Alejandra is designing a game of chance. For one part of the game,

Question

Alejandra is designing a game of chance. For one part of the game, a player is to randomly choose 3 marbles, without replacement, from a box containing B blue marbles, R red marbles, and no other marbles. Alejandra correctly determined the positive integers B and R so that the number of possible selections in which 2 blue marbles and 1 red marble are chosen is twice the number of possible selections in which 2 red marbles and 1 blue marble are chosen.

The positive integers B and R that Alejandra determined must be such that B is the number that is ___ 1 ___ the number that is ___ 2 ___ R.

Based on the information provided, select for  1  and for  2  the options that create the most accurate statement. Make only two selections, one in each column.

GMATCoachBen · Answer

This one was on Exam 4. There is another similar version posted here:  https://gmatclub.com/forum/alejandra-is-designing-a-game-of-chance-for-one-part-of-the-game-422148.html#p3305806

GMATCoachBen · Answer

We need to translate this into an equation:

"the number of possible selections in which 2 blue marbles and 1 red marble are chosen is twice the number of possible selections in which 2 red marbles and 1 blue marble are chosen."

For the 2 blue and 1 red, note that "And" means "multiply".  We are choosing 2 blue out of B total blue marbles, and 1 red out of R total red marbles. Let's use this timesaving formula for combinations, when we are choosing 2 out of N: (NC2) =  \frac{N(N-1) }{ 2} . (This formula for "pairs" can come up in other contexts, such as handshakes or games played between 2 teams.)

(BC2) * (RC1) =  \frac{B(B-1) }{ 2}   * R

For the 2 red and 1 blue, we use the same method:

(RC2) * (BC1) =  \frac{R(R-1) }{ 2}   * B

Then, let's set up our full equation. It says that 2 blue and 1 red is twice the number for 2 red and 1 blue:

\frac{B(B - 1) }{ 2}   * R = 2 *  \frac{R(R - 1) }{ 2}   * B

We simplify, by crossing off the B and R on both sides, and 2 on the bottom on both sides:

(B - 1)= 2(R - 1)

B = 2R - 1

Finally, we read carefully and double-check that we are filling in the blanks correctly, so that it matches our equation:

"𝐵 is the number that is ___ 1 ___ the number that is ___ 2 ___ 𝑅."

B is  1 less than  the number that is  twice  R.

sayan640 · Answer

B c 2 * R c 1 = 2 * R c 2 * B c 1
B^2 = B(2R -1)
B = 2r -1

Ans

GMATinsight · Answer

Alejandra correctly determined the positive integers 𝐵 and 𝑅 so that the number of possible selections in which 2 blue marbles and 1 red marble are chosen is twice the number of possible selections in which 2 red marbles and 1 blue marble are chosen. B C 2*R C 1 = 2* B C 1*R C 2 B(B-1)*R/2 = 2*R(R-1)*B/2 i.e. B-1 = 2(R-1) i.e. B = 2R-1 So, B is the number that is 1 less than twice the number R. hence the answer --- GMATinsight | www.GMATinsight.com GMAT FOCUS PREP Expert Youtube: www.Youtube.com/GMATinsight (1100+ Quant and DI prep videos FREE)

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.

1	2
		2 more than
		1 more than
		1 less than
		2 less than
		half
		twice

Alejandra is designing a game of chance. For one part of the game,

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 Two-part Analysis (TPA) Questions

Alejandra is designing a game of chance. For one part of the game,

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