Olympiad Test : Pattern - Class 6 MCQ

The solution involves examining a pattern in the figures:

• Figure 1: Calculate (112 ÷ 14) × 2 = 16.
• Figure 2: Calculate (168 ÷ 24) × 2 = 14.
• Figure 3: Calculate (144 ÷ 16) × 2 = 18.

The missing number is 18, which matches option C.

In the first figure: Calculate 4 × 6 and 18 × 3. Add them together:

• 4 × 6 = 24
• 18 × 3 = 54
• 24 + 54 = 78

In the Second figure: Compute 3 × 5 and 24 × 4. Then, sum them:

• 3 × 5 = 15
• 24 × 4 = 96
• 15 + 96 = 111

In the third figure: Find 2 × 7 and 21 × 4. Add these results:

• 2 × 7 = 14
• 21 × 4 = 84
• 14 + 84 = 98

Therefore, correct Answer is 98.

To solve the pattern, observe the following calculations:

• In Figure I: 1 + 2 = 3 → 3² = 9
• In Figure II: 3 + 4 = 7 → 7² = 49
• Next: 5 + 4 = 9 → 9² = 81
• Finally: 7 + 6 = 13 → 13² = 169

Therefore, the missing number is 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 
Therefore, Correct Answer is 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
Therefore, Correct Answer is 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 
Therefore, Correct Answer is 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 
Therefore, Correct Answer is 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
Therefore, Correct Answer is 441.

From Figure I: 2 × 4 × 8 × 6 = 384
From Figure II: 3 × 5 × 6 × 7 = 630
From Figure III: 3 × 8 × 7 × 9 = 1512 
Therefore, Correct Answer is 1512.

From figure I:
√25 + √16 + √81 + √1 = 5 + 4 + 9 + 1 = 19
⇒ 19² = 361

From figure II:
√81 + √64 + √49 + √4 = 9 + 8 + 7 + 2 = 26
⇒ 26² = 676

From figure III:
√121 + √49 + √64 + √36 = 11 + 7 + 8 + 6 = 32
⇒ 32² = 1024
Therefore, Correct Answer is 1024.

From figure I:
√49 + √81 + √36 + √64 = 7 + 9 + 6 + 8 = 30

From figure II:
√81 + √25 + √16 + √49 = 9 + 5 + 4 + 7 = 25

From figure III:
√121 + √81 + √25 + √49 = 11 + 9 + 5 + 7 = 32
Therefore, Correct Answer is 32.

From figure I: 7 × 2 × 3 = 42
From figure II: 8 × 3 × 2 = 48
From figure III: 7 × 6 × 4 = 168
Therefore, Correct Answer is 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 
Therefore, Correct Answer is 80.

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

In the first row A, D, G:

• From A to D: 2 letters difference (B, C).
• From D to G: 2 letters difference (E, F).

In the second row D, I, N:

• From D to I: 4 letters difference (E, F, G, H).
• From I to N: 4 letters difference (J, K, L, M).

In the third row I, P, ?:

• From I to P: 6 letters difference (J, K, L, M, N, O).
• Therefore, the next letter after P, moving 7 letters forward (Q, R, S, T, U, V, W), is W.

Thus, the correct answer is W.

In the first row, 8 × 2 + 17 = 16 + 17 = 33,
In the second row; 12 × 2 + 5 = 24 + 5 = 29
In the third row; missing number 10 × 2 + 13 = 20 + 13 = 33.

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

Let's analyze the given sequence: 2, 6, 12, 20, __, 42.

We can observe the pattern by finding the differences between consecutive numbers:

• 6 - 2 = 4
• 12 - 6 = 6
• 20 - 12 = 8

The differences are increasing by 2 each time (4, 6, 8).

Following this pattern, the next difference should be 10.

So, the next number is:

20 + 10 = 30

Therefore, the missing number is 30.

In the figure,
9 × 7 = 63
7 × 2 = 14
2 × 15 = 30
15 × 9 = 135
∴ The missing term must be 135.
Hence, (c) is the correct answer.

In column 1:

⇒ 9 × 5 = 45 - 2 = 43

And,

In column 2:

⇒ 7 × 4 = 28 - 2 = 26

Similarly,

In column 3:

⇒ 9 × 7 = 63 - 2 = 61 

Hence, the correct answer is "61".