Prob

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📘 Comprehensive Syllabus & Examination Guide

Prob

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

🎯 Mapped Subjects & Topic Question Distribution

Total Question Pool 100%
14 MCQs
Combined Active Syllabus
Prob
14 MCQs
Topic Pool
📊 Question Pool Structure
14 MCQs across fundamental, intermediate, and advanced concept tiers.
⚡ Recommended Pacing
45 to 60 seconds per MCQ. Flag complex problems and preserve 10 minutes for final revision.
⚖️ Scoring & Negative Marking
+1 mark per correct answer. In competitive tests with negative marking, -0.25 applies for incorrect guesses.

💡 Strategic Preparation & Exam Hall Guidelines

To maximize your score on Prob, 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

📝 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
Prob Hard • Intelligence Tests
Ali is 20 years younger than 3/5 of his actual age. What is the present age of Ali?
✓ Correct Answer: 50 years
📖 Step-by-Step Solution & Conceptual Rationale:
Derived from the equation x−3/5x=20⟹2/5x=20⟹x=50.
Sample Question 2
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
✓ Correct Answer: B - 12 miles
📖 Step-by-Step Solution & Conceptual Rationale:
Javed: 8+4=12. Usman: 8+16=24. Difference: 24−12=12.
Sample Question 3
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
✓ Correct Answer: C - 10
📖 Step-by-Step Solution & Conceptual Rationale:
C+F=15 and 4C+2F=50. Solving for C yields 10 cats and 5 fowls.
Sample Question 4
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
✓ Correct Answer: C - 37 years
📖 Step-by-Step Solution & Conceptual Rationale:
C is 14; B is 42; A is 42−5=37. [Note: key refers to present age].
Sample Question 5
Prob Hard • Intelligence Tests
Find a number which when divided by 4 exceeds 80 by as much as it short of 160 now.
✓ Correct Answer: 120
📖 Step-by-Step Solution & Conceptual Rationale:
Derived from the equation x/4−80=160−x/4⟹2x/4=240⟹x/4=120.
Sample Question 6
Prob Hard • Intelligence Tests
Two numbers consist of the same two digits in reverse order. If the difference is 54, what are the numbers?
✓ Correct Answer: (28, 82)
📖 Step-by-Step Solution & Conceptual Rationale:
82−28=54; these two digits (2, 8) in reverse satisfy the problem's criteria.
Sample Question 7
Prob Hard • Intelligence Tests
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
D 28 years
✓ Correct Answer: C - 24 years
📖 Step-by-Step Solution & Conceptual Rationale:
B−3/4B=6⟹1/4B=6⟹B=24.
Sample Question 8
Prob Hard • Intelligence Tests
Multiply a number 2 and add 3... added 3 first and multiplied by 2... got 20. Correct answer?
A 19
B 23
C 17
D 20
✓ Correct Answer: C - 17
📖 Step-by-Step Solution & Conceptual Rationale:
Second student: 2(x+3)=20⟹x=7. First student: 2(7)+3=14+3=17.
Sample Question 9
Prob Hard • Intelligence Tests
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 Answer: C - 8
📖 Step-by-Step Solution & Conceptual Rationale:
Let R be right: R+3R=32⟹4R=32⟹R=8.
Sample Question 10
Prob Hard • Intelligence Tests
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 Answer: D - 15, 75
📖 Step-by-Step Solution & Conceptual Rationale:
x/5x=1/5; (x+5)/(5x+5)=1/4⟹4x+20=5x+5⟹x=15.
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