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QOTD#12 On Monday, Janice started training for a marathon
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01 Nov 2016, 17:26
01 Nov 2016, 17:26
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81% (01:15) correct
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On Monday, Janice started training for a marathon and ran one mile that day. On Tuesday, Janice ran one mile more than she did on Monday. She continues this training process for 12 days. The sum of the total number of miles Janice ran has how many distinct prime factors?
Drill 3
Question: 9
Page: 290
Question: 9
Page: 290
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Re: QOTD#12 On Monday, Janice started training for a marathon
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01 Nov 2016, 17:33
01 Nov 2016, 17:33
Expert Reply
Explanation
Adding the numbers together won’t take long, but there is a shortcut to this problem.Match up the smallest number of miles (1) with the largest number of miles (12), and then the second smallest (2) with the second largest (11), etc. until all the numbers are matched up.
1 12
2 11
3 10
4 9
5 8
6 7
The sum of each of these 6 pairs is 13, which means you could multiply 13 by 6 = 78 to get the total number of miles. Next, find the prime factors of 78. We already know it’s divisible by 13 and 6 (because we had multiplied those together to get 78). Given that 13 is prime, you now need to find the prime factors of 6, which are 2 and 3. All together we have 3 prime factors at the bottom of the prime factor tree, so that’s our answer.
Hence 3 is the correct answer.
test.jpg [ 4.32 KiB | Viewed 9859 times ]
Adding the numbers together won’t take long, but there is a shortcut to this problem.Match up the smallest number of miles (1) with the largest number of miles (12), and then the second smallest (2) with the second largest (11), etc. until all the numbers are matched up.
1 12
2 11
3 10
4 9
5 8
6 7
The sum of each of these 6 pairs is 13, which means you could multiply 13 by 6 = 78 to get the total number of miles. Next, find the prime factors of 78. We already know it’s divisible by 13 and 6 (because we had multiplied those together to get 78). Given that 13 is prime, you now need to find the prime factors of 6, which are 2 and 3. All together we have 3 prime factors at the bottom of the prime factor tree, so that’s our answer.
Hence 3 is the correct answer.
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test.jpg [ 4.32 KiB | Viewed 9859 times ]
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Re: QOTD#12 On Monday, Janice started training for a marathon
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25 Nov 2016, 17:28
25 Nov 2016, 17:28
2
sandy wrote:
On Monday, Janice started training for a marathon and ran one mile that day. On Tuesday, Janice ran one mile more than she did on Monday. She continues this training process for 12 days. The sum of the total number of miles Janice ran has how many distinct prime factors?
Day 1: 1 mile
Day 2: 2 miles
Day 3: 3 miles
Day 4: 4 miles
.
.
.
Day 12: 12 miles
Total mileage = 1 + 2 + 3 +....+ 11 + 12
Useful formula: 1 + 2 + 3 + 4 + ...+ n = (n)(n + 1)/2
So, 1 + 2 + 3 +....+ 11 + 12 = (12)(12 + 1)/2
= (12)(13)/2
= (6)(13)
= 78
The sum of the total number of miles Janice ran has how many distinct prime factors?
We need to find the prime factorization of 78..
78 = (6)(13)
= (2)(3)(13)
There are three prime factors.
Answer: 3
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