either 16-pound or 40-pound boxes

[sanju09]

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



https://www.urch.com/forums/gmat-problem-solving

[srcc25anu]

let no of 16-pound box be X
let no of 40-pound box be Y

we have the equation 16X + 40Y <1200

maximum no of 40-pound boxes should be less than 30 as 30*40 = 1200
hence next best option <30 = 25 therefore B

[fitzgerald23]

Let the 16 lb boxes = x
Let the 40 lb boxes = 50-x

16x + 40(50-x)<1200
16x + 2000 -40x<1200
-24x<-800
x>33.3

You cant have a fraction of a box so the minimum for x = 34. So you have 34 of the 16 pound boxes and 16 of the 40 pound boxes. Answer D.

[Night reader]

given - Let's call the number of 16-pound box=Y and 40-pound box=X. Then X+Y=50 and 16Y+40X<1,200. Find the greatest possible X-?

solution: Y=50-X; 16(50-X)+40X<1,200
24X<400, X<16.67 Amongst all answer choices the greatest possible number after 16.67 is 16

While we can have the fraction of the box even (this would simply mean +1 box) we are under two cut-offs: weight less 1,200 and the greatest possible number after all. Choice E is also < 1,200 BUT is not the greatest possible number.

answer D.

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



https://www.urch.com/forums/gmat-problem-solving

[GMATGuruNY]

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

https://www.urch.com/forums/gmat-problem-solving

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.