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Finding this hard to Understand--Please help!!!

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Finding this hard to Understand--Please help!!!

by dddanny2006 » Wed Aug 14, 2013 2:11 pm
A souvenir shop made $2,400 in revenue selling Large and small Postcards .The large postcard costs twice as much as the small postcards,and the souvenir sold 950 large postcards, and it sold nothing besides the two sizes, then how many small postcards did it sell?

(1) A large postcard costs $2.
(2) If the cart had sold 20% fewer postcards, its revenue would have been reduced by 4 1/6%.



I do understand (1)


But when it comes to (2) I fail to understand.


From statement 2-- Number of large cards equals 950. Let S be number of small cards,and x be the price of the small card,2x price of the large card
So we have the equation
950(2x)+(0.8)S(x)=2300

There is no way one can find out the value of S without knowing the price x.

Please explain why the answer is D.


Thanks alot.
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by [email protected] » Wed Aug 14, 2013 4:54 pm
Hi dddanny2006,

The DS question is built around a "system" of equations. By knowing the rules of "system math", you can sometimes avoid the calculations and still come up with the correct answer.

**Based on what you wrote below the question, in the original question, does Fact 2 state it was 20% fewer SMALL postcards sold? If so, then this becomes even easier to solve.**

Based on the prompt, we have this equation (I've combined the two equations that we would form into one big equation and I've used the variables that you used):

950(2x) + S(x) = 2400

Here we have 2 variables, but only one equation. Since the prompt asks us to solve for S, we need one more unique equation that includes x, S or both.

Fact 1 tells us that 2x = 2, so with the value of x, we can plug in and solve for S.
We'd get:
950(2) + S(1) = 2400
S = 500
Fact 1 is SUFFICIENT

Fact 2 would give us the equation that you wrote:
950(2x) + .8S(x) = 2300

Since the 20% drop = $100 of lost revenue, we have this:
.2S(x) = 100
S(x) = 500

Now, plug THAT back into the original equation. You'd have:
950(2x) + 500 = 2400

Solve for x. You'll get x = 1, which you can plug in and get S = 500
Fact 2 is SUFFICIENT

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by ganeshrkamath » Thu Aug 15, 2013 8:34 pm
dddanny2006 wrote:A souvenir shop made $2,400 in revenue selling Large and small Postcards .The large postcard costs twice as much as the small postcards,and the souvenir sold 950 large postcards, and it sold nothing besides the two sizes, then how many small postcards did it sell?

(1) A large postcard costs $2.
(2) If the cart had sold 20% fewer postcards, its revenue would have been reduced by 4 1/6%.
Let P be the price of a small postcard,
S be the number of small postcards,
and L be the number of large postcards.

Given:
2PL + PS = 2400
L = 950
1900P + PS = 2400
P (1900 + S) = 2400 ________________ (1)

To find: S

Statement 1: 2P = 2
P = 1
This is sufficient to calculate S from (1).

Statement 2:
S' + L' = 0.8(S + L)
100 - 4 1/6 = 95.833
0.95833 * 2400 = 2PL' + PS'
There is no way to calculate P' and S' from this information. So we cannot calculate S from this statement.
Hence, this is insufficient.

Choose A
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by ganeshrkamath » Thu Aug 15, 2013 8:37 pm
dddanny2006 wrote:From statement 2-- Number of large cards equals 950. Let S be number of small cards,and x be the price of the small card,2x price of the large card
So we have the equation
950(2x)+(0.8)S(x)=2300
Why did you assume in statement 2 that it's only the small cards which are reduced by 80% in number?
The statement just says "20% fewer postcards". This means it's the total number of cards, right?
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by lunarpower » Sat Aug 17, 2013 5:19 am
ganeshrkamath wrote:The statement just says "20% fewer postcards". This means it's the total number of cards, right?
Right.

So, the question was probably transcribed incorrectly at some point (perhaps in the original source... yikes!)
It's most likely supposed to say "small" in front of "postcards" in that statement.
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