CAT Questions

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Nepalese President Bidya Devi Bhandari is arriving in New Delhi on a five-day visit to India. This will be Bhandari's first foreign trip after assuming the office in October 2015, following the promulgation of the new Constitution in Nepal.

Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.
[-ve sign means emptying]

The third pipe alone can empty the cistern in 100 min.

The number of words beign with A is 4! 

The number of words beign with E is 4! 

The number of words beign with M is 4! 

The number of words beign with R is 4!

Number of words beign with VA is 3! 

Words beign with VE are VEAMR 

VEARM

VEMAR

VEMRA

VERAM

VERMA 

Therefore, The Rank of the word VERMA = 4 x 4! + 3! + 6 = 96 + 6 + 6 =108             

Total no of ways = (14 – 1)! = 13!

Number of favorable ways = (12 – 1)! = 11!

So, required probability = 11!×3!13! = 39916800×66227020800 = 24625

The first train covers 180 kms in 5 hrs

=> Speed = 180/5 = 36 kmph

Now the second train covers the same distance in 1 hour less than the first train => 4 hrs

=> Speed of the second train = 180/4 = 45 kmph

Now, required difference in distance in 1 hour = 45 - 36 = 9 kms.

Let x, x+2, x+4, x+6, x+8 and x+10 are six consecutive odd numbers.

Given that their average is 52

Then, x + x+2 + x+4 + x+6 + x+8 + x+10 = 52×6

6x + 30 = 312

x = 47

So Product = 47 × 57 = 2679

Here the given series follows a pattern that,

2² - 0 = 4  

3² - 1 = 8  

4² - 2 = 14

5² - 3 = 22

6² - 4 = 32

Hence, the missing number is 32

Method 2 ::

The difference between 4 and 8 is 4, the difference between 8 and 14 is 6, the difference between 14 and 22 is 8. So the next difference between 22 and the next number will be 10 since it follows (4,6,8,10 - add +2 each time)

Hence, 22 + 10 = 32 is the missing number.

Speed on return trip = 150% of 50 = 75 km/hr.

Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.