Q

[Suyog]

In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 0


havent given any effort to solve!
posting it directly...

[kajcha]

Has to be 2

147000 can be written as 7*7*2*1000

Since 7 is not a factor of 1000. There are 2 Red beads removed.

[Suyog]

147000 can be written as 7*7*2*1000 ???

147000 = 7*7*5*3*2*100

now its 2

Thanks!

[wongee]

Can you explain this? How does the factorization imply that it is 2? Thanks!

[kajcha]

wongee, 147000 = 147*1000

Now 147 can be written as 7*7*3. We know that 1000 cannot have 7 as a factor. So there can be only 2 7s as factor.