacher

83 posts
5 Brent@GMATPrepNow

GMAT Prep Now Teacher

76 posts
See More Top Beat The GMAT Experts