Data Sufficiency Question...HELP PLEASE!

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Data Sufficiency Question...HELP PLEASE!

by soneee » Mon Aug 05, 2013 2:56 pm
1. Every pupil in a school was given one ticket for a concert. The school was charged a total of $6000 for these tickets, all of which were of equal value. What was the price of one ticket?

If the price of each ticket had been one dollar less, the total cost would have been 1,200 less.
If the price of each ticket had been $2 more, the total bill would have increased by 40%.
A. statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
B. statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
C. both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
D. each statement alone is sufficient
E. statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
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by [email protected] » Mon Aug 05, 2013 3:39 pm
Hi soneee,

This question should have been put in the DS forum, but since it's here, I'll answer it.

The prompt tells us that a certain number of tickets worth an equal price totals $6,000. We are asked about the price of one ticket.

Based on this info, I'm going to call the variables:
T = number of tickets
P = price of one ticket

So, we have TP = 6,000

Fact 1 tells us that if the price dropped 1 dollar, the total of all tickets would be 1200 less
This can be written as:

(T)(P-1) = 4800

Combined with the info we had before:
TP = 6000

We have a "system" (2 variables with 2 unique equations).
This Fact is SUFFICIENT because we can solve the system using algebra and there would be only one answer (T=1200, S=5, if you're curious)

Fact 2 tells us if the price increased by $2, the total would be 40% higher.
This can be written as:
T(P+2) = (1.4)(6,000)
T(P+2) = 8400

Combined with the original info:
TP = 6000

We have another system, so this too is SUFFICIENT.

Final Answer:D

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