Game of Cards

[askaichin]

In a particular card game, odd numbered cards are assigned a value of 2, even numbered cards a value of 3, and the face cards and aces a value of 7. Each player draws X cards per round and multiplies the resulting point values together. If a player's score is 2058 after the first round, what could be the value of X?

A 4
B 5
C 6
D 7
E 8

[kvcpk]

In a particular card game, odd numbered cards are assigned a value of 2, even numbered cards a value of 3, and the face cards and aces a value of 7. Each player draws X cards per round and multiplies the resulting point values together. If a player's score is 2058 after the first round, what could be the value of X?

A 4
B 5
C 6
D 7
E 8

2058= 2*1029 = 2*3*343 = 2* 3 *7^3

So 5 cards would have been picked.

[askaichin]

Above reply not clear. Pls detail out the solution.
Thanks

[kvcpk]

Above reply not clear. Pls detail out the solution.
Thanks

My mistake. Was leaving and wrote it in a hurry.
Let me explain:

2058 can be written as 2 * 3* 7^3

The question says that the value will be multiplied each time.

Suppose say value of first picked card is A (A can be 2 or 3 or 7)
Value of second card picked is B(B can be 2 or 3 or 7)

Assuming only 2 cards are picked, the total value is A*B

If more card are picked, the value will be A*B*C*D....

Now A*B*C*D.... = 2* 3* 7^3

Any number can be written as product of primes. We know that the primes involved are only 2,3,7
Hence A*B*C*.... can be written as
2^m * 3^n * 7^p

Hence 2^m * 3^n * 7^p = 2^1* 3^1* 7^3
Hence m=1, n=1, p=3

Which means one 2-valued card
one 3-valued card and
three 7-valued cards are picked.

Total = 1+1+3 = 5

Let me know if you have any troubles understanding this.

[askaichin]

Thank you for the detailed solution. I think you have cleared my doubts with these type of questions.

Thanks Again

[kvcpk]

Thank you for the detailed solution. I think you have cleared my doubts with these type of questions.

Thanks Again

Glad it helped