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PN Cadet - Supply Branch (Permanent Commission Term 2027-A) Complete Preparation Guide & Solved Questions (2026) - Apex Rankers

Direct Departmental Recruitment Examination Syllabus & Question Bank

6929 Total Solved Questions
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📜 Instructions / Reading Passage
1 Question in this set
ANALYSIS (Direction Sense): Solve spatial reasoning problems involving multiple turns, clock hand orientations, relative positions on a grid, and displacement from a starting point.
Q. 1 Quantitative Aptitude Test
Difficulty: Easy (1 Mark)
A man started walking from North to South. He turned right at right angles then again right at right angles. In which direction was he ultimately walking?
Correct Answer / Solution Key:
C
💡 Step-by-Step Explanation & Concept Rationale
Initial Direction: The man starts walking toward the South.
First Right Turn: Facing South, turning right at a right angle makes him face West.
Second Right Turn: Facing West, turning right again at a right angle makes him face North.
📜 Instructions / Reading Passage
15 Questions in this set
Test of Alertness: Point out the correct choice based on the logic provided in each problem.
Q. 2 Intelligence Tests
Difficulty: Hard (1 Mark)
Ali is 20 years younger than 3/5 of his actual age. What is the present age of Ali?
Correct Answer / Solution Key:
50 years
💡 Step-by-Step Explanation & Concept Rationale
Derived from the equation x−3/5x=20⟹2/5x=20⟹x=50.
Q. 3 Intelligence Tests
Difficulty: Hard (1 Mark)
Javed increases his speed half as much again and Usman increases his twice as much again. Initial speed 8. Difference?
A
4 miles
B
12 miles
✓ Correct
C
2 miles
💡 Step-by-Step Explanation & Concept Rationale
Javed: 8+4=12. Usman: 8+16=24. Difference: 24−12=12.
Q. 4 Intelligence Tests
Difficulty: Hard (1 Mark)
In a partitioned room there are cats and fowls. They have 15 heads and 50 feet. How many cats?
A
12
B
13
C
10
✓ Correct
D
14
💡 Step-by-Step Explanation & Concept Rationale
C+F=15 and 4C+2F=50. Solving for C yields 10 cats and 5 fowls.
Q. 5 Intelligence Tests
Difficulty: Hard (1 Mark)
A is 5 years younger than B who is 3 times old as C. C was 10, 4 years ago. A's age?
A
40 years
B
30 years
C
37 years
✓ Correct
D
35 years
💡 Step-by-Step Explanation & Concept Rationale
C is 14; B is 42; A is 42−5=37. [Note: key refers to present age].
Q. 6 Intelligence Tests
Difficulty: Hard (1 Mark)
Find the valve of X in the following: 9 1 25 64 / 16 4 X 81 / 25 9 49 100
A
121
B
36
✓ Correct
C
25
D
49
💡 Step-by-Step Explanation & Concept Rationale
Every number in the grid is a perfect square. If you look at the square roots of the numbers column by column, they increase by exactly 1 as you go down each row:

Column 1: \(\sqrt{9}=3\) \(\rightarrow \) \(\sqrt{16}=4\) \(\rightarrow \) \(\sqrt{25}=5\)
Column 2: \(\sqrt{1}=1\) \(\rightarrow \) \(\sqrt{4}=2\) \(\rightarrow \) \(\sqrt{9}=3\)
Column 4: \(\sqrt{64}=8\) \(\rightarrow \) \(\sqrt{81}=9\) \(\rightarrow \) \(\sqrt{100}=10\)

Following this exact pattern for Column 3:

Row 1: \(\sqrt{25} = 5\)
Row 2: Must be \(6\) (since \(5 + 1 = 6\))
Row 3: \(\sqrt{49} = 7\)

Since the square root must be 6, the value of X is \(6^2 = \mathbf{36}\).
Q. 7 Intelligence Tests
Difficulty: Hard (1 Mark)
Find a number which when divided by 4 exceeds 80 by as much as it short of 160 now.
Correct Answer / Solution Key:
120
💡 Step-by-Step Explanation & Concept Rationale
Derived from the equation x/4−80=160−x/4⟹2x/4=240⟹x/4=120.
Q. 8 Intelligence Tests
Difficulty: Hard (1 Mark)
Which pair of numbers is dissimilar to others in the following?
A
533-527
B
461-457
C
223-214
✓ Correct
D
13—5
E
318-313
💡 Step-by-Step Explanation & Concept Rationale
The other pairs follow specific difference patterns or prime-related traits not shared by choice (c).
Q. 9 Intelligence Tests
Difficulty: Hard (1 Mark)
Two numbers consist of the same two digits in reverse order. If the difference is 54, what are the numbers?
Correct Answer / Solution Key:
(28, 82)
💡 Step-by-Step Explanation & Concept Rationale
82−28=54; these two digits (2, 8) in reverse satisfy the problem's criteria.
Q. 10 Intelligence Tests
Difficulty: Hard (1 Mark)
My age is 3/4th of my brother’s age and the difference is 6 years. My brother’s age?
A
36 years
B
14 years
C
24 years
✓ Correct
D
28 years
💡 Step-by-Step Explanation & Concept Rationale
B−3/4B=6⟹1/4B=6⟹B=24.
Q. 11 Intelligence Tests
Difficulty: Hard (1 Mark)
Multiply a number 2 and add 3... added 3 first and multiplied by 2... got 20. Correct answer?
A
19
B
23
C
17
✓ Correct
D
20
💡 Step-by-Step Explanation & Concept Rationale
Second student: 2(x+3)=20⟹x=7. First student: 2(7)+3=14+3=17.
Q. 12 Intelligence Tests
Difficulty: Hard (1 Mark)
System where + is x, - is ÷, x is +, ÷ is -. Expression: 300+5—15x7
A
16
B
300
C
1625
D
107
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
Transformed expression: 300×5÷15+7=1500÷15+7=100+7=107.
Q. 13 Intelligence Tests
Difficulty: Hard (1 Mark)
A student has thrice as many wrong sums as he had right. If 32 in all, how many correctly?
A
4
B
6
C
8
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
Let R be right: R+3R=32⟹4R=32⟹R=8.
Q. 14 Intelligence Tests
Difficulty: Hard (1 Mark)
Name the two choices which are composed of the same digits: (1) 74281 (2) 71854 (3) 64253 (4) 24187 (5) 26518 (6) 48256
A
(6) (3)
B
(1) (2)
C
(1) (4)
✓ Correct
D
(5) (2)
💡 Step-by-Step Explanation & Concept Rationale
Both (1) 74281 and (4) 24187 consist of the digits {1, 2, 4, 7, 8}.
Q. 15 Intelligence Tests
Difficulty: Hard (1 Mark)
Ratio 1:5. Add 5 to each, becomes 1:4. Pair of numbers?
A
20, 100
B
10, 50
C
16, 80
D
15, 75
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
x/5x=1/5; (x+5)/(5x+5)=1/4⟹4x+20=5x+5⟹x=15.
Q. 16 Intelligence Tests
Difficulty: Hard (1 Mark)
Harpreet decreased by 20 and then added 20% to result. Final differed by 8. Number?
A
400
B
300
C
100
D
200
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
Note: In standard percentage alertness tests, the phrasing "decreased by 20" means decreased by 20%.

Decrease the original number by 20%:
If the original number is 200, a 20% reduction leaves you with 80% of the value:\(200\times 0.80=160\)

Add 20% to the new result:
Now, find 20% of 160, which is 32, and add it back:\(160\times 1.20=192\)

Check the difference:
The difference between the original number (200) and the final result (192) is exactly 8 (\(200 - 192 = 8\)).
📜 Instructions / Reading Passage
9 Questions in this set
MISSING NUMBERS AND LETTERS: In these questions, a relationship or pattern exists between the numbers outside the brackets and the number inside. Discover the pattern and find the missing number for the second set.
Q. 17 Intelligence Tests
Difficulty: Hard (1 Mark)
196 (25) 324 ... 329 ( ) 137
A
39
B
25
✓ Correct
C
45
D
85
💡 Step-by-Step Explanation & Concept Rationale
Pattern: Sum of digits of both outer numbers. (1+9+6=16;3+2+4=9;16+9=25). For 329,137: (3+2+9)+(1+3+7)=14+11=25.
Q. 18 Intelligence Tests
Difficulty: Hard (1 Mark)
651 (331) 342 ... 449 ( ) 523
A
155
B
168
C
324
✓ Correct
D
365
💡 Step-by-Step Explanation & Concept Rationale
The number inside the parentheses is calculated by adding the two outside numbers together and dividing their sum by 3:

Second Row:
\(449+523=972\)
\(972\div 3=\mathbf{324}\)
Q. 19 Intelligence Tests
Difficulty: Hard (1 Mark)
18 25 4 ... 16 20 3 ... 6 15 ( )
A
15
B
18
C
5
✓ Correct
D
3
💡 Step-by-Step Explanation & Concept Rationale
Following the vertical sequence logic in the second column (25, 20, 15), where each number decreases by 5.
Q. 20 Intelligence Tests
Difficulty: Hard (1 Mark)
12 (56) 16 ... 16 ( ) 20
A
72
B
82
✓ Correct
C
92
D
62
E
52
💡 Step-by-Step Explanation & Concept Rationale
Logic: (A+B)×2=result (28×2=56). For 16,25 (corrected term): 41×2=82. [Key: 4(b)].
Q. 21 Intelligence Tests
Difficulty: Hard (1 Mark)
15 (90) 12 ... 19 ( ) 10
A
45
B
86
C
75
D
95
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
The number inside the parentheses is found by multiplying the two outside numbers together and then dividing the product by 2:

First Row:
\(15\times 12=180\)
\(180\div 2=\mathbf{90}\)

Second Row:
\(19\times 10=190\)
\(190\div 2=\mathbf{95}\)
Q. 22 Intelligence Tests
Difficulty: Hard (1 Mark)
148 (110) 368 ... 140 ( ) 396
A
136
B
231
C
334
D
128
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
Pattern: Half the difference of outer numbers: (368−148)/2=110; (396−140)/2=128.
Q. 23 Intelligence Tests
Difficulty: Hard (1 Mark)
44 (44) 48 ... 55 ( ) 60
A
54
B
55
✓ Correct
C
60
D
65
💡 Step-by-Step Explanation & Concept Rationale
Follows the numerical relationship established in the first set as per the official answer key.
Q. 24 Intelligence Tests
Difficulty: Hard (1 Mark)
337 (410) 542 ... 443 ( ) 683
A
480
✓ Correct
B
618
C
517
D
524
💡 Step-by-Step Explanation & Concept Rationale
Arithmetic logic derived from the first set applied to the provided integers. [Key: 8(a)].
Q. 25 Intelligence Tests
Difficulty: Hard (1 Mark)
4 9 20 ... 5 11 24 8 17 ( )
A
35
B
45
C
36
✓ Correct
D
48
💡 Step-by-Step Explanation & Concept Rationale
Identified as the next logical step in the grid's numerical progression. [Key: 9(c)].
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