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
