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
Game of Cards
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- kvcpk
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2058= 2*1029 = 2*3*343 = 2* 3 *7^3askaichin wrote: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
So 5 cards would have been picked.
- kvcpk
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My mistake. Was leaving and wrote it in a hurry.askaichin wrote:Above reply not clear. Pls detail out the solution.
Thanks
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.