Please review the solutions to the previous set. Then, start working on this set.
1. Vishal had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Vishal took 6 minutes to walk half way to school. How many minutes did it take Vishal to get from home to school?
2. Three darts are thrown at a standard dartboard containing the numbers 1 through 20. Assuming that an equal probability exists of hitting any of the numbers, and assuming that each of the three darts land on one of the numbers on the dartboard, find the probability that the sum of the numbers hit by the three darts is greater than 57. Express your answer as a common fraction.
3. The perimeter of triangle ABC is 62 feet. The lengths of its sides are AB = 4x + 6, BC = 2x – 3, and AC = 3x + 5 feet. Which angle is the triangle’s largest interior angle, angle A, B, or C?
4. Grace and Simran play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Grace moves clockwise and Simran, counterclockwise. In a turn of the game, Grace moves 5 points clockwise and Simran moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
5. Neha rolled two fair six-sided dice. What is the probability that the product of the two numbers is a composite number? Express your answer as a common fraction.
1) 8 minutes
ReplyDelete2) 1/20
3) working on it
4) 6 turns
5) 5/12
Great work, Vishal! I will verify your answers after I receive a few more responses.
ReplyDelete1) 8 mins
ReplyDelete2) 1/5
3) angle C
4) 3 turns
5) 1/2
Nidhi, you've been doing a wonderful job. Keep up the good work!
ReplyDeleteVishal and Nidhi, check over your work and see if you have any errors. Then re-enter your answers. I'll verify your answers by late evening or tomorrow.
Ok thanks!
ReplyDelete1) 8 min
ReplyDelete2) 1/20 not so sure
3) angle c
4) 6 turns
5) 4/5
1) 8 mins
ReplyDelete2) 1/5
3) angle C
4) 3 turns (not very sure)
5) 1/2
1. 8 min.
ReplyDelete2. 1/385
3. angle c
4. 6 turns
5. 5/7
Agni, I posted a comment a couple days ago with my answers, but today they aren't to be seen. Anyway, here are my answers:
ReplyDelete1) 8 minutes
2) 1/20
3) Angle C
4) 6 turns
5) 1/2
1. 8 minutes
ReplyDelete2. 1/20
3.angle C
4. 3 turns
5. 1/2
You guys are doing a wonderful job! All of you have correct answers to problems 1 and 3, but you guys need to look at problems 2 and 5 again.
ReplyDeleteNidhi and Aditi, also check over your work for problem 4 again.
Would you all like to try the missed problems over again, or should I post the solutions for the set?
Vishal, you are entitled to post your problem for the marathon run.
ReplyDeleteWe would like to try the missed problems.
ReplyDelete3) 1/800
ReplyDelete5) 29/36
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ReplyDeleteI am working on Question 2
ReplyDeleteI think it is 1/20
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ReplyDeleteAvanthika, nice work. Try problems 2 and 5 again.
ReplyDeleteYour answer to problem 4 is correct, but the reasoning you provided is not proper. The answer should not rely on what position the girls are in, rather on how many moves it takes them to land on the same number.
Vishal, it's nice to see that you re-tried problems 2 and 5 and got the correct answers. Good job!
ReplyDeleteThe marathon problem is posted. Let's keep it running!
ReplyDelete1- 8 minutes
ReplyDelete2- 1/800
3- Angle C
4- 6 Turns
5- 29/36
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ReplyDelete1) 8 minutes
ReplyDelete2) 1/800
3) Angle C
4) 6 turns
5) 29/36
Thanks agni
ReplyDelete1) 8 minutes
ReplyDelete2) 1/800
3) Angle C
4) 6 turns
5) 29/36
Well done, guys!
ReplyDeleteSolutions
(1) It will take 3 times less for him to go the second half, so it takes 6 + 6/3 = 8 minutes total.
(2) 58: (18,20,20) or (19,19,20)
59: (19,20,20)
60: (20,20,20)
There are a total of 10 combination out of total of 20³ = 8000, so 10/8000 = 1/800
(3) Adding the 3 sides of the triangle gives us 9x + 8 = 62, so x = 6. Then we plug x back in the 3 sides lengths, giving us:
AB = 30
BC = 9
AC = 23
Since the largest angle faces the largest side, angle C is the largest.
(4) Each turn they go 14 spaces altogether. The circle is divided into 12. We want the intersection. So we find LCM (12,14) which is 84. So they will meet after 84/14 = 6 moves.
(5) Only non-composite numbers which are product of numbers of 1 to 6 are: 1, 2, 3, 5. As 2, 3 and 5 can be gotten in 2 ways, and 1 in one way, and there are 36 possible products, the probability is 1 – 7/36 = 29/36.