Problem Solving

Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A's has 60% fewer booklets than each box of Team B's. Which of the following could be the total number of booklets distributed by the two groups?

a)2,000
b)3,200
c)4,100
d)4,800
e)4,900


c

Say Team B distributes x boxes, each of which contains y booklets. Hence Team B distributes xy booklets.

Then Team A distributes 1.6x boxes (60% greater than x), each of which contains .4y booklets (60% less than y). Hence Team A distributes (1.6x)(.4y) booklets, or .64xy booklets.

Together, Team A and Team B distribute .64xy + xy booklets, or 1.64xy booklets. Now we have this equation:

1.64xy = (total # of booklets)

This means we need an answer choice that divides by 1.64 and leaves an integer, as xy must be a whole number. Manipulating our equation a bit, we get

164xy = 100 * (total # of booklets)

and since 164 = 4 * 41,

4xy = (100 * (total # of booklets))/41

So the total # of booklets must be divisible by 41. Only C is, so that's our answer!

jose.mario.amaya wrote:Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A's has 60% fewer booklets than each box of Team B's. Which of the following could be the total number of booklets distributed by the two groups?

a)2,000
b)3,200
c)4,100
d)4,800
e)4,900


c

Team B:
Let the number of boxes = 10.
Let the booklets per box = 10.
Total booklets = 10*10 = 100.

Team A:
Since team A distributes 60% more boxes, the number of boxes = 1.6(10) = 16.
Since each box contains 60% fewer booklets, booklets per box = 10 - .6(10) = 4.
Total booklets = 16*4 = 64.

Total booklets for the two teams = 100+64 = 164.
The correct answer choice will be a multiple of 164 that ends in 0.
5*164 = 820.
5*820 = 4100.

The correct answer is C.

Hello,

I was trying to solve this problem as follows:

Boxes of booklets:
Team B distributes 100
Team A distributes 160

Booklets in each box:
Team B has x
Team A has 0.40x

Total Booklets distributed:
Team B is 100x
Team A is 160(0.40x)

So, 100x + 160(0.40x) = 164x

However, I am lost after this point. Can you please assist?

Thanks,
Sri

gmattesttaker2 wrote:Hello,

I was trying to solve this problem as follows:

Boxes of booklets:
Team B distributes 100
Team A distributes 160

Booklets in each box:
Team B has x
Team A has 0.40x

Total Booklets distributed:
Team B is 100x
Team A is 160(0.40x)

So, 100x + 160(0.40x) = 164x

However, I am lost after this point. Can you please assist?

Thanks,
Sri

Hey Sri,

Well you are almost there.

Total number of books = 164x ie; 4*41*x. Look at the answer choices. There is only one answer choice which has 41 as a factor.

C

Regards
Anup

anuprajan5 wrote:

gmattesttaker2 wrote:Hello,

I was trying to solve this problem as follows:

Boxes of booklets:
Team B distributes 100
Team A distributes 160

Booklets in each box:
Team B has x
Team A has 0.40x

Total Booklets distributed:
Team B is 100x
Team A is 160(0.40x)

So, 100x + 160(0.40x) = 164x

However, I am lost after this point. Can you please assist?

Thanks,
Sri

Hey Sri,

Well you are almost there.

Total number of books = 164x ie; 4*41*x. Look at the answer choices. There is only one answer choice which has 41 as a factor.

C

Regards
Anup

Hello Anup,

Hope all is well. Thank you very much for the explanation. It is clear now.

Best Regards,
Sri