Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 04 May 2015, 02:50

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A vending machine randomly dispenses four different types of

Author Message
TAGS:
Director
Joined: 05 Jan 2008
Posts: 707
Followers: 3

Kudos [?]: 146 [0], given: 0

A vending machine randomly dispenses four different types of [#permalink]  21 Mar 2008, 22:18
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (01:50) wrong based on 1 sessions
A vending machine randomly dispenses four different types of fruit
candy. There are twice as many apple candies as orange candies,
twice as many strawberry candies as grape candies, and twice as
many apple candies as strawberry candies. If each candy cost $0.25, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy? A$3.00
B $20.75 C$22.50
D $42.75 E$45.00
_________________

Persistence+Patience+Persistence+Patience=G...O...A...L

CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2142 [1] , given: 359

Re: PS: Vending Machine [#permalink]  22 Mar 2008, 21:56
1
KUDOS
Expert's post
we have:
the number of apple candies = Na=40
the number of orange candies = No=20
the number of strawberry candies= Ns = 20
the number of grape candies = Ng = 10

our question: "what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?"

If we get 40 candies, we can get only 40 apple candies and therefore N=40 does not guaranty that we will have always 3 of each type.

If we get 60 candies, we may get 40 apple candies and 20 orange candies - no guarantees
If we get 80 candies, we may get 40 apple candies, and 20 orange candies, and 20 strawberry - no guarantees
If we get 82 candies, we may get 40 apple candies, and 20 orange candies, 20 strawberry, and 2 grape candies - no guarantees
If we get 83 candies, we will always get at least three of each type of candy: 3 apple, 3 orange, 3 strawberry, and 3 grape candies, that is, we will get 3 of each type regardless chance.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Current Student
Joined: 08 Jan 2009
Posts: 330
GMAT 1: 770 Q50 V46
Followers: 23

Kudos [?]: 105 [1] , given: 7

Re: Probabilty and Ratios [#permalink]  15 Sep 2011, 15:19
1
KUDOS
This question isn't that tough when you break it all down.

We are given the following ratios:
Code:
A   O   S   G
2   1
2    1
2        1

Consolidate these ratios:
Code:
A   O   S   G
4   2    2   1

We have 90 items, so using the ratio above we have these pieces:
Code:
A   O   S   G
40  20  20 10

Now we need at least three of each type. Think about the worst case, if we buy 40, we might get all of A. If we buy 60, we might get all of A and O, if we buy 80 we might get A, O and S, so we need to buy another three and now we have guaranteed we have A,O,S and G.

83 * $0.25 =$20.75

B.
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2142 [0], given: 359

Re: PS: Vending Machine [#permalink]  21 Mar 2008, 23:04
Expert's post
B

from: "There are twice as many apple candies as orange candies,
twice as many strawberry candies as grape candies, and twice as
many apple candies as strawberry candies."

we can conclude following ratio: 4:2:2:1 or 40:20:20:10

To satisfy the condition of buying at least three of
each type of candy, we have to buy N=40+20+1=61
P=61*0.25$=15.25$
So, I picked B.

BTW, 90*0.25$=22.5$, Therefore, C,D,E are out.
A is too small. So B remains
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

SVP
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
Followers: 19

Kudos [?]: 441 [0], given: 1

Re: PS: Vending Machine [#permalink]  22 Mar 2008, 01:30
prasannar wrote:
A vending machine randomly dispenses four different types of fruit
candy. There are twice as many apple candies as orange candies,
twice as many strawberry candies as grape candies, and twice as
many apple candies as strawberry candies. If each candy cost $0.25, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy? A$3.00
B $20.75 C$22.50
D $42.75 E$45.00

I confused this: "three of each type of candy", if it means "each type three" I think A win. What do you think?
_________________
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2142 [0], given: 359

Re: PS: Vending Machine [#permalink]  22 Mar 2008, 01:43
Expert's post
I've found my mistake

at least three of each type of candy: 3 apple, 3 orange, 3 strawberry, and 3 grape candies.

N=40+20+20+3=83
P=83*0.25=20.75$_________________ HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame SVP Joined: 04 May 2006 Posts: 1936 Schools: CBS, Kellogg Followers: 19 Kudos [?]: 441 [0], given: 1 Re: PS: Vending Machine [#permalink] 22 Mar 2008, 18:41 walker wrote: I've found my mistake at least three of each type of candy: 3 apple, 3 orange, 3 strawberry, and 3 grape candies. N=40+20+20+3=83 P=83*0.25=20.75$

Walker,
Why not N = 10 + 20 + 20 + 3 ?

You are deserved to 51!
_________________
Director
Joined: 05 Jan 2008
Posts: 707
Followers: 3

Kudos [?]: 146 [0], given: 0

Re: PS: Vending Machine [#permalink]  22 Mar 2008, 19:46
sondenso wrote:
walker wrote:
I've found my mistake

at least three of each type of candy: 3 apple, 3 orange, 3 strawberry, and 3 grape candies.

N=40+20+20+3=83
P=83*0.25=20.75$Walker, Why not N = 10 + 20 + 20 + 3 ? You are deserved to 51! Sondenso, What is the guarantee that the last 3 are Grape Candies, they could be very well Apple[since Orange and Strawberry are completely used as we picked 20,20 of them] thus to make sure there are 3 of each, we need to make sure, we pick up ALL of the rest of the candies but for the least number variant. Hope this helps _________________ Persistence+Patience+Persistence+Patience=G...O...A...L SVP Joined: 04 May 2006 Posts: 1936 Schools: CBS, Kellogg Followers: 19 Kudos [?]: 441 [0], given: 1 Re: PS: Vending Machine [#permalink] 22 Mar 2008, 21:20 prasannar wrote: sondenso wrote: walker wrote: I've found my mistake at least three of each type of candy: 3 apple, 3 orange, 3 strawberry, and 3 grape candies. N=40+20+20+3=83 P=83*0.25=20.75$

Walker,
Why not N = 10 + 20 + 20 + 3 ?

You are deserved to 51!

Sondenso,

What is the guarantee that the last 3 are Grape Candies, they could be very well Apple[since Orange and Strawberry are completely used as we picked 20,20 of them] thus to make sure there are 3 of each, we need to make sure, we pick up ALL of the rest of the candies but for the least number variant.

Hope this helps

Hey, this concept have just come up to me. I tried to understand the logic. But Honestly, I did not understand. Do you guys mind writting it in more detail? Many thanks.
_________________
SVP
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
Followers: 19

Kudos [?]: 441 [0], given: 1

Re: PS: Vending Machine [#permalink]  22 Mar 2008, 23:11
walker wrote:
we have:
the number of apple candies = Na=40
the number of orange candies = No=20
the number of strawberry candies= Ns = 20
the number of grape candies = Ng = 10

our question: "what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?"

If we get 40 candies, we can get only 40 apple candies and therefore N=40 does not guaranty that we will have always 3 of each type.

If we get 60 candies, we may get 40 apple candies and 20 orange candies - no guarantees
If we get 80 candies, we may get 40 apple candies, and 20 orange candies, and 20 strawberry - no guarantees
If we get 82 candies, we may get 40 apple candies, and 20 orange candies, 20 strawberry, and 2 grape candies - no guarantees
If we get 83 candies, we will always get at least three of each type of candy: 3 apple, 3 orange, 3 strawberry, and 3 grape candies, that is, we will get 3 of each type regardless chance.

Walker, thanh you

_________________
Intern
Joined: 10 Aug 2011
Posts: 3
Location: United States
GPA: 3.83
Followers: 0

Kudos [?]: 5 [0], given: 1

Probabilty and Ratios [#permalink]  15 Sep 2011, 15:02
A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.25, and there are exactly 90 candies in the machine, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy? A$3.00
B $20.75 C$22.50
D $42.75 E$45.00
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5453
Location: Pune, India
Followers: 1332

Kudos [?]: 6777 [0], given: 177

Re: Probabilty and Ratios [#permalink]  15 Sep 2011, 21:16
Expert's post
sameer1986 wrote:
A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.25, and there are exactly 90 candies in the machine, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy? A$3.00
B $20.75 C$22.50
D $42.75 E$45.00

Given:
Apple:Orange = 2:1
Strawberry:Grape = 2:1
Apple: Strawberry = 2:1
So if we have 1 Grape candy, we have 2 strawberry ones and 4 apple ones, which means we have 2 Orange candies.
So in all we would have 1+2+4+2 = 9 candies
Since we actually have 90 candies, we must have 10 Grape, 20 Strawberry, 40 Apple and 20 Orange candies.

If we need at least three of each type and the machine dispenses them randomly, we have to take the worst case scenario (we will have to buy maximum number of candies). In the worst case, we will get the grape candies at the end. We will end up buying all other 80 candies and then get 3 grape candies because only grape candies will be left. So we will need to buy 83 (\$20.75) candies.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Manager
Joined: 08 Sep 2011
Posts: 77
Concentration: Finance, Strategy
Followers: 3

Kudos [?]: 2 [0], given: 5

Re: PS: Vending Machine [#permalink]  18 Sep 2011, 11:57
B. (40+20+20+3)* .25 = 20.75

I also missed the wording 3 of each kind.
Re: PS: Vending Machine   [#permalink] 18 Sep 2011, 11:57
Similar topics Replies Last post
Similar
Topics:
Jamal can fill the vending machine in 45 minutes. When his 2 19 Mar 2012, 10:38
33 A vending machine is designed to dispense 8 ounces of coffee 13 27 Apr 2010, 05:21
A vending machine is designed to dispense 8 oz. of coffee 9 31 Aug 2007, 17:01
A vending machine is designed to dispense 8 ouces of coffee 6 27 Nov 2006, 17:13
A vending machine is designed to dispense 8 ounces of coffee 1 25 Sep 2006, 21:39
Display posts from previous: Sort by