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A man is a climbing up a 100-foot high mountain. Each day...

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A man is a climbing up a 100-foot high mountain. Each day...

by Vincen » Wed Feb 21, 2018 1:44 am
A man is a climbing up a 100-foot high mountain. Each day he climbs 30 feet but then falls 20 feet. How long does it take him to reach the top assuming that once he reaches the top he does not fall?

A. 7
B. 8
C. 9
D. 10
E. 11

The OA is B.

Experts, is there a fast way to solve this PS question? What is the best approach? Thanks in advanced.
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by Jay@ManhattanReview » Mon Mar 12, 2018 2:40 am
Vincen wrote:A man is a climbing up a 100-foot high mountain. Each day he climbs 30 feet but then falls 20 feet. How long does it take him to reach the top assuming that once he reaches the top he does not fall?

A. 7
B. 8
C. 9
D. 10
E. 11

The OA is B.

Experts, is there a fast way to solve this PS question? What is the best approach? Thanks in advanced.
On each day except the final day, the man climbs 30 - 20 = 10 feet.

On the final day, he would climb between 10 to 30 feet since it is given that once he reaches the top, he does not fall.

Let's assume that on the final day he climbed 30 feet, thus, he must have climbed 100 - 30 = 70 feet on the previous days. Since on each day, he climbed 10 feet and if 70 is divisible by 10, we can conclude that he climbed 30 feet on the final day. Now since 70 is divisible by 10, thus, he climbed for 70/10 = 7 days excluding the final day.

Thus, it takes 7 + 1 = 8 days to reach the top.

The correct answer: B

Hope this helps!

-Jay
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by GMATGuruNY » Mon Mar 12, 2018 3:00 am
Vincen wrote:A man is a climbing up a 100-foot high mountain. Each day he climbs 30 feet but then falls 20 feet. How long does it take him to reach the top assuming that once he reaches the top he does not fall?

A. 7
B. 8
C. 9
D. 10
E. 11
Look for a PATTERN.
Every day the man climbs 20 feet from the height of the preceding day, then falls 20 feet.

1st day --> climb = 0+30 = 30, fall = 30-20 = 10.
2nd day --> climb = 10+30 = 40, fall = 40-20 = 20.
3rd day --> climb = 20+30 = 50, fall = 50-20 = 30.

As indicated by the values in blue, every day the climb increases by 10.
Thus:
4th day --> climb = 60
5th day --> climb = 70
6th day --> climb = 80
7th day --> climb = 90
8th day --> climb = 100.

The correct answer is B.
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by Scott@TargetTestPrep » Tue Mar 13, 2018 4:18 pm
Vincen wrote:A man is a climbing up a 100-foot high mountain. Each day he climbs 30 feet but then falls 20 feet. How long does it take him to reach the top assuming that once he reaches the top he does not fall?

A. 7
B. 8
C. 9
D. 10
E. 11
Notice that on the last day, he will not fall. So on the last day he will climb 30 feet, which means he has 70 feet to climb before the last day. For those 70 feet, each day the man climbs a net distance of 30 - 20 = 10 feet, so it will take 70/10 = 7 days to climb those 70 feet. Since he needs one more day to climb the last 30 feet, he needs a total of 8 days to climb to the top.

Answer: B

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