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A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?

  • a)
    30

  • b)
    24

  • c)
    20

  • d)
    60

Correct answer is option 'A'. Can you explain this answer?
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A red light flashes three times per minute and a green light flashes f...
A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. So red light fashes after every 1/3 min and green light flashes every 2/5 min. LCM of both the fractions is 2 min.

Hence, they flash together after every 2 min. So in an hour they flash together 30 times.
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Solution:
Given, 25 * 36 * 52

Prime factorization of 25 = 5^2
Prime factorization of 36 = 2^2 * 3^2
Prime factorization of 52 = 2^2 * 13

So, 25 * 36 * 52 = 2^4 * 3^2 * 5^2 * 13

To find perfect squares, we need even powers of all prime factors.

Number of ways to choose the power of 2: 5 ways (0, 2, 4, 6, 8)
Number of ways to choose the power of 3: 3 ways (0, 2, 4)
Number of ways to choose the power of 5: 3 ways (0, 2, 4)
Number of ways to choose the power of 13: 2 ways (0, 2)

So, the total number of factors with even powers of prime factors = 5 * 3 * 3 * 2 = 90

Since we need perfect squares, we need to exclude the factors with odd powers of prime factors.

Number of ways to choose the power of 2: 2 ways (1, 3)
Number of ways to choose the power of 3: 2 ways (1, 3)
Number of ways to choose the power of 5: 2 ways (1, 3)
Number of ways to choose the power of 13: 1 way (1)

So, the total number of factors with odd powers of prime factors = 2 * 2 * 2 * 1 = 8

Therefore, the total number of factors that are perfect squares = 90 - 8 = 82

Hence, the correct option is (B) 24.
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Directions for Questions: Answer the questions on the basis of the information given below.From ISBT, buses ply on 6 different routes viz. 414, 413, 427, 966, 893 and 181 at an interval of 10 min, 10 min, 12 min, 15 min, 20 min and 30 min, not necessarily in that order, to four different destinations viz. Mehrauli, Badarpur, Uttam Nagar and Azadpur. There is at least one bus for each destination. Further information is also known:i. Two buses to the same destination cannot start at the same time.ii. If the timings of two buses plying different routes but heading towards the same destination clash, then the bus of the route number having the shorter time interval will skip this journey.iii. Buses on two different routes ply between ISBT and Mehrauli.iv. The difference between the time intervals of a route to Mehrauli and Uttam Nagar is equal to the difference between the time intervals of the two routes to Uttam Nagar.v. Buses on a route to Mehrauli leaves after every 10 min.vi. 414 leaves for Badarpur after every 30 min.vii. Time intervals between two different routes heading towards the same destination cannot be equal.viii. Buses on one of the routes to Uttam Nagar leave after every 15 min.ix. Buses to any destination can leave from ISBT with an interval of at least one minute or an integral multiple of one minute.(2015)Q.If 427 leaves to Mehrauli after every 10 min, then in a given hour a minimum of how many buses can ply on route 427?

Directions for Questions: Answer the questions on the basis of the information given below.From ISBT, buses ply on 6 different routes viz. 414, 413, 427, 966, 893 and 181 at an interval of 10 min, 10 min, 12 min, 15 min, 20 min and 30 min, not necessarily in that order, to four different destinations viz. Mehrauli, Badarpur, Uttam Nagar and Azadpur. There is at least one bus for each destination. Further information is also known:i. Two buses to the same destination cannot start at the same time.ii. If the timings of two buses plying different routes but heading towards the same destination clash, then the bus of the route number having the shorter time interval will skip this journey.iii. Buses on two different routes ply between ISBT and Mehrauli.iv. The difference between the time intervals of a route to Mehrauli and Uttam Nagar is equal to the difference between the time intervals of the two routes to Uttam Nagar.v. Buses on a route to Mehrauli leaves after every 10 min.vi. 414 leaves for Badarpur after every 30 min.vii. Time intervals between two different routes heading towards the same destination cannot be equal.viii. Buses on one of the routes to Uttam Nagar leave after every 15 min.ix. Buses to any destination can leave from ISBT with an interval of at least one minute or an integral multiple of one minute.(2015)Q.Which of the following statements is necessarily TRUE?

Directions for Questions: Answer the questions on the basis of the information given below.From ISBT, buses ply on 6 different routes viz. 414, 413, 427, 966, 893 and 181 at an interval of 10 min, 10 min, 12 min, 15 min, 20 min and 30 min, not necessarily in that order, to four different destinations viz. Mehrauli, Badarpur, Uttam Nagar and Azadpur. There is at least one bus for each destination. Further information is also known:i. Two buses to the same destination cannot start at the same time.ii. If the timings of two buses plying different routes but heading towards the same destination clash, then the bus of the route number having the shorter time interval will skip this journey.iii. Buses on two different routes ply between ISBT and Mehrauli.iv. The difference between the time intervals of a route to Mehrauli and Uttam Nagar is equal to the difference between the time intervals of the two routes to Uttam Nagar.v. Buses on a route to Mehrauli leaves after every 10 min.vi. 414 leaves for Badarpur after every 30 min.vii. Time intervals between two different routes heading towards the same destination cannot be equal.viii. Buses on one of the routes to Uttam Nagar leave after every 15 min.ix. Buses to any destination can leave from ISBT with an interval of at least one minute or an integral multiple of one minute.(2015)Q.If condition (iii) is not there, then what can be the minimum difference between the time intervals between the buses plying to Uttam Nagar?

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A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?a)30b)24c)20d)60Correct answer is option 'A'. Can you explain this answer?
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