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# A game is played with a deck of cards all numbered with either 2, 3, 5

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A game is played with a deck of cards all numbered with either 2, 3, 5 [#permalink]

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28 Apr 2017, 07:09
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Difficulty:

45% (medium)

Question Stats:

69% (01:45) correct 31% (02:31) wrong based on 61 sessions

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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
[Reveal] Spoiler: OA

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Re: A game is played with a deck of cards all numbered with either 2, 3, 5 [#permalink]

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28 Apr 2017, 08:34
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nguyendinhtuong 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

Hi,

We are looking for factors of 5733000....
Three ZERO in the end means three 2s and three 5s...
Let's look at 5733... Sum of digits is 5+7+3+3=18..
So 5733 is surely a multiple of 9..
5733=3*3*7*7*13...
So ans is 2 7-spot .... D

However Q is flawed as there are 11 cards which will TOTAL up to 5733000, when multiplied.
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Re: A game is played with a deck of cards all numbered with either 2, 3, 5 [#permalink]

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20 Sep 2017, 06:28
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.
Re: A game is played with a deck of cards all numbered with either 2, 3, 5   [#permalink] 20 Sep 2017, 06:28
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