QUESTION :
At a farmers market, a florist sells only roses, and customers can buy in 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.
ANSWER:
METHOD 1-LONG CUT !
We can let the number of individual roses sold = r and the number of bouquets sold = b. We need to determine the number of roses sold.
Statement One Alone:
The florist made $190.
We can create the following equation:
2r + 19b = 190
2r = 190 – 19b
2r = 19(10 – b)
r = [19(10 – b)]/2
Since r must be an integer, 19(10 – b) must be a multiple of 2. Since 19 is NOT a multiple of 2, 10 – b must be a multiple of 2. Thus b could equal 0, 2, 4, 6, 8, or 10. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
The florist sold at least 95 roses.
The information in statement two is not sufficient to determine how many total roses were sold. We can eliminate answer choice B.
Statements One and Two Together:
Using the information in statements one and two, we know that:
If b = 2, then r = 76, and thus a total of (2 x 12) + 76 = 100 roses were sold.
Or
If b = 4, then r = 57, and thus a total of (4 x 12) + 57 = 105 roses were sold.
Since we see that either 100 or 105 roses could have been sold, the statements together are not sufficient to answer the question.
METHOD 2- SHORT CUT !
S1: if the florist made $190, it’s possible he sold 95 individual roses for $2 each. It’s also possible that he sold 10 bouquets for $19 each. At a dozen roses per bouquet, he’d have sold 10*12 = 120 roses. Because we don’t have a unique value for the number of roses sold, this statement is not sufficient alone.
S2: Clearly not sufficient on its own. He could have sold 95 roses or 96, etc.
Together: We can use the same cases we used in S1. He may have sold 95 roses individually. Or he may have sold 10 bouquets for a total of 120 roses. Together the statements are not sufficient.
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