marbles

[sunilrawat]

Barry plays a game in which he has a jar of marbles, some blue, some pink, some orange, and some yellow, to which he assigns point values of 2, 4, 5, and 7, respectively. After removing some marbles, Barry finds that the product of the point values of the marbles he has removed is 56,000. What could be the total number of blue and orange marbles he removed?

3
4
6
10
11

OA A

[gmatclubmember]

Barry plays a game in which he has a jar of marbles, some blue, some pink, some orange, and some yellow, to which he assigns point values of 2, 4, 5, and 7, respectively. After removing some marbles, Barry finds that the product of the point values of the marbles he has removed is 56,000. What could be the total number of blue and orange marbles he removed?

3
4
6
10
11

56000 can be obtained as 7*2*2*2(8)*2*5(10)*2*5(10)*2*5(10) (=7*8*10*10*10).----------First condition
We have to find Blue (2) and Orange(5).
So orange marbles will be 3 from First condition.
Minimum blue required would be 0, since 3 Pinks can give us the same no. (2*2(4)*2*2(4)*2*2(4)).
3+0 = 3 ... so i will go with

A. 3

If we dont consider Pink that we either can have 2 Blue or 4 blue or 6 blue, if we add these to 3 orange then we get 5 or 7 or 9. none of which is in the answer options. so we have to go with 0 blue marbles which gives us 3 oranges in all.
OA A

[prashant.mishra]

Write 56000 in powers of its prime factors.

Thus 56000= 56*1000-> 2^3 * 7 * 10^3 -> 2^3 * 7 * 2^3 * 5^3 -> 2^6 * 7 * 5^3

Thus one thing is clear: There were 3 orange marbles that were removed. We have to find out the total number of blue and orange marbles combined. Thus our answer will be of the form 3+x, and we have to find out x. Lets examine in how many ways can we write 2^6 by considering the values of marbles.

2(value of blue marbles) ^6 -> thus x becomes 6 and total nuber of marbles removed possibly could be 6+3=9 ; not there in options, so eliminated.

4(value of pink marbles) * 2(value of blue marbles)^4 -> x becomes 4 and x+3=7 ; not there in the options; so OUT.

4 * 4 * 2^2 -> x becomes 2 and 3+x becomes 5; not there in options so OUT again.

so the only thing that remains is 4 * 4 * 4 -> x=0 then 3+x=3 which is present in the options !! That is your answer.

IMO A.

Barry plays a game in which he has a jar of marbles, some blue, some pink, some orange, and some yellow, to which he assigns point values of 2, 4, 5, and 7, respectively. After removing some marbles, Barry finds that the product of the point values of the marbles he has removed is 56,000. What could be the total number of blue and orange marbles he removed?

3
4
6
10
11

OA A

[cans]

b=2 and 0=5.
56000 = 7*2^6*5^3
thus orange=3.
blue=6
thus 9,7, 5,3 possible.
IMO A