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B
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Difficulty:
65%
(hard)
Question Stats:
58% (02:09) correct
42%
(01:52)
wrong
based on 230
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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.
(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.
16 Nov 2018, 09:45
Kudos
Bookmarks
IMHO
Answer should be B .
Let me explain.
as per the question we are given total amount spend = $111. and we are asked to find the number of men?
Statement 1 = we are given total no. of people. But from that we can't tell how many of them are men. Hence Insufficient
Statement 2 = We are given avg cost of meal for women and avg cost of meal for men
thus we can write --> 19W + 27M = 111 (where 19W is total cost of mean for women and 27M is the total cost of meal for men).
so 19W+ 27M = 111
or 19W = 111 - 27M
or 19W = 3 (37 - 9M)
Variable M can take only value from 1 to 4 and for other value we will get sum as negative which is not possible.
and only for M = 2 , Variable W is an integer ( W = 3 )
Hence Statement 2 is sufficient
Answer should be B .
Let me explain.
as per the question we are given total amount spend = $111. and we are asked to find the number of men?
Statement 1 = we are given total no. of people. But from that we can't tell how many of them are men. Hence Insufficient
Statement 2 = We are given avg cost of meal for women and avg cost of meal for men
thus we can write --> 19W + 27M = 111 (where 19W is total cost of mean for women and 27M is the total cost of meal for men).
so 19W+ 27M = 111
or 19W = 111 - 27M
or 19W = 3 (37 - 9M)
Variable M can take only value from 1 to 4 and for other value we will get sum as negative which is not possible.
and only for M = 2 , Variable W is an integer ( W = 3 )
Hence Statement 2 is sufficient
20 Jul 2019, 08:19
Kudos
Bookmarks
chand567
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
