Data Sufficiency

AAPL wrote:Veritas Prep

At a farmers market, a florist sells only roses, and customers can buy into two quantities: individual roses sell for $2 each and bouquets of one dozen roses sell for $19. How many roses did the florist sell?

1) The florist made $190.
2) The florist sold at least 95 roses.

OA E

Say he sold x numbers of individual roses and y numbers of bouquets of one dozen roses.

Thus, the total number of roses sold = x + 12y.

Given: Total sales = 2x + 19y

We have to get the value of x + 12y.

Let's take each statement one by one.

1) The florist made $190.

2x + 19y = 190.

x = (190 - 19y)/2
x = 19(10 - y)/2

y can have any value from 2, 4, 6, and 8; thus, accordingly, x will have respective values. No unique value of x + 12y. Insufficient.

2) The florist sold at least 95 roses.

Certainly insufficient.

(1) and (2) together

From x = 19(10 - y)/2:

@y = 2, we have x = 19(10 - 2)/2 = 76; thus, x + 12y = 76 + 12*2 = 76 + 24 = 100 ≥ 95. The number roses sold can be 100.

@y = 4, we have x = 19(10 - 4)/2 = 57; thus, x + 12y = 57 + 12*4 = 57 + 48 = 105 ≥ 95. The number roses sold can be 105.

No unique value of x + 12y. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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