CAT Questions

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$$\begin{gathered} ?2 = 2×78-21+8+49-148 \\ = 57 - 21 \\ =36 \\ => ? = ±6 \end{gathered}$$

48, 54, 63, 81 and 105 are divisible by 3 but not 35.

Given Number series is :

3   4   14   48   576   27648

It follows a pattern that,

3

4

4 x 3 = 12   but not 14

12 x 4 = 48

48 x 12 = 576

576 x 48 = 27648

Hence, the odd one in the given Number Series is 14.

The series given follow the pattern

+2, +2+4, +2+4+6, +2+4+6+8, +2+4+6+8+10,...

Here ? = 7 + 2 + 4 = 13.

Water in 60 gm mixture=60 x 75/100 = 45 gm. and Milk = 15 gm.

After adding 15 gm. of water in mixture, total water = 45 + 15 = 60 gm and weight of a mixture = 60 + 15 = 75 gm.

So % of water = 100 x 60/75 = 80%.

Given series is 

12        16         32          68         ?

Here it follows a pattern that,

12

12 + (2x2) = 16

16 + (4x4) = 32

32 + (6x6) = 68

68 + (8x8) = 132

6th to the left of 17th letter to the right of 7th letter from the left = 6th to the left of (17+7 =) 24th letter from the left = (24-6 =) 18th letter from the left.

Thus, we have to count from the left and we have to find out 18th letter from the left that falls into the second section of English alphabet.

Here, both the first half and the second half of the English alphabet have been reversed and we have to count from the left end, then the required letter can be found out using the formula given below. Suppose , the first and the second reversed sections of the English alphabet are α and  βrespectively.Then,

  The required letter = 2α+β+1-(required position of letter from left side)

Therefore, The required letter = 26 + 13 + 1 - 18 = 22 = V

The given series follows a pattern that,

19 x 19 x 19 = 6859

18 x 18 x 18 = 5832

17 x 17 x 17 = 4913

16 x 16 x 16 = 4096

15 x 15 x 15 = 3375

So, the missing number in the given series = 4913