Purple balls

Expert replies

Cheese12: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Nov 24, 2010 12:57 am; Thanked: 3 times

by Cheese12 » Sun Oct 02, 2011 6:57 am

In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?

A) 1
B) 2
C) 3
D) 4
E) 5

Im stuck with this problem and dont know how to proceed.. My working..

Total points = 88000
factor using primes -> 88000 = (2^6)*(5^3)*(11)

from question we know that ... 88000= B*5G*Px*R11

and 11>x>5... so x = 8 or 10...8= 2^3... and 10= 2*5... both can be a fit into the formula..
also.. what about the Blue balls(B) ?... they could be any number.. and still hold true if x was 8 or 10...

OA:B

Source: Beat The GMAT — Problem Solving | Sun Oct 02, 2011 6:57 am

knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Sun Oct 02, 2011 7:34 am

Actually, u've answered ur own question. 10=2*5 so the 5 would be a part of the green chips picked up. Secondly, when u have 2^6 i.e. 64 left you need to find a number between 5 and 11 which when multiplied by itself a certain number of times would give u 64. Only the number 8 when multiplied twice i.e. 8^2 gives u 64. Hence, there are two chips of 8 that were picked up. Hence, B. Hope that clears ur doubts.

edvhou812: Master | Next Rank: 500 Posts; Posts: 143; Joined: Sat Nov 06, 2010 9:06 pmFollowed by: 1 member; Thanked: 10 times

by edvhou812 » Sun Oct 02, 2011 7:55 am

88,000=11^1*2^6*5^3
2^6=64=8*8
5<8<11
B

I don't know what to say, really. Three minutes to the biggest battle of our professional lives. You find out life's this game of inches, so is football. Because in either game - life or football - the margin for error is so small. I mean, one half a step too late or too early and you don't quite make it. One half second too slow, too fast and you don't quite catch it. I'll tell you this, in any fight it's the guy whose willing to die whose gonna win that inch. That's football guys, that's all it is. Now, what are you gonna do?

Cheese12: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Nov 24, 2010 12:57 am; Thanked: 3 times

by Cheese12 » Sun Oct 02, 2011 8:08 am

knight247 wrote:Actually, u've answered ur own question. 10=2*5 so the 5 would be a part of the green chips picked up. Secondly, when u have 2^6 i.e. 64 left you need to find a number between 5 and 11 which when multiplied by itself a certain number of times would give u 64. Only the number 8 when multiplied twice i.e. 8^2 gives u 64. Hence, there are two chips of 8 that were picked up. Hence, B. Hope that clears ur doubts.

Hi Knight247,

that means... B*5G*Px= 2^6 * 5^3
so this can mean that G=3,2,1 ... if G=1 and say x = 10=5*2.. that means we have two 10's (2 5's and 2 2's) ..

so then the formula becomes... B =2^4... which is possible right ?

please help to point out my mistake here... thanks!!!

knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Sun Oct 02, 2011 8:24 am

It is not B*5G*Px. It should be 5^(the number of times G is picked up) as it is the product of all the Gs picked up and not the sum of them. Similarly for other chips.

88,000=11^1 * 2^6 * 5^3

So we have, 1 Red Chip, 3 Green chips and 2^6 which is not defined yet. We don't consider Blue chips because their value is one, so picking a blue chip multiple times would not affect the product of the points. So the mistake u've made is that u've considered 5G when it should be
5^(the number of times G is picked up). Remember it is the product of all points.Similarly for other chips.

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review