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Quant Question from Princeton Mock:

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Quant Question from Princeton Mock:

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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!

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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.
Statements (1) and (2) TOGETHER are NOT sufficient. Your Answer

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.

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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

Final Answer: B

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

_________________
Contact Rich at Rich.C@empowergmat.com

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Junior | Next Rank: 30 Posts Default Avatar
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Thanks a lot Rich Smile

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