BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

either 16-pound or 40-pound boxes

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

either 16-pound or 40-pound boxes

by sanju09 » Thu Mar 24, 2011 3:58 am
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
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 423
Joined: Fri Jun 11, 2010 7:59 am
Location: Seattle, WA
Thanked: 86 times
Followed by:2 members

by srcc25anu » Thu Mar 24, 2011 4:02 am
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
Top
Master | Next Rank: 500 Posts
Posts: 219
Joined: Mon Mar 08, 2010 8:51 pm
Thanked: 62 times
Followed by:5 members
GMAT Score:750

by fitzgerald23 » Thu Mar 24, 2011 9:58 am
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.
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Thu Mar 24, 2011 10:47 am
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.
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



https://www.urch.com/forums/gmat-problem-solving
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Mar 24, 2011 11:21 am
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

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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1