A dart board is made of three concentric circles such that hitting the

Question

A dart board is made of three concentric circles such that hitting the area of the innermost circle will give 10 points, hitting the area of the second circle excluding the area of the innermost circle will give 5 points and hitting the area of the outermost circle excluding the area of the second circle will give 2 points. If in 6 shots 15 points have been earned then in how many ways could that have been done?

A. 64

B. 56

C. 50

D. 36

E. 26

Are You Up For the Challenge: 700 Level Questions

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Official Answer

B

A. 64

B. 56

C. 50

D. 36

E. 26

Are You Up For the Challenge: 700 Level Questions

chetan2u · Answer

SO the numbers that can be earned are 5, 2 and 10 in 6 shots..

(1) If he gets a 10 in one shot, only possibility is that he gets a 5 in one more and remaining are wash-out, that is no point.
10, 5, 0, 0, 0, 0 ........ways = 6!/4!=30

(II) If he gets a 5 in one shot, two possibilities-
a) he gets a 5 in two more and remaining are wash-out, that is no point.
5, 5, 5, 0, 0, 0 ........ways = 6!/3!3!=20
a) he gets a 2 in remaining 5.
5, 2, 2, 2, 2, 2 ........ways = 6!/5!=6

Total 20+30+6=56

B

GMATWhizTeam · Answer

Solution 
We can get a 15 in 6 shots in the following three cases:
 • Case 1: we get (10, 5, 0, 0, 0, 0, 0)
 o Total number of ways in which we can get one 10, one 5 and four 0s in 6 shots  = 6C2*1 * 2! = 30  ways 
• Case 2: we get (5, 5, 5, 0, 0, 0)
 o Total number of ways in which we can get, three 5s and three 0s in 6 shots  = 6C3*1 = 20  ways 
• Case 3: We get (2, 2, 2, 2, 2, 5)
 o Total number of ways in which we can get five 2s and one five  = 6C1*1 = 6  ways 
• Thus, the total number of ways to earn 15 points in 6 shots  = 30 + 20 + 6 = 56  
Thus, the correct answer is  Option B.

Lipun · Answer

Since the total score is 15 and the possible scores are 2, 5, and 10, one of the scores must be 5 (you can use the even odd concept, but here it is clearly evident).
=> The rest of the sum must be 10.
1) 10 can be obtained in only way using 10 directly. So, the scores becomes   = 6!/4! combinations = 30
2) 10 can be obtained using 5 2s. Possible combination   = 6 combinations
3) 10 can be obtained using 2 5s. Possible combination   = 6!/(3!*3!) = 20

Total: 20+30+6=56

Ans: B

vipulshahi · Answer

Points on hitting inner most circle = 10
Points on hitting outer circle excluding inner circle = 5 
Points on hitting outer most circle = 2

in 6 shots = 15 points

n*10 + m*5 + q*2 = 15

1) In first case, its possible that ( 2,2,2,2,2,5)  
Total no. of ways = 6C1 = 6
2) In second case, its possible that ( 5,5,5,,0,0,0)  
Total no. of ways = 6C3 = 20
3) In third case, its possible that ( 10,5,0,0,0,0)  
Total no. of ways = 6C2 * 2! = 30

Total no. of ways = 30+20+6 = 56

Answer: B

HoneyLemon · Answer

A dart board is made of three concentric circles such that hitting the area of the innermost circle will give 10 points, hitting the area of the second circle excluding the area of the innermost circle will give 5 points and hitting the area of the outermost circle excluding the area of the second circle will give 2 points. If in 6 shots 15 points have been earned then in how many ways could that have been done?

A. 64

B. 56

C. 50

D. 36

E. 26

Are You Up For the Challenge: 700 Level Questions

Show Answer

Official Answer

B

the points that can be earned are 5, 2 and 10

in 6 shots 15 points .

Case 1 :   
 10 , 5 ,0 ,0,0,0 .

No of ways = 6! / 4! = 30

Case 2 :

5,5,5,0,0,0

No of ways = 6! / (3! * 3!)= 20

Case 3 :

5 ,2,2,2,2,2

No of ways = 6! / (5!)= 6

Total no of ways 20+30+6=56

B is the ans .

sambitspm · Answer

Kindly see the attachment.
B = 56

hacorus · Answer

Bunuel, are you sure the prompt is complete? Shouldn't it mention that missing the board means 0 points?

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