GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 May 2019, 00:09

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A lottery winner from State F must match, in any order, 6 balls random

Author Message
TAGS:

### Hide Tags

Manager
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 73
GMAT 1: 750 Q50 V42
WE: Education (Education)
A lottery winner from State F must match, in any order, 6 balls random  [#permalink]

### Show Tags

27 Aug 2017, 21:42
2
1
00:00

Difficulty:

95% (hard)

Question Stats:

35% (02:33) correct 65% (02:04) wrong based on 44 sessions

### HideShow timer Statistics

A lottery winner from State F must match, in any order, 6 balls randomly chosen from a single pool of balls numbered from 1 to 50. A lottery winner from State G must match, in any order, 5 balls randomly chosen from a first pool of balls numbered from 1 to 50 AND a “megaball,” randomly chosen from a second set of balls numbered from 1 to 50. The number of winning combinations in a single drawing of the lottery in State G is what percentage greater than the number of winning combinations in a single drawing of the lottery in State F?
A. 11%
B. 85%
C. 111%
D. 567%
E. 667%

_________________
Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com
Manager
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 73
GMAT 1: 750 Q50 V42
WE: Education (Education)
Re: A lottery winner from State F must match, in any order, 6 balls random  [#permalink]

### Show Tags

27 Aug 2017, 22:04
For F: Total combination is $$50C_6$$ = $$\frac{50*49*48*47*46*45}{6*5*4*3*2*1}$$

For G: Total combination is $$50C_5$$*$$5C_1$$ = $$\frac{50*49*48*47*46}{5*4*3*2*1}$$*$$\frac{50}{1}$$

% greater = $$\frac{change}{smaller}$$*100

change = $$\frac{50*49*48*47*46}{5*4*3*2*1}$$*$$\frac{50}{1}$$ - $$\frac{50*49*48*47*46*45}{6*5*4*3*2*1}$$

= $$\frac{50*49*48*47*46}{5*4*3*2*1}$$ (50 - $$\frac{45}{6}$$)

% greater = $$\frac{\frac{50*49*48*47*46}{5*4*3*2*1}(50 - \frac{45}{6})}{\frac{50*49*48*47*46*45}{6*5*4*3*2*1}}$$*100

= $$\frac{50 - \frac{45}{6}}{\frac{45}{6}}$$*100

= $$\frac{50*6 - 45}{45}$$*100

=566.66%

Thus Option D
_________________
Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com
Manager
Joined: 27 Dec 2016
Posts: 232
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Re: A lottery winner from State F must match, in any order, 6 balls random  [#permalink]

### Show Tags

28 Aug 2017, 02:47
HolaMaven wrote:
For F: Total combination is $$50C_6$$ = $$\frac{50*49*48*47*46*45}{6*5*4*3*2*1}$$

For G: Total combination is $$50C_5$$*$$5C_1$$ = $$\frac{50*49*48*47*46}{5*4*3*2*1}$$*$$\frac{50}{1}$$

% greater = $$\frac{change}{smaller}$$*100

change = $$\frac{50*49*48*47*46}{5*4*3*2*1}$$*$$\frac{50}{1}$$ - $$\frac{50*49*48*47*46*45}{6*5*4*3*2*1}$$

= $$\frac{50*49*48*47*46}{5*4*3*2*1}$$ (50 - $$\frac{45}{6}$$)

% greater = $$\frac{\frac{50*49*48*47*46}{5*4*3*2*1}(50 - \frac{45}{6})}{\frac{50*49*48*47*46*45}{6*5*4*3*2*1}}$$*100

= $$\frac{50 - \frac{45}{6}}{\frac{45}{6}}$$*100

= $$\frac{50*6 - 45}{45}$$*100

=566.66%

Thus Option D

HolaMaven , can you explain the one that I highlighted?

If 5C1 then it should be $$\frac{5}{1}$$.
_________________
There's an app for that - Steve Jobs.
Math Expert
Joined: 02 Aug 2009
Posts: 7684
A lottery winner from State F must match, in any order, 6 balls random  [#permalink]

### Show Tags

02 Sep 2017, 20:36
HolaMaven wrote:
A lottery winner from State F must match, in any order, 6 balls randomly chosen from a single pool of balls numbered from 1 to 50. A lottery winner from State G must match, in any order, 5 balls randomly chosen from a first pool of balls numbered from 1 to 50 AND a “megaball,” randomly chosen from a second set of balls numbered from 1 to 50. The number of winning combinations in a single drawing of the lottery in State G is what percentage greater than the number of winning combinations in a single drawing of the lottery in State F?
A. 11%
B. 85%
C. 111%
D. 567%
E. 667%

Hi...
Let's see the combinations of each..

Here you can do with probability too

State F
First ball picking probability is 1/50, next 1/49 and so on..
Since ORDER is not important, these 6 can be picked in 6! Ways..
So prob = $$\frac{1}{50}* \frac{1}{49}.....\frac{1}{45}*6!$$

State G
Similarly $$\frac{1}{50}* \frac{1}{49}.....\frac{1}{46}*5!*1/50$$
Final 1/50 is the megaball..

%={ $${\frac{1}{50}* \frac{1}{49}.....\frac{1}{45}*6!-\frac{1}{50}* \frac{1}{49}.....\frac{1}{46}*5!*1/50$$}/{$$\frac{1}{50}* \frac{1}{49}.....\frac{1}{46}*5!*1/50$$}*100

={$${\frac{6}{45}-\frac{1}{50}$$}/$$\frac{1}{50}$$*100
= $$\frac{5100}{9}=567%$$

D
_________________
Manager
Joined: 12 Sep 2016
Posts: 65
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.15
A lottery winner from State F must match, in any order, 6 balls random  [#permalink]

### Show Tags

06 Sep 2017, 08:18
Even though the concept is rather easy, the question is too calculation intensive to appear on the GMAT.
A lottery winner from State F must match, in any order, 6 balls random   [#permalink] 06 Sep 2017, 08:18
Display posts from previous: Sort by