Problem Solving

talaangoshtari wrote:A pantry holds x cans of beans, twice as many cans of soup, and half as many cans of tomato paste as there are cans of beans. If there are no other cans in pantry, which of the following could be the total number of cans in the pantry?

A.6
B.7
C.36
D.45
E.15

The KEY CONCEPT here is that the number of each type of can must be an INTEGER.
The relatively small answer choices suggest that we can just test possible values of x.

Try x = 1
In other words, there is 1 can of beans
There are half as many cans of tomato paste as there are cans of beans.
This means that there are 1/2 cans of tomato paste.
NO GOOD

Try x = 2
In other words, there are 2 cans of beans
There are half as many cans of tomato paste as there are cans of beans.
This means that there is 1 can of tomato paste.

There are twice as many cans of soup as there are cans of beans.
So, there are 4 cans of soup

Total cans = 2 + 1 + 4 = 7

Answer: B

Cheers,
Brent

Hi talaangoshtari,

The number of each type of can is related to the numbers of the OTHER types of cans, so we can use some algebra to look for a pattern....

X = number of cans of beans
2X = number of cans of soup
X/2 = number of cans of tomato paste

Total cans = X + 2X + X/2 = 3.5X cans

Since we MUST have an INTEGER number of cans (we can't have 'half' a can), X MUST be an even number.

So if X can be 2, 4, 6, 8, 10, etc......

Then the total number of cans can be 7, 14, 21, 28, 35, etc. In other words, the total number of cans is a multiple of 7....

Looking at the answer choices, only one option fits...

Final Answer: B

GMAT assassins aren't born, they're made,
Rich