Quantitative Aptitude - Arithmetic Ability Questions

Here the given number series is 5  11  21  44  ?  175

Now the given series follows a pattern, that

x2 + 1, x2 - 1, x2 + 2, x2 - 2, x2 + 3, x2 - 3,...

Then the missing number is x2 - 2

= 44 x 2 - 2 = 88 - 2 = 86

Hence, the missing number in the number series is 86.

Let the two conditioners be A and B

'A' cools at 40min

'B' at 45min

Together = (a x b)/(a + b)

= (45 x 40)/(45 + 40)

= 45 x 40/85

= 21.1764

= 22 min (approx).

1 x 1 + 1 x 1 = (1 + 1) = 2

2 x 2 + 2 x 2 = (4 + 4) = 8

8 x 3 + 3 x 3 = (24 + 9) = 33

33 x 4 + 4 x 4 = (132 + 16) = 148

148 x 5 + 5 x 5 = (740 + 25) = 765.

Suppose B joined for x months . Then,  ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.

So, B joined for 8 months.

Let the numbers 13a and 13b.

Then, 13a x 13b = 2028

=>ab = 12.

Now, the co-primes with product 12 are (1, 12) and (3, 4).

[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]

So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).

Clearly, there are 2 such pairs.

Speed =   6005×60 m/sec= 2 m/sec = 2 x (18/5) km/hr = 7.2 km/hr