broall wrote:

A game is played with a deck of cards all numbered with either 2, 3, 5, or 7 spots. The point value of a card is its number of spots, unless it is a red card, in which case the point value of the card is 13. In one instance, ten cards are drawn from the container. If the product of the point values of the removed cards is 5,733,000, how many black 7-spot cards were drawn?

A. 5

B. 4

C. 3

D. 2

E. 0

Source: GMAT Free

I quickly understood how to solve this problem but it took me a while to actually find out how many prime factors there were.

The average time here is 1 minute 45 seconds for a right answer. Is there a faster way to solve this out without doing the following steps:

1) 5,733,000 = 5,733 X 10^3

2) 5,733 / 7 = 819

3) 819 / 7 = 117

4) 117 / 7 = 16.71 > because this is a fraction there is only 2 prime factors of 7.

So there must be two black 7 cards. This process took me over 2 minutes.

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Also echoing what was already said. This question is fundamentally flawed because 11 cards must be drawn.