GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 21 Jan 2020, 05:30

### 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

# There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chose

Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Jul 2018
Posts: 20
There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chose  [#permalink]

### Show Tags

09 Dec 2019, 07:16
1
00:00

Difficulty:

85% (hard)

Question Stats:

44% (03:30) correct 56% (02:41) wrong based on 27 sessions

### HideShow timer Statistics

There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chosen at random from the purse, what is the probability of getting more than 55 cents?
(1 Dime = 10 Cents ; 1 Quarter = 25 Cents)

A. 1/5
B. 1/20
C. 1/2
D. 19/20
E. 4/5
Senior Manager
Joined: 13 Feb 2018
Posts: 495
GMAT 1: 640 Q48 V28
Re: There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chose  [#permalink]

### Show Tags

09 Dec 2019, 08:41
1
1
Let's count the probability of getting 55 cents or less and then subtract the result from 1
We cant get less than 55 as there are only three 10 cent coins and the rest three are 25 cent-coins
We can get 55 cents if we pull one 25 cents and three 10 cents
dime, quarter, quarter, quarter: 3/6*3/5*2/4*1/3=1/20
dime, quarter, quarter, quarter --> can be arranged in 4!/3!=4 ways

probability of getting 55 cents is 1/20*4=1/5
probability of getting more than 55 cents is 1-1/5=4/5

IMO
Ans: E
Intern
Joined: 27 Jul 2018
Posts: 20
Re: There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chose  [#permalink]

### Show Tags

09 Dec 2019, 19:28
Three Dimes: 10, 10, 10
Three Quarters: 25, 25, 25

Four Coins are picked.

So the minimum total we can get is 10+10+10+25 = 30+25 = 55
Which means any other total (combination) gives more than 55. Which means what is the probability of getting anything other than 55.

Well 55 is only one instance, so finding Probability for it is easy. So we are picking 4 coins.

Key- DL: Dimes Left, QL: Quarters Left, TCL: Total Coins Left
(DL/TCL)*(DL/TCL)*(DL/TCL)*(QL/TCL)*4 = (3/6)*(2/5)*(1/4)*(3/3)*4 = (1/20)*4 = 1/5

The probability of getting total 55 is 1/5 so the probability of getting anything but 55 is
= 1-(1/5) = (5-1)/5 = 4/5 (E)
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9997
Location: Pune, India
Re: There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chose  [#permalink]

### Show Tags

09 Dec 2019, 22:43
1
1
07tiger wrote:
There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chosen at random from the purse, what is the probability of getting more than 55 cents?
(1 Dime = 10 Cents ; 1 Quarter = 25 Cents)

A. 1/5
B. 1/20
C. 1/2
D. 19/20
E. 4/5

3 Dimes, 3 Quarters (3D, 3Q)

If we take only 1 quarter and all 3 dimes, we make exactly 55 cents. But we need more than 55 cents so we must take at least 2 quarters.

2 ways of making more than 55 cents:

Q, Q, D, D -> Probability = (3/6)*(3/5)*2 = 3/5 (Note that probability of picking 4 is the same as probability of discarding 2, a Q and a D)

Q, Q, Q, D -> Probability = (3/6)*(2/5) = 1/5 (The probability of picking these 3 is the same as the probability of discarding 2 Ds)

Total probability = 3/5 + 1/5 = 4/5

_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 21 May 2018
Posts: 3
There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chose  [#permalink]

### Show Tags

10 Dec 2019, 00:02
2
2 combinations of dimes & quarters are possible
1 dime & 3 quarters >>3c1*3c3 = 3 combinations
2 dimes & 2 quarters >> 3c2*3c2 = 9 combinations
Total 12 combinations

Sample space = 6c4 = 15 combinations

probability = 12/15=4/5

Ans:E
There are 3 dimes and 3 quarters in a coin purse. If 4 coins are chose   [#permalink] 10 Dec 2019, 00:02
Display posts from previous: Sort by