sanju09 wrote:Grain is sold in either 16-pound or 40-pound boxes. If 50 boxes of grain were sold and the total weight of the grain sold was less than 1200 pounds, what is the greatest possible number of 40-pound boxes that could have been sold?
(A) 33
(B) 25
(C) 17
(D) 16
(E) 15
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We can plug in the answer choices, which represent the number of 40-pound boxes sold.
Average weight per box < 1200/50 < 24.
Since 24 is closer to 16 than to 40, more than half of the boxes sold must have been 16-pound boxes.
Thus, fewer than 1/2*50 = 25 of the boxes sold must have been 40-pound boxes.
Eliminate A and B.
Answer choice C: 17 40-pound boxes sold, 33 16-pound boxes sold
Total weight = 17*40 + 33*16 = 680 + 528 = 1208. Just a little too big.
Eliminate C.
Since 17 40-pound boxes results in a total weight just over 1200, the greatest number of 40-pound boxes that could have been sold = 17-1 = 16.
The correct answer is
D.
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