In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20

Question

In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

gmatforce · Accepted Answer

The question asks about how many balls MUST be taken out in order to make sure we took out 8 of the same color.

Now, in this case we have to be sure about our answer when we can say we have taken out 8 balls of same color.

Favorable case will be if we take out first eight balls and all of them are of the same color. But that is a favorable case and may not always be true.

A worst case will be when you are 100% sure that you have achieved the desired result.

As in this case: if you draw out first 28 balls and they are 7 of each color, W, R, B, G.
Now you know that any ball you take out next will be of any one of the above colors and hence you'll have 8 ball of same color.

So ans is 29.

I hope it's clear.

Bunuel · Answer

Check other  Worst Case Scenario Questions  from our  Special Questions Directory  to understand the concept better.

GMAT TIGER · Answer

Thats 29 in C.

I love these types of questions..

arora2m · Answer

I don't get why there will be 7 of each when we draw out 28 balls. Could you please elaborate?

IEsailor · Answer

Arora2m this one is for you :

Black Blue Yellow Green
 1 1 1 1
 1 1 1 1
.
.
.
.
.

similar pattern 7 times. the next ball will have to be from either of the colors and making the total tally of that color to 8 balls

sathana87 · Answer

HI where do we come across these type of questions in og 11.If you could point out the question numbers it will be really greatful asap.

amit2k9 · Answer

nice question.

take 7 out of each color.7*4 + 1 = 29

longhaul123 · Answer

Can someone please elaborate the concept in this question. Why do we have to consider each ball of different color??

shashankism · Answer

This is a very simple question. 
Jar contains 15 WB, 25 RB, 10 BB, 20 GB.

Now to ensure that there must be 8 balls of same colour, 
the best case will be, we take out 8 ball of same colour & 
the worst case will be when we take out 7 balls of each colours and then we take out any ball. 
The last ball's colour will be the colour of the 8 balls with same colour and other 7 balls will be of their respective colour.

So to ensure that we have 8 balls of same colour we need to take out 7+7+7 +8 = 29 balls.

Answer C.

ScottTargetTestPrep · Answer

The worst case scenario would be having to draw 7 balls of each color so that we wouldn’t have 8 balls of any one color. However, if we were to remove just one more ball, regardless of the color, we would then have 8 balls of one color. Thus, we need to remove 7 x 4 + 1 = 29 balls.

Answer: C

Salsanousi · Answer

The maximum we can take out before we have 8 of the same color is 7 of each color.

7 * 4 = 28

Then any additional ball we take will complete a set of 8.

So 29

Answer choice C

Posted from my mobile device

MathRevolution · Answer

The minimum we need 7 balls for each color.  White ,  Red ,  Blue , Green]

=>  7  +  7  +  7  +  7  = 28.

The next ball will be of either of the color   White ,  Red ,  Blue , Green]  and when added to 28 will make 8 balls of the same color for any color.

=> 28 + 1 = 29

Answer C

Fdambro294 · Answer

I believed there was some underlying trick I was missing.....

We have:

White..................Red.....................Blue.......................Green
15.......................25.......................10..........................20

We need to keep pulling balls out blindly. How many balls do we need to pull out such that in every possible scenario we MUST have 8 balls of the Same color?

Worst luck in the world:

1st) we pull out 7 White

2nd) we pull out 7 Red

3rd) we pull out 7 Blue

4th) we pull out 7 Green
_________________________

at this point we have pulled out 28 Balls and we do NOT have 8 balls of the same color.

On our next pull, not matter which color we pull, it will complete a Series of 8 Identical Colors.

29 Pulls of Balls guarantees that we will have 8 balls of the same color

Answer: 29

-C-

janbol · Answer

Does anyone have list links that are similar to this question?

Thanks in advance!

Bunuel · Answer

It's already given above.

Check other  Worst Case Scenario Questions  from our  Special Questions Directory  to understand the concept better.

luisdicampo · Answer

Deconstructing the Question  
There are  4 colors .
We want to be sure to get  8 balls of the same color .
Key idea: use the worst-case (pigeonhole principle).

Step-by-step  
In the worst case, we avoid getting 8 of any color by taking at most 7 from each color.

All colors have at least 8 balls available, so we can take:
 7+7+7+7=28

The next ball guarantees 8 of some color:
 28+1=29

Answer: 29

In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20

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

In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20

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