CAT Questions

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The given number series 9, 19, 21, 43, 45, ... follows a pattern that

ALternately (x 2 + 1) and  (x 1 + 2)

9 

9 x 2 + 1 = 19

19 x 1 + 2 = 21

21 x 2 + 1 = 43

43 x 1 + 2 = 45

45 x 2 + 1 = 91

Hence, the next number in the given sequence is 91.

Bhubaneswar, the capital city of the state Odisha in India, is called as The Cathedral City of India and the Temple City of India. With Puri and Konark it forms the Golden Triangle, one of eastern India's most visited destinations.

Let the speed of the boat = p kmph

Let the speed of the river flow = q kmph

From the given data,

2 x 28p + q = 28p - q

=> 56p - 56q -28p - 28q = 0

=> 28p = 84q

=> p = 3q.

Now, given that if

$$\begin{gathered} 283q + 2q + 283q - 2q = 67260 \\ => 285q + 28q = 67260 \\ => q = 3 kmph \\ => x =3q = 9 kmph \end{gathered}$$

Hence, the speed of the boat = p kmph = 9 kmph and the speed of the river flow = q kmph = 3 kmph.

Because the letters are the same, concentrate on the number series, which is a simple 2, 3, 4, 5, 6 series, and follows each letter in order.

Let the cost price of a ball is Rs.x
Given, on selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls
The equation is :
17x - 720 = 5x
Solving the equation
we get x = 60
Therefore, cost price of a ball is Rs. 60.

How to find the years which have the same Calendars : 

 Leap year calendar repeats every 28 years. 

Here 28 is distributed as 6 + 11 + 11.

Rules:

a) If given year is at 1st position after Leap year then next repeated calendar year is Given Year + 6.

 b) If given year is at 2nd position after Leap year then next repeated calendar year is Given Year + 11.

 c) If given year is at 3rd position after Leap year then next repeated calendar year is Given Year + 11. 

Now, the given year is 2018

We know that 2016 is a Leap year.

2016  2017  2018  2019  2020

 LY    1st     2nd    3rd    LY

Here 2018 is at 2 nd position after the Leap year.

According to rule ( b) the calendar of 2018 is repeated for the year is 2018 + 11 = 2029.