Mental Ability Test (Questions 41 – 45)
Direction: Out of nine cells of a square, one cell is left blank (?). Discover the pattern governing the numbers in the grid to find the correct alternative for the blank cell.
Q41. Find the missing number (?) in the matrix:
| 5 | 47 | 13 |
| 18 | 14 | 18 |
| 8 | 2 | ? |
Figure 41: 3x3 Number Matrix
Correct Answer: (a) 3
Explanation:
Observe the relationship between the numbers in each column:
Observe the relationship between the numbers in each column:
- Column 1: $(18 - 8) \div 2 = 10 \div 2 = 5$
- Column 2: $(14 - 2) \times 4 - 1 = 47$ or $(14 + 2) \times 3 - 1 = 47$
- Row 1: $5 + 13 = 18 \implies 47 - 18 = 29$
- Row 2: $18 + 18 = 36 \implies 36 - 14 = 22$
- Row 3: Applying column logic $(18 - ?) \times 2 - 1 = 29 \implies 18 - 15 = 3$.
Q42. Find the missing number (?) in the matrix:
| 3 | 4 | 49 |
| 7 | 3 | 100 |
| 4 | ? | 64 |
Figure 42: 3x3 Number Matrix
Correct Answer: (d) 4
Explanation:
Examine each row from left to right:
$(4 + ?)^2 = 64$
Since $\sqrt{64} = 8$:
$4 + ? = 8 \implies ? = 8 - 4 = 4$.
Examine each row from left to right:
- Row 1: $(3 + 4)^2 = 7^2 = 49$
- Row 2: $(7 + 3)^2 = 10^2 = 100$
$(4 + ?)^2 = 64$
Since $\sqrt{64} = 8$:
$4 + ? = 8 \implies ? = 8 - 4 = 4$.
Q43. Find the missing number (?) in the matrix:
| 9 | 1 | 8 |
| 7 | ? | 4 |
| 10 | 4 | 6 |
Figure 43: 3x3 Number Matrix
Correct Answer: (a) 3
Explanation:
Analyze the numbers along each row:
$7 - ? = 4 \implies ? = 7 - 4 = 3$.
Analyze the numbers along each row:
- Row 1: $9 - 1 = 8$ (First number minus second number equals third number)
- Row 3: $10 - 4 = 6$
$7 - ? = 4 \implies ? = 7 - 4 = 3$.
Q44. Find the missing number (?) in the matrix:
| 3 | 4 | 5 |
| 8 | 6 | ? |
| 12 | 5 | 13 |
Figure 44: 3x3 Number Matrix
Correct Answer: (a) 10
Explanation:
Each row forms a Pythagorean triple ($a^2 + b^2 = c^2$):
$8^2 + 6^2 = 64 + 36 = 100 = 10^2$
So, the missing number is 10.
Each row forms a Pythagorean triple ($a^2 + b^2 = c^2$):
- Row 1: $3^2 + 4^2 = 9 + 16 = 25 = 5^2$
- Row 3: $12^2 + 5^2 = 144 + 25 = 169 = 13^2$
$8^2 + 6^2 = 64 + 36 = 100 = 10^2$
So, the missing number is 10.
Q45. Find the missing number (?) in the matrix:
| 10 | 2 | 5 |
| 12 | 3 | 2 |
| 45 | ? | 5 |
Figure 45: 3x3 Number Matrix
Correct Answer: (a) 3
Explanation:
Look at the multiplication pattern in each row:
Look at the multiplication pattern in each row:
- Row 1: $10 \div 2 = 5$ or $2 \times 5 = 10$
- Row 2: $12 \div 3 = 4$, and $4 \div 2 = 2$ or $(12 \div 3) \times 2 = 8$
- Column 1: $(10 \times 12) \div 8 \dots$
- Row Operations: First number = Second number $\times$ Third number $\times K$
For Row 1: $10 = 2 \times 5 \times 1$
For Row 2: $12 = 3 \times 2 \times 2$
For Row 3: $45 = ? \times 5 \times 3 \implies 45 = ? \times 15 \implies ? = 3$.
Mental Ability Test (Questions 46 – 55)
Direction: In each of the following questions, a number series is given with one term missing (?). Identify the rule pattern to find the correct alternative.
Q46. Complete the series: 2, 6, 12, 20, 30, 42, 56, ?
Correct Answer: (d) 72
Explanation:
Observe the sequence of terms expressed as $n \times (n + 1)$:
$56 + 16 = 72$.
Observe the sequence of terms expressed as $n \times (n + 1)$:
- $1 \times 2 = 2$
- $2 \times 3 = 6$
- $3 \times 4 = 12$
- $4 \times 5 = 20$
- $5 \times 6 = 30$
- $6 \times 7 = 42$
- $7 \times 8 = 56$
- $8 \times 9 = 72$
$56 + 16 = 72$.
Q47. Complete the series: 7, 26, 63, 124, 215, 342, ?
Correct Answer: (c) 511
Explanation:
Each number follows the pattern $n^3 - 1$:
Each number follows the pattern $n^3 - 1$:
- $2^3 - 1 = 8 - 1 = 7$
- $3^3 - 1 = 27 - 1 = 26$
- $4^3 - 1 = 64 - 1 = 63$
- $5^3 - 1 = 125 - 1 = 124$
- $6^3 - 1 = 216 - 1 = 215$
- $7^3 - 1 = 343 - 1 = 342$
- $8^3 - 1 = 512 - 1 = 511$
Q48. Complete the series: 3, 7, 6, 5, 9, 3, 12, 1, 15, ?
Correct Answer: (d) -1
Explanation:
This is an alternating series split into two independent sub-series:
$1 - 2 = -1$.
This is an alternating series split into two independent sub-series:
- 1st Series (Odd positions): 3, 6, 9, 12, 15 (Increasing by +3)
- 2nd Series (Even positions): 7, 5, 3, 1, ? (Decreasing by -2)
$1 - 2 = -1$.
Q49. Complete the series: 8, 3, 11, 14, 25, ?
Correct Answer: (c) 39
Explanation:
This series follows a Fibonacci-type addition pattern, where each term is the sum of the preceding two terms:
This series follows a Fibonacci-type addition pattern, where each term is the sum of the preceding two terms:
- $8 + 3 = 11$
- $3 + 11 = 14$
- $11 + 14 = 25$
- $14 + 25 = 39$
Q50. Complete the series: 31, 13, 45, 54, 36, ?
Correct Answer: (d) 63
Explanation:
The terms are grouped in pairs where the second term is formed by reversing the digits of the first term:
The terms are grouped in pairs where the second term is formed by reversing the digits of the first term:
- Pair 1: 31 → 13
- Pair 2: 45 → 54
- Pair 3: 36 → 63
Q51. Complete the series: 4, 13, 22, 31, 40, ?
Correct Answer: (c) 49
Explanation:
The series progresses with a constant common difference of +9:
The series progresses with a constant common difference of +9:
- $4 + 9 = 13$
- $13 + 9 = 22$
- $22 + 9 = 31$
- $31 + 9 = 40$
- $40 + 9 = 49$
Q52. Complete the series: 5, 12, 20, 29, 39, ?
Correct Answer: (d) 50
Explanation:
Check the pattern of increasing differences between consecutive numbers:
Check the pattern of increasing differences between consecutive numbers:
- $5 + 7 = 12$
- $12 + 8 = 20$
- $20 + 9 = 29$
- $29 + 10 = 39$
- $39 + 11 = 50$
Q53. Complete the series: 2, 5, 14, 41, 122, ?
Correct Answer: (d) 365
Explanation:
Each term is generated using the pattern $\text{Term} \times 3 - 1$:
$122 + 243 = 365$.
Each term is generated using the pattern $\text{Term} \times 3 - 1$:
- $2 \times 3 - 1 = 6 - 1 = 5$
- $5 \times 3 - 1 = 15 - 1 = 14$
- $14 \times 3 - 1 = 42 - 1 = 41$
- $41 \times 3 - 1 = 123 - 1 = 122$
- $122 \times 3 - 1 = 366 - 1 = 365$
$122 + 243 = 365$.
Q54. Complete the series: 2, 3, 10, 12, 18, 21, 26, 30, ?
Correct Answer: (a) 34
Explanation:
This sequence splits into two alternating sub-series:
$26 + 8 = 34$.
This sequence splits into two alternating sub-series:
- 1st Series (Odd positions): 2, 10, 18, 26, ? (Increasing by +8)
- 2nd Series (Even positions): 3, 12, 21, 30 (Increasing by +9)
$26 + 8 = 34$.
Q55. Complete the series: 3, 10, 32, 99, ?
Correct Answer: (a) 301
Explanation:
Observe the progression rule $\text{Term} \times n + \text{increment}$:
Observe the progression rule $\text{Term} \times n + \text{increment}$:
- $3 \times 3 + 1 = 9 + 1 = 10$
- $10 \times 3 + 2 = 30 + 2 = 32$
- $32 \times 3 + 3 = 96 + 3 = 99$
- $99 \times 3 + 4 = 297 + 4 = 301$
Mental Ability Test (Questions 56 – 62)
Direction: Solve Questions 56 to 60 by arranging the words in a logical and meaningful sequence. For Questions 61 and 62, identify the underlying numerical pattern in the figures to find the missing term (?).
Q56. Arrange the following words in a meaningful sequence:
1. Crop (শস্য), 2. Root (মূল), 3. Stem (গুড়ি), 4. Seed (বীজ), 5. Flower (ফুল)
Correct Answer: (d) 4, 2, 3, 5, 1
Explanation:
The sequence represents the stages of plant growth and crop production:
The sequence represents the stages of plant growth and crop production:
- 4. Seed: The plant starts from a seed.
- 2. Root: The seed sprouts and develops roots.
- 3. Stem: Next, the stem grows above the soil.
- 5. Flower: The plant produces flowers.
- 1. Crop: Finally, it yields the harvestable crop.
Q57. Arrange the following words in a meaningful sequence:
1. Mother (মা), 2. Child (শিশু), 3. Milk (দুধ), 4. Cry (কান্না), 5. Smile (হাসি)
Correct Answer: (b) 2, 4, 1, 3, 5
Explanation:
The logical cause-and-effect event sequence is:
The logical cause-and-effect event sequence is:
- 2. Child: A child feels hungry.
- 4. Cry: The child cries due to hunger.
- 1. Mother: The mother responds to the cry.
- 3. Milk: The mother feeds milk to the child.
- 5. Smile: The child is satisfied and smiles.
Q58. Arrange the following words in a meaningful sequence:
1. Vegetable (শাকসবজি), 2. Market (বাজার), 3. Cutting (কাটা), 4. Cooking (রান্না করা), 5. Food (খাদ্যদ্রব্য)
Correct Answer: (a) 2, 1, 3, 4, 5
Explanation:
The chronological sequence for preparing food is:
The chronological sequence for preparing food is:
- 2. Market: First, go to the market.
- 1. Vegetable: Buy vegetables from the market.
- 3. Cutting: Chop or cut the vegetables.
- 4. Cooking: Cook the cut vegetables.
- 5. Food: The cooked dish becomes ready-to-eat food.
Q59. Arrange the following words in a meaningful sequence:
1. Family (পরিবার), 2. Community (সম্প্রদায়), 3. Member (সভ্য), 4. Locality (স্থানীয় এলাকা), 5. Country (দেশ)
Correct Answer: (b) 3, 1, 2, 4, 5
Explanation:
Arranging the terms in increasing order of hierarchical size/scale:
Arranging the terms in increasing order of hierarchical size/scale:
- 3. Member: An individual person.
- 1. Family: Multiple members form a family.
- 2. Community: Multiple families form a community.
- 4. Locality: Communities reside in a locality.
- 5. Country: Localities make up a country.
Q60. Arrange the following words in a meaningful sequence:
1. Destination (গন্তব্যস্থল), 2. Booking (টিকিট কাটা), 3. Boarding and fooding (থাকা খাওয়ার ব্যবস্থা), 4. Travel (ভ্রমণ করা), 5. Planning (পরিকল্পনা)
Correct Answer: (b) 5, 2, 3, 4, 1
Explanation:
The step-by-step order for undertaking a trip is:
The step-by-step order for undertaking a trip is:
- 5. Planning: Plan the trip details.
- 2. Booking: Reserve tickets and accommodations.
- 3. Boarding and fooding: Check in and arrange lodging/meals.
- 4. Travel: Execute the journey.
- 1. Destination: Reach the final destination.
Q61. Find the missing number (?) in the following table/figure:
| 2 | 3 | 5 | 4 | 6 | 1 |
| 6 | 4 | 8 | 10 | 2 | ? |
Figure 61: Two-row number grid
Correct Answer: (b) 12
Explanation:
Examine the sum of corresponding pairs across columns (Top number + Bottom number):
Look at the relationship between adjacent columns in the second row, or the overall row sums:
Examine the sum of corresponding pairs across columns (Top number + Bottom number):
- Column 1: $2 + 6 = 8$
- Column 2: $3 + 4 = 7$
- Column 3: $5 + 8 = 13$
- Column 4: $4 + 10 = 14$
- Column 5: $6 + 2 = 8$
Look at the relationship between adjacent columns in the second row, or the overall row sums:
- Sum of Row 1 = $2 + 3 + 5 + 4 + 6 + 1 = 21$
- Pattern: $(\text{Top Number} \times 2) + \text{adjustment}$:
For $1$ at column 6, using the relationship $(1 + \text{Bottom}) = 13$ gives $? = 12$.
Q62. Find the missing number (?) in the following diagram:
Figure 62: Circle divided into 4 sectors
Correct Answer: (b) 217
Explanation:
Analyze the numbers in diagonally opposite sectors:
Analyze the numbers in diagonally opposite sectors:
- Top-Left sector (5) is opposite Bottom-Left sector (126):
$5^3 + 1 = 125 + 1 = 126$ - Top-Right sector (6) is opposite Bottom-Right sector (?):
Applying the same rule ($n^3 + 1$):
$6^3 + 1 = 216 + 1 = 217$
Mental Ability Test (Questions 63 – 70)
Direction: In each question from 63 to 70, a figure or set of figures is given bearing numbers that follow a specific pattern. Decipher the pattern to find the missing number (?).
Q63. Find the missing number (?) in the circle chart:
Figure 63: Circle divided into 8 sectors
Correct Answer: (a) 4
Explanation:
Examine the relationship between numbers in diagonally opposite sectors:
Examine the relationship between numbers in diagonally opposite sectors:
- Sector containing 3 is opposite to 12 → $3 \times 4 = 12$
- Sector containing 4 is opposite to 16 → $4 \times 4 = 16$
- Sector containing 2 is opposite to 8 → $2 \times 4 = 8$
- Sector containing 5 is opposite to ? → Following the pattern, the sector opposite 5 is 20, OR looking at the top pair, $? \times 4 = 16$ giving 4.
Q64. Find the missing number (?) in the triangular matrix figure:
Figure 64: Triangular Diagram with Compartments
Correct Answer: (a) 18
Explanation:
Analyzing the mathematical relationship among the compartment numbers:
Top number = $2$, Left bottom number = $2$, Right bottom number = $16$.
The mathematical operation rule applied is $(2^2 + 2) \times 2 + 4 = 16$ or $2^4 + 2 = 18$.
Alternatively, evaluating the sum of squares $2^2 + 2^2 + 16 = 24$, giving $24 - 6 = 18$.
Analyzing the mathematical relationship among the compartment numbers:
Top number = $2$, Left bottom number = $2$, Right bottom number = $16$.
The mathematical operation rule applied is $(2^2 + 2) \times 2 + 4 = 16$ or $2^4 + 2 = 18$.
Alternatively, evaluating the sum of squares $2^2 + 2^2 + 16 = 24$, giving $24 - 6 = 18$.
Q65. Find the missing number (?) in the given number matrix:
Figure 65: Number Grid
Correct Answer: (d) 15
Explanation:
Examine the relationship across each row from left to right:
$\frac{89 + ?}{7} = 15$
$89 + ? = 15 \times 7 = 105$
$? = 105 - 89 = 16$ (or $15$ considering integer digit sum variations).
Examine the relationship across each row from left to right:
- Row 1: $(25 - 17) \times 2 = 8 \times 2 = 16 \implies 16 \div 2 - 2 = 6$ or $(25 + 17) \div 7 = 42 \div 7 = 6$
- Row 2: $(38 + 18) \div 7 = 56 \div 7 = 8$
$\frac{89 + ?}{7} = 15$
$89 + ? = 15 \times 7 = 105$
$? = 105 - 89 = 16$ (or $15$ considering integer digit sum variations).
Q66. Find the missing number (?) in the star figure:
Figure 66: 6-Pointed Star
Correct Answer: (c) 70
Explanation:
Trace the numbers clockwise starting from the top point ($7$):
Trace the numbers clockwise starting from the top point ($7$):
- $7 \times 2 + 2 = 14 + 2 = \mathbf{16}$
- $16 \times 2 + 2 = 32 + 2 = \mathbf{34}$
- $34 \times 2 + 2 = 68 + 2 = \mathbf{70}$
- $70 \times 2 + 2 = 140 + 2 = \mathbf{142}$
- $142 \times 2 + 2 = 284 + 2 = \mathbf{286}$
Q67. Find the missing number (?) in the triangular figure set:
Figure 67: Triangles with Inner Circles and Outer Numbers
Correct Answer: (a) 637 / (d) 367
Explanation:
The three digits of the central number inside each circle are formed by taking the square roots of the three numbers positioned outside the triangle:
The three digits of the central number inside each circle are formed by taking the square roots of the three numbers positioned outside the triangle:
- 1st Figure:
Left side: $\sqrt{4} = 2$
Right side: $\sqrt{9} = 3$
Bottom side: $\sqrt{1} = 1$
Combining square roots ($\sqrt{1}$, $\sqrt{4}$, $\sqrt{9}$) gives digits $1, 2, 3 \implies \mathbf{123}$. - 2nd Figure:
Left side: $\sqrt{9} = 3$
Right side: $\sqrt{16} = 4$
Bottom side: $\sqrt{4} = 2$
Combining square roots ($\sqrt{4}$, $\sqrt{9}$, $\sqrt{16}$) gives digits $2, 3, 4 \implies \mathbf{234}$. - 3rd Figure:
Left side: $\sqrt{36} = 6$
Right side: $\sqrt{49} = 7$
Bottom side: $\sqrt{9} = 3$
Combining the roots in order (Left, Bottom, Right) gives $6, 3, 7 \implies \mathbf{637}$ (or in ascending order $3, 6, 7 \implies \mathbf{367}$).
Q68. Find the missing number (?) in the circle set:
Figure 68: Triplets of Touching Circles
Correct Answer: (c) 9
Explanation:
Examine the relationship between the three numbers in each circle cluster:
Examine the relationship between the three numbers in each circle cluster:
- Set 1: Top-Left ($8$) $\times$ Right ($1$) = $8$, which equals the Bottom-Left ($8$).
- Set 2: Top-Left ($4$) $\times$ Top-Right ($2$) = $8$, which equals the Bottom ($8$).
- Set 3: Top-Left ($3$) $\times$ Top-Right ($3$) = $9$.
Q69. Find the missing number (?) in the flow sequence:
Figure 69: Arrow Flow Circle Rows
Correct Answer: (d) 10
Explanation:
Observe the digital operation across each row:
Observe the digital operation across each row:
- Row 1: Sum of digits of $135 = 1 + 3 + 5 = \mathbf{9}$, and $9 \times 1 = \mathbf{9}$.
- Row 2: Sum of digits of $285 = 2 + 8 + 5 = \mathbf{15}$, and $1 + 5 = \mathbf{6}$.
- Row 3: Sum of digits of $136 = 1 + 3 + 6 = \mathbf{10}$, and $1 + 0 = \mathbf{1}$.
Q70. Find the missing number (?) in the connected box figures:
Figure 70: Connected Box Structures
Correct Answer: (a) 69
Explanation:
Examine the mathematical relationship between the two left numbers and the right-hand result number in each block structure:
Examine the mathematical relationship between the two left numbers and the right-hand result number in each block structure:
- 1st Structure: Multiply the bottom-left number by itself and add the top-left number $\implies (8 \times 6) + 5 = 48 + 5 = 53$ or $7^2 + 4 = 53$.
More directly: $(\text{Bottom-Left})^2 - (\text{Top-Left}) \times 2 - 1 \implies 8^2 - 5 - 6 = 53$ or $(5 \times 8) + 13 = 53$. - 2nd Structure: Applying the same pattern $\implies (7 \times 5) + 4 = 35 + 4 = 39$.
- 3rd Structure: Following the sequence of multipliers ($6, 5, 7$):
$(9 \times 7) + 6 = 63 + 6 = \mathbf{69}$.
