Data Sufficiency

The attendees at a certain convention purchased a total of 15,000 books. How many of these attendees were female?

1. There was a total of 4, 000 attendees at the convention.

2. The male attendees purchased an average (arithmetic mean) of 3 books each, and the females purchased an average of 5 books each.

I would appreciate it if someone could walk me through this problem. Thanks.

tonebeeze wrote:The attendees at a certain convention purchased a total of 15,000 books. How many of these attendees were female?

1. There was a total of 4, 000 attendees at the convention.

2. The male attendees purchased an average (arithmetic mean) of 3 books each, and the females purchased an average of 5 books each.

I would appreciate it if someone could walk me through this problem. Thanks.

x -> men
y-> women
Total books sold = 15000
y = ?

Statement 1 :
x+y = 4000

Insufficient

Statement 2:
3x+5y = 15000 -> Insufficient

Combining 1 and 2 :

Two independent equations in x and y, hence sufficient.

C

I don't understand why this is unsolvable. Help me to understand. What is wrong with this logic:

x + y = 4,000
3x + 5y = 15,000

Multiply the first equation by (-3) and you get: -3x - 3y = -12,000

Now combine the equations:

-3x - 3y = -12,000
3x + 5y = 15,000
2y = 3,000
y = 1,500

Women in attendance: 1,500..... Men in attendance: 2,500

Check the solution with information in the original question:

4,000 total attendees, 15,000 books were sold, women each bought 5 books on average, men bought 3 books on average:

1,500 women x 5 books per woman = 7,500 books sold
2,500 men x 3 books per man = 7,500 books sold

Total attendees: 4,000...... total books sold: 15,000

The equation seems solved..... where am I going wrong?

Thx,

Brian

Where are you seeing that it is unsolvable? I agree that it should be C, though I used a different method to get there.