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

Redeem

Word problem - Grain sacks ordering

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 167
Joined: Fri Mar 09, 2012 8:35 pm
Thanked: 39 times
Followed by:3 members

Word problem - Grain sacks ordering

by adthedaddy » Thu Sep 24, 2015 7:41 pm
Tom has 45 bushels of wheat, 63 bushels of rice, and 18 bushels of quinoa. He wants to order sacks of a single size such that he can fill each sack completely full of one type of grain without having any extra grain left over. What is the minimum number of sacks that Tom must order?

A) 9
B) 14
C) 18
D) 21
E) 42

OA = B
"Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma - which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary" - Steve Jobs
Top
Source: — Problem Solving |
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 Sep 24, 2015 8:14 pm
adthedaddy wrote:Tom has 45 bushels of wheat, 63 bushels of rice, and 18 bushels of quinoa. He wants to order sacks of a single size such that he can fill each sack completely full of one type of grain without having any extra grain left over. What is the minimum number of sacks that Tom must order?

A) 9
B) 14
C) 18
D) 21
E) 42
Let x = the number of bushels that each sack can hold.
Since no bushels are to be left over, the value of x must divide evenly into 45, 63 and 18.
To MINIMIZE the required number of sacks, we must MAXIMIZE how many bushels each sack can hold.
In other words, we must maximize the value of x.

45 = 3*3*5.
63 = 3*3*7.
18 = 3*3*2.
The values in red indicate that the greatest possible value of x = 3*3 = 9.

If x=9, then the values in blue represent how many sacks will be required to hold each type of grain:
5 sacks, each holding 9 bushels of wheat, for a total of 45 bushels of wheat.
7 sacks, each holding 9 bushels of rice, for a total of 63 bushels of rice.
2 sacks, each holding 9 bushels of quinoa, for a total of 18 bushels of quinoa.
Thus, the minimum number of sacks = 5+7+2 = 14.

The correct answer is B.
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
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Sep 25, 2015 12:12 am
This question is asking (in a clever way) for the GREATEST COMMON FACTOR of 45, 63, and 18. Whatever that factor is will be the size of the sack.

GCF(18, 45, 63) = 9, so that's our size.

We then have to split the grain up into sacks of size 9, so we need 45/9 + 63/9 + 18/9 sacks, or 14 sacks, and we're done.
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri Sep 25, 2015 9:11 am
Hi adthedaddy,

In this 'word problem', to answer this question in an efficient way, you really have to note the details about the sacks...

1) The sacks must be a SINGLE SIZE (so each sack will be the same size).
2) Each sack must be COMPLETELY FILLED with JUST ONE TYPE of grain (so we can't mix grains and we can't have a 'fraction' of a sack of grain).

Once you note these 'restrictions', the math itself is pretty straight-forward....

With 45 bushels of wheat, we can have any of the following options:
1 sack of 45 bushels each
3 sacks of 15 bushels each
5 sacks of 9 bushels each
9 sacks of 5 bushels each
15 sacks of 3 bushels each
45 sacks of 1 bushel each

The same can be done with the 63 bushels or rice and the 18 bushels of quinoa (although you don't really need to write down all of the options - you just have to see if any of the options that 'fit' the 45 bushels of wheat will also fit the 63 bushels of rice AND the 18 bushels of quinoa). From there, you should note that each of those numbers is ALSO divisible by 9.

Since the question asks for the MINIMUM number of sacks, we have to maximize the SIZE of each sack. A 9-bushel sack is the biggest one that 'fits' all three numbers, so we have...

45/9 = 5 sacks of wheat
63/9 = 7 sacks of rice
18/9 = 2 sacks of quinoa

5+7+2 = 14 total sacks

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Master | Next Rank: 500 Posts
Posts: 126
Joined: Sat Jun 07, 2014 5:26 am
Thanked: 3 times

by sandipgumtya » Sat Sep 26, 2015 6:35 am
Hi Rich,
The language of the problem is still not clear to me.Can u pl explain once more what the problem is actually asking.

Thanks
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sat Sep 26, 2015 8:59 am
Hi sandipbumtya,

In real basic terms, we need to pour 3 different amounts of grain into a certain number of sacks so that the following conditions are met:

1) Each sack MUST be the same size.
2) Each sack MUST be completely filled with JUST 1 type of grain.
3) We want the MINIMUM (re: least) number of sacks possible.

That third point is the 'key' - to have the least number of sacks, we need each sack to be as BIG as possible.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Post new topic Post Reply
• Page 1 of 1