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Data Sufficiency - Page 443 - Kaplan GMAT 2010-2011 Edition

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Data Sufficiency - Page 443 - Kaplan GMAT 2010-2011 Edition

by alivapriyada » Mon Jul 12, 2010 3:17 am
A coffee cart make $2,400 in revenue. If a large cup of coffee costs twice as much as a small cup, the cart sold 950 large cups, and it sold nothing besides the two sizes, then how many small cups of coffee did it sell?

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

Book Answer is (D). I'm not sure how statement No. 2 is sufficient.
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by 4GMAT_Mumbai » Mon Jul 12, 2010 3:56 am
Hi,

Interesting Q. Thanks !

Let Rs x be the price of a small cup and y be the quantity of small cups sold.

Then, Rs 2x is the price of a large cup.

According to the question:

2x. 950 + x . y = 2400

According to stmt 2:

2x. 950 + x * 0.8 * y = 2400 * (95 5/6 %)

From equation 1, you can get an expression for x * y.

From equation 2, you can get an expression for x * y.

When one equates the expressions obtained in the previous steps, one gets a linear equation in one unknown, x. Using this, x could be derived. Once x is derived, using the earlier equations y can also be derived.

Hence, stmt 2 is sufficient.

Hope this helps. Thanks.
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by sanju09 » Mon Jul 12, 2010 3:58 am
alivapriyada wrote:A coffee cart make $2,400 in revenue. If a large cup of coffee costs twice as much as a small cup, the cart sold 950 large cups, and it sold nothing besides the two sizes, then how many small cups of coffee did it sell?

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

Book Answer is (D). I'm not sure how statement No. 2 is sufficient.

If a small cup costs $x, then a large cup would cost $2 x, such that

950 × $2 x + number of small cups sold × $x = $2,400

Or the number of small cups sold = (2400 - 1900 x)/x.

Hence, all we need is just x, which can be obtained by the cost of a cup of either size.

(1) Sufficient.
(2) Or 20 percent of the small cups sold would cost 2400 × 25/600 = $100. In other words, $500 was the revenue from the sale of small cups that must equal (2400 - 1900 x). [spoiler]Hence, sufficient

D[/spoiler]
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by amising6 » Mon Jul 12, 2010 4:25 am
alivapriyada wrote:A coffee cart make $2,400 in revenue. If a large cup of coffee costs twice as much as a small cup, the cart sold 950 large cups, and it sold nothing besides the two sizes, then how many small cups of coffee did it sell?

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

Book Answer is (D). I'm not sure how statement No. 2 is sufficient.
given small cup cost=x
large cup cost 2x
let a be number of large cup sold
let b be number of small number of cup sold
a+b=950 ----- eq(1)
a*2x+b*x=2400 --- eq2
so basically we need to solve 4 variable so we should have 4 equation

let see statement 1)A large cup of coffee costs $2
so now we know 2x=2 so x=1
so we have two equation a+b=950
substituting value of x in eq 2 w e get 2a+b=2400 so 2 variable 2 equation thus statement 1 is sufficient

lets c statement 2)If the cart had sold 20% fewer small cups, its revenue would have been reduced by 4 1/6%.
so 20% fewer smaller up so now smaller cup sold 0.8b
large cup sold remain a
revenue decrease by 25/6 %
so new revenue 2400 - 25/6%of 2400 let say this 2000( i have assumed some random value)
so new equation will be a+0.8b=2000 ----- eq 3
s now we have 2 equation one equation 2 and eq 3
again we can solve
so statement 2 is sufficient

hence D
Ideation without execution is delusion
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