Math

Change Setup
๐Ÿ“˜ Comprehensive Syllabus & Examination Guide

Math

Official curriculum roadmap, subject/topic distribution, negative marking rules, pacing guidelines, and solved sample questions.

๐ŸŽฏ Mapped Subjects & Topic Question Distribution

Total Question Pool 100%
651 MCQs
Combined Active Syllabus
Reasoning
2 MCQs
Topic Pool
Prob
14 MCQs
Topic Pool
Series
156 MCQs
Topic Pool
Logic
58 MCQs
Topic Pool
Geometry
12 MCQs
Topic Pool
Business
2 MCQs
Topic Pool
Algebra
29 MCQs
Topic Pool
Arithmetic
38 MCQs
Topic Pool
๐Ÿ“Š Question Pool Structure
651 MCQs across fundamental, intermediate, and advanced concept tiers.
โšก Recommended Pacing
45 to 60 seconds per MCQ. Flag complex problems and preserve 10 minutes for final revision.
โš–๏ธ Scoring & Negative Marking
+1 mark per correct answer. In competitive tests with negative marking, -0.25 applies for incorrect guesses.

๐Ÿ’ก Strategic Preparation & Exam Hall Guidelines

To maximize your score on Math, candidates are advised to follow a structured three-pass approach. In the First Pass, solve all direct recall and formula-based questions within 30 seconds each to secure foundational marks. In the Second Pass, tackle multi-step analytical and quantitative reasoning problems. In the Third Pass, review marked questions and verify calculations.

Practice with the interactive player below to evaluate your speed and accuracy under real exam pressure. Every question features full mathematical formulas, step-by-step worked solutions, and conceptual explanations vetted by Apex Rankers Academy subject matter specialists.

Ready to test your knowledge? Launch interactive 1-by-1 practice with instant feedback, bookmarking, and step-by-step rationales.
Solved Blueprint Examples

๐Ÿ“ Pre-Rendered Solved Sample Questions & Detailed Solutions

Showing 10 solved representative questions

Review the solved problems below to understand question phrasing, answer choices, and step-by-step solution logic prior to starting the full interactive practice drill:

Sample Question 1
Reasoning Easy • Quantitative Aptitude Test
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?
โœ“ Correct Answer: C
๐Ÿ“– Step-by-Step Solution & Conceptual 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.
Sample Question 2
Prob Hard • Intelligence Tests
Ali is 20 years younger than 3/5 of his actual age. What is the present age of Ali?
โœ“ Correct Answer: 50 years
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Derived from the equation xโˆ’3/5x=20โŸน2/5x=20โŸนx=50.
Sample Question 3
Prob Hard • Intelligence Tests
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
C 2 miles
โœ“ Correct Answer: B - 12 miles
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Javed: 8+4=12. Usman: 8+16=24. Difference: 24โˆ’12=12.
Sample Question 4
Prob Hard • Intelligence Tests
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
D 14
โœ“ Correct Answer: C - 10
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
C+F=15 and 4C+2F=50. Solving for C yields 10 cats and 5 fowls.
Sample Question 5
Prob Hard • Intelligence Tests
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
D 35 years
โœ“ Correct Answer: C - 37 years
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
C is 14; B is 42; A is 42โˆ’5=37. [Note: key refers to present age].
Sample Question 6
Series Hard • Intelligence Tests
Find the valve of X in the following: 9 1 25 64 / 16 4 X 81 / 25 9 49 100
A 121
B 36
C 25
D 49
โœ“ Correct Answer: B - 36
๐Ÿ“– Step-by-Step Solution & Conceptual 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 \(6^2 = \mathbf{36}\).
Sample Question 7
Prob Hard • Intelligence Tests
Find a number which when divided by 4 exceeds 80 by as much as it short of 160 now.
โœ“ Correct Answer: 120
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Derived from the equation x/4โˆ’80=160โˆ’x/4โŸน2x/4=240โŸนx/4=120.
Sample Question 8
Logic Hard • Intelligence Tests
Which pair of numbers is dissimilar to others in the following?
A 533-527
B 461-457
C 223-214
D 13โ€”5
E 318-313
โœ“ Correct Answer: C - 223-214
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
The other pairs follow specific difference patterns or prime-related traits not shared by choice (c).
Sample Question 9
Prob Hard • Intelligence Tests
Two numbers consist of the same two digits in reverse order. If the difference is 54, what are the numbers?
โœ“ Correct Answer: (28, 82)
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
82โˆ’28=54; these two digits (2, 8) in reverse satisfy the problem's criteria.
Sample Question 10
Prob Hard • Intelligence Tests
My age is 3/4th of my brotherโ€™s age and the difference is 6 years. My brotherโ€™s age?
A 36 years
B 14 years
C 24 years
D 28 years
โœ“ Correct Answer: C - 24 years
๐Ÿ“– Step-by-Step Solution & Conceptual Rationale:
Bโˆ’3/4B=6โŸน1/4B=6โŸนB=24.
Practice All 651 Questions Interactively Test your knowledge in real-time with continuous progress saving, instant scoring, and performance analytics.