Byrne and some of his friends go out to dinner and spend $111, excludi

Question

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.

soapbolt · Answer

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

BrentGMATPrepNow · Answer

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

prabsahi · Answer

Here is my approach the above problem.

Statement 1 : There are a total of five people at the table, including Byrne.

No idea how many of these 5 people are men and women.

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 the number of women be 'w' and number of men be 'm'

19w + 27m = 111

Lets try solving this expression quickly so that we can save some time here.

Now we see 111 is a multiple of 3 and 27 is also a multiple of three but 19 is not ..So 19*women we can try number of women as multiple of 3..so 3,6...
But 6 cant be the one since 19*6=114 which is greater than total number.Also max number of members is 5 so 6 is ruled out

Now if w=3 then m=6 since from quetion we know total =5

Putting w=3 in above expression gives.

19*3 +27*2 = 111((which is possible and both men and women are integers)

Therefore statement B is sufficient!!

Alternative approach.

19w = 111 - 27m
 = 3(37 - 9m)

Maximum value of m from above expression cant be greater than 4.

Also from above expression its clear that RHS is a multiple of 3 so LHS that is 19w has to be a multiple of 3

so again only possible value of w=3 so m=2  We dont need to try any other value .Since w=6 is not possible..max number of members is 5

Hope its helps!!

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