CAT Questions

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Given nuber series is 15, 30, ? , 40, 8, 48 

Here the number series follows a pattern that

15

15 x 2 = 30

30 ÷ 3 = 10

10 x 4 = 40

40 ÷ 5 = 8

8 x 6 = 48

Hence, the missing number in the series is 10.

The earth moves round the sun.

Apply a3 + b3 + c3 - 3abca2 + b2 + c2 - ab - bc - ca = a + b + c

Hence the answer is  1.5 + 4.7 + 3.8 = 10.

Variable means changes or shifts timely. Hence, synonym of variable is shifting.

25% of 25% means

25/100 of 25/100

i.e, 1/4 of 1/4

or in other words 1/4 x 1/4=1/16

Hence, the answer is 1/16 = 0.0625.

Let A, B, C be the respective events of solving the problem and A , B, C be the respective events of not solving the problem. Then A, B, C are independent event

∴A, B, C are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

 PA=12, PB=23, PC= 34

∴ P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  = PA∩B∩C 

                  = PAPBPC         ∵ A, B, C are Independent                       

                  =  12×23×34  

                  = 14  

Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                = 1-14= 3/4

Here the given series is 396, 462, 572, 427, 671, 264.

In all the terms, the middle digit is the sum of first and third digit except 427.

So the Odd number in the given series is 427.