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Convention Attendees

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Convention Attendees

by tonebeeze » Sun Jan 02, 2011 9:05 pm
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.
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Source: — Data Sufficiency |
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by anshumishra » Sun Jan 02, 2011 9:11 pm
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
Thanks
Anshu

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by brian91480 » Mon Feb 24, 2014 7:58 pm
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
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by Bill@VeritasPrep » Mon Feb 24, 2014 8:35 pm
Where are you seeing that it is unsolvable? I agree that it should be C, though I used a different method to get there.
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by [email protected] » Mon Feb 24, 2014 9:11 pm
Hi brian91480,

Every DS question has at least 1 solution. The information in the two Facts that follow the prompt can help you to narrow down the possibilities. If there's just 1 answer, then a given Fact is SUFFICIENT. If there's more than 1 (meaning "different") answers, then a given Fact is INSUFFICIENT.

Here, both Fact 1 and Fact 2, when dealt with individually, would lead to multiple answers. Thus, they're both INSUFFICIENT.

Combining Facts, as you've seen/solved, produces just 1 answer. So, the Facts are COMBINED SUFFICIENT.

Final Answer: C

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