Byrne and some of his friends go out to dinner and spend $111, excluding tax and tip. If the group included both men and

[BTGModeratorVI]

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.

Answer: B
Source: Princeton Review

[Brent@GMATPrepNow]

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.

Answer: B
Source: Princeton Review

Given: Byrne and some of his friends go out to dinner and spend $111, excluding tax and tip.

Target question: How many men were in the group?

Statement 1: There are a total of five people at the table, including Byrne.
No idea how many of these 5 people are men.
Statement 1 is NOT SUFFICIENT

Statement 2: The women order meals that cost an average of $19 and the men order meals that cost an average of $27.
Let M = # of men in the group
Let W = # of women in the group
Since the total cost is $111, we can write: 19W + 27M = 111
Since W and M must be POSITIVE INTEGERS, we can see that there aren't many possible solutions to the red equation above.
Since we're told there's at least 1 woman, let's start there.

If W = 1, we get: 19(1) + 27M = 111
Simplify: 27M = 92
So, M = 92/27, which does NOT simplify to be a POSITIVE INTEGER.
So, it cannot be the case that there is 1 woman

If W = 2, we get: 19(2) + 27M = 111
Simplify: 27M = 73
So, M = 73/27, which does NOT simplify to be a POSITIVE INTEGER.
So, it cannot be the case that there are 2 women

If W = 3, we get: 19(3) + 27M = 111
Simplify: 27M = 73
So, M = 54/27 = 2
So, it's POSSIBLE that the group has 3 women and 2 men

If W = 4, we get: 19(4) + 27M = 111
Simplify: 27M = 35
So, M = 35/27, which does NOT simplify to be a POSITIVE INTEGER.
So, it cannot be the case that there are 4 women

If W = 5, we get: 19(5) + 27M = 111
Simplify: 27M = 16
So, M = 16/27, which does NOT simplify to be a POSITIVE INTEGER.
So, it cannot be the case that there are 5 women

If W = 6, we get: 19(6) + 27M = 111
Simplify: 27M = -3
At this point, we can STOP, since all integer values of W greater than 5 will result in a negative number of men (which is impossible).

Since there was only ONE CASE in which W and M are POSITIVE INTEGERS, we can be certain that the answer to the target question is there are 2 men in the group
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

[deloitte247]

Given that Byrne and his friends spent $111 on dinner excluding tax and tip.
Question => how many men were in the group?
Let the number of men = M
Let the number of women = W
Find M

Statement 1 => There are a total of five people at the table including Byrne
Therefore, Byrne and his friends = 5 people
5 people which consists of both men and women spent $111 on dinner, the number of men or women from this 5 friends is unknown so the target question cannot be answered and statement 1 is NOT SUFFICIENT

Statement 2=> The women order meals that cost an average of $19 and the men order meals that cost an average of $27
If 1 man spent $27, then M men spent $27M
If 1 woman spent $19, then women spent $19W
19W + 27M = 111
The value of W and M has to be a whole number, positive integers and at least 1 because we are dealing with human head-count and they cannot be 0 due to their average cost. So, by using trial and error;
If W = 1 then 19 (1) + 27M = 111 ; M = 92/27
If W = 2 then 19 (2) + 27M = 111 ; M = 73/27
If W = 3 then 19 (3) + 27M = 111 ; M = 54/27 = 2
If W = 4 then 19 (4) + 27M = 111 ; M = 35/27
If W = 5 then 19 (5) + 27M = 111 ; M = 16/27
If W = 6 then 19 (6) + 27M = 111 ; M = -3/27 = -1/9
$$When\ W\ge6,$$
The value of M become negative and the only case that satisfies the value of M is when W = 3 then M = 2, hence number of men = 2
Statement 2 alone is SUFFICIENT
Answer = B