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

Question

Competition Mode Question

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

freedom128 · Answer

5733000 = 2^3 *5^3 *3^2 *7^2 *13^1

Beside 1 red card with thirteen spots, there are (3+3+2+2)=10 cards in total. We have 2 black cards with seven spots.

Final answer is (D)

Posted from my mobile device

Stonely · Answer

2*5*2*5*2*5*7*7*13*3*3 why do I get 11 cards? Regardless the# is 2

Posted from my mobile device

eakabuah · Answer

From the given question, the value of a red card drawn is 13 while that of a black card is equal to the number of spots. So if a black card with seven spots is drawn from the deck, then 5733 must be a multiple of the powers of 7. The number of powers of 7 in 5733 is equal to the number of black cards drawn with 7 spots on them.

5733/7 = 819/7 = 117. Since 117 is not divisible by 7, there are two powers of 7 in 5733, implying two black cards with 7 spots on them were drawn as part of the 10 cards drawn.

The answer is D.

5733/7 = 819/7 = 117. Since 117 is not divisible by 7, there are two powers of 7 in 5733, implying two black cards with 7 spots on them were drawn as part of the 10 cards drawn.

The answer is D.

Archit3110 · Answer

5733000 when divided by 7 max 2 cards possible and 2,3,5,13 for others
IMO D ; 2

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

unraveled · Answer

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

Since 5,733,000 is multiple of 2, 3, 5 and 7 and 13, number of cards having 7 spots would be answer. 
 5,733,000 = 3^2 * 7^2 * 13 * 2^3 * 5^3

Hence, 2 number of cards have 7 spots numbered.

Answer D.

ostrick5465 · Answer

5,733,000 = 2^{3} * 3^{2} * 5^{3}*7^{2}*13  Maybe choice D
but 11 card was removed.
=> nonsense ???????

Jawad001 · Answer

Given that, 
 the product of the point values of the removed cards is 5,733,000
 
 5,733,000 = 3x3 x 7 x 7 x 13 x 1000

Therefore, 2 black 7-spot cards were drawn(D)

TheNightKing · Answer

I absolutely adore how these questions are framed. I mean why would you ask the number of 7s. Let's write a big paragraph about it and then ask.

Coming back to the question. Just find prime factors of 5733. Don't bother about 00. You will find it has 2 7s. Hence D.

Brilliant. !

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards