A box contains 3 red balls, 4 green balls, 5 yellow balls, 6

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Sun Mar 17, 2019 11:22 pm

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[GMAT math practice question]

A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?

A. 10
B. 12
C. 15
D. 18
E. 21

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Mar 18, 2019 5:54 am

Max@Math Revolution wrote:[GMAT math practice question]

A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?

A. 10
B. 12
C. 15
D. 18
E. 21

Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 5 of the same color:
3 red
4 green
4 yellow
4 blue
4 white
Sum = 3+4+4+4+4 = 19

Implication:
It is possible to remove 19 balls without selecting 5 of the same color.
Thus, to GUARANTEE that 5 of the same color are removed, we must remove ONE MORE ball:
19+1 = 20

The correct answer is not among the answer choices.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Mar 19, 2019 5:57 pm

Max@Math Revolution wrote:[GMAT math practice question]

A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?

A. 10
B. 12
C. 15
D. 18
E. 21

We could have 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls, and 4 white balls drawn, that is, a total of 19 balls drawn, without 5 balls of a single color drawn. However, the next ball drawn will be yellow, blue or white, and we will have 5 balls of a single color drawn. Therefore, we need to draw 20 balls to guarantee that at least 5 balls of a single color will be drawn.

Answer: 20

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Mar 20, 2019 12:32 am

=>

The maximum number of draws we can make without drawing 5 balls of a single color is 3 + 4 + 4 + 4 + 4 = 14. This occurs when we draw 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls and 4 white balls. If we draw one more ball, then we will have drawn 5 balls of a single color.

Thus, to guarantee that we have drawn at least 5 balls of a single color, we must draw 14+1 = 15 balls.

Therefore, C is the answer.
Answer: C

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Wed Mar 20, 2019 6:34 am

Max@Math Revolution wrote:=>

The maximum number of draws we can make without drawing 5 balls of a single color is 3 + 4 + 4 + 4 + 4 = 14. This occurs when we draw 3 red balls, 4 green balls, 4 yellow balls, 4 blue balls and 4 white balls. If we draw one more ball, then we will have drawn 5 balls of a single color.

Thus, to guarantee that we have drawn at least 5 balls of a single color, we must draw 14+1 = 15 balls.

Therefore, C is the answer.
Answer: C

The highlighted calculation adds up to 19 not 14

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