Problem Solving

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

OA is D

grandh01 wrote: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

The correct answer should be D and here is why:

This question deals with prime factorization. We know this because all of the colors are prime numbers. So we need to prime factor out 147,000. We notice that red is 7 points... so we only care about 7. After factoring out we get 147,000= 2^3*3*5^3*7^2. Notice that there are 2 7's "in" 147,000. So that is our answer. Does this help?

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

147000 = 7*21*1000 = 7*7*3*2*5*2*5*2*5 = 7^2 * 3 * 2^3 * 5^3.
So, 2 beads of value 7, One bead of value 3, 3 beads of value 2 and 3 beads of value 5 are removed.

The answer isD.2