Olympiad Test : Pattern - Class 6 MCQ

From figure 1  (112 ÷ 14) × 2 = 16
From figure 2  (168 ÷ 24) × 2 = 14
From figure 3  (144 ÷ 16) × 2 = 9 × 2 = 18 

From figure 1  4 × 6 + 18 × 3 = 24 + 54 = 78
From figure 2  3 × 5 + 24 × 4 = 15 + 96 = 111
From figure 3  2 × 7 + 21 × 4 = 14 + 84 = 98 

From figure I 1 + 2 = 3 → 3² = 9
From figure II 3 + 4 = 7 → 7² = 49
5 + 4 = 9 → 9² = 81
7 + 6 = 13 →13² = 169

From figure I    2² × 3² = 4 × 9 = 36
From figure II   4² × 5² = 16 × 25 = 400
From figure III  6² × 7² = 36 × 49 = 1764 

From figure I   (14 + 24) – 2 = 38 – 2 = 36
From figure II  (23 + 35) – 3 = 58 – 3 = 55
From figure III (34 + 45) – 4 = 79 – 4 = 75

From figure I   5 × 2 + 1 × 3 = 10 + 3 = 13
From figure II  2 × 4 + 5 × 3 = 8 + 15 = 23
From figure III 3 × 4 + 5 × 7 = 12 + 35 = 47 

From figure I   7 × 4 – 5 × 3 = 28 – 15 = 13
From figure II  9 × 6 – 7 × 3 = 54 – 21 = 33
From figure III 8 × 9 – 7 × 5 = 72 – 35 = 37 

From figure I  1 + 7 + 3 + 2 = 13 → 13² = 169
From figure II  1 + 5 + 2 + 7 = 15 → 15² = 225 
From figure III  2 + 7 + 3 + 9 = 21 → 21² = 441

2 × 4 × 8 × 6 = 384
3 × 5 × 6 × 7 = 630
3 × 8 × 7 × 9 = 1512 

From figure I   7 × 2 × 3 = 42
From figure II  8 × 3 × 2 = 48
From figure III 7 × 6 × 4 = 168

From figure I 1 × 5 + 3 × 4 = 5 + 12 = 17
From figure II 1 × 7 + 4 × 6 = 7 + 24 = 31
From figure III 4 × 6 + 7 × 8 = 24 + 56 = 80 

In the first row, 16 × 14 – 14 = 210
In the second row, 14 × 12 – 12 = 156 
∴ Missing number = 12 × 10 – 10 = 110 

If you observe there are two alphabets difference between ADG

Similarly, there are four alphabets difference between DIN

And, there are 6 alphabets difference between I and P, next alphabet will be the 7th alphabet after P.

A (2 alphabets) D (2 alphabets) G

D (4 alphabets) I (4 alphabets) N

I (6 alphabets) P (6 alphabets) W

So the answer is W

In the first row, 8 × 2 + 17 = 33°,
In the second row; 12 × 2 + 5 = 29 
∴ Missing number = 10 × 2 + 13 = 33 

In the first row, 2 + 2 = 4 and 44 = 256 In the third row, 4 + 2 = 6 and 66 = 46656
In the second row, 3 + 2 = 5
So, missing number = 55 = 3125 

In the first row, 11 × 2 + (6 ÷ 2) = 25
In the second row, 6 × 2 + (8 ÷ 2) = 16
∴ In the third row, missing number
= 5 × 2 + (12 ÷ 2) = 10 + 6 = 16

In the first row, (85 ÷ 5) + 3 = 20
In the second row, (126 ÷ 6) + 3 = 24 
∴ In the third row, missing number
= (175 ÷ 7) + 3 
= (25 + 3) = 28 

Find the missing number, let's analyze the pattern in the sequence:

1. The given sequence is: 2, 6, 12, 20, __, 42

2. Now, let's find the differences between consecutive terms:

   
3. The differences are 4, 6, 8.

4. Notice that these differences are increasing by 2 each time (4, 6, 8). So, the next difference should be 10.

5. Therefore, add 10 to the last known term (20):

   

6. The missing number is 30.

7. The complete sequence is 2, 6, 12, 20, 30, 42.