BTGModeratorVI wrote: ↑Sun Apr 05, 2020 9:11 am
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
