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# Nancy purchased a consignment of c red roses at a cost of d

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Nancy purchased a consignment of c red roses at a cost of d [#permalink]  16 May 2019, 16:29
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Nancy purchased a consignment of c red roses at a cost of d dollars. She made bouquets with the roses and each bouquet contained d roses. She sold each bouquet at a price of c dollars. Overall, she made a profit.

 Quantity A Quantity B c d

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: Nancy purchased a consignment of c red roses at a cost of d [#permalink]  14 Jan 2020, 06:39
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Let's Calculate Cost of Each Bouquet
c red roses at a cost of d dollars
=> Cost of 1 Rose = d/c dollars
=> Cost of 1 bouquet = d roses = d * d/c dollars = $$\frac{ d^2}{c}$$ dollars
=> Selling Price of 1 bouquet = c dollars and she made a profit => Selling price > Cost price
c > $$\frac{ d^2}{c}$$
As c is positive so we can cross multiply both sides by c and we get
$$c^2 > d^2$$
As, both d and c are positive so we can take square root on both the sides and we will get
c > d
So, Quantity A is greater than Quantity B
Hope it helps!
Carcass wrote:
Nancy purchased a consignment of c red roses at a cost of d dollars. She made bouquets with the roses and each bouquet contained d roses. She sold each bouquet at a price of c dollars. Overall, she made a profit.

 Quantity A Quantity B c d

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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Re: Nancy purchased a consignment of c red roses at a cost of d   [#permalink] 14 Jan 2020, 06:39
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