A box has 10 balls, either red or blue. If two balls are to be drawn s

Question

A box has 10 balls, either red or blue. If two balls are to be drawn simultaneously from the box, what is the number of red balls?

(1) The probability that the two balls drawn will be red is 1/15.
(2) The probability that one of the balls drawn will be red and the other will be blue is 7/15.

IanStewart · Answer

This is almost an exact copy of an official question, with the "less than half" restriction removed (which makes S2 insufficient in this version). The original version is here, with complete solutions:

https://gmatclub.com/forum/a-box-contai ... 99940.html

The writing in the official question is much better than in this one (the question here technically doesn't make any sense - the number of red balls does not depend on the fact that we're selecting two of them, but that's what the wording here implies), so the official version is the one worth studying.

HoneyLemon · Answer

1> -- R(R-1) = 6 => R = 3 --  Sufficient

2> R B / 90 = 7/15 = > not Sufficient

So A is the ans

Mallard · Answer

Let r - no. of red balls and b- no. of blue balls
r+b = 10 (given)
Statement 1: Prob(two reds) = 1/15
Hence, rC2 / 10C2 = 1/15
=> r(r-1) = 6 
=> r=3
sufficent

Statment 2 : Prob (one of each r and b) = 7/15
Hence, (rC1*bC1)/ 10C2 = 7/15
=> r*b = 21
and r+b = 10 (given)
=> r,b =3,7 
But, it doesn't tell us if r is 3 or 7
Hence, not sufficient

Correct answer - A

CEdward · Answer

This is how I thought about it.

R = ?

St1- P(two red) = 1/15

(r/10) x (r-1/ 9) = 1/15 <--- r is the number of reds
Sufficient.

St2 - P(blue and red) = 7/15

i) blue,red : b/10 x r/9
ii) red,blue: r/10 x b/9

(b/10 x r/9) + (r/10 x b/9) = rb / 45

Insufficient

Answer is A.

vibhor1902 · Answer

Can anyone please explain option 2

Bunuel · Answer

Check better version of this question with proper solutions here: https://gmatclub.com/forum/a-box-contai ... 99940.html TOPIC IS LOCKED.

A box has 10 balls, either red or blue. If two balls are to be drawn s

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 Data Sufficiency (DS) Questions

A box has 10 balls, either red or blue. If two balls are to be drawn s

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