HCF

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📘 Comprehensive Syllabus & Examination Guide

HCF

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

🎯 Mapped Subjects & Topic Question Distribution

Total Question Pool 100%
3 MCQs
Combined Active Syllabus
HCF
3 MCQs
Topic Pool
📊 Question Pool Structure
3 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 HCF, 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.

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Solved Blueprint Examples

📝 Pre-Rendered Solved Sample Questions & Detailed Solutions

Showing 3 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
HCF Medium • Quantitative Aptitude Test
The H.C.F. of two numbers is 12 and their sum is 96. All the pairs of such numbers is
A 13, 84 : 86, 60
B 18, 60 : 20, 90
C 30, 80: 80, 70
D None of these
✓ Correct Answer: C - 30, 80: 80, 70
📖 Step-by-Step Solution & Conceptual Rationale:
Standard logic: (13,84) has HCF 12 but sum not 96. (86, 60) doesn't fit. Similarly B and C are also wrong.
Sample Question 2
HCF Medium • Quantitative Aptitude Test
In finding the G.C.M. of two numbers, the last divisor is 41 and the quotients are 2,4, 2 the numbers are:
A 700, 400
B 820, 369
C 800, 500
D 900, 600
✓ Correct Answer: B - 820, 369
📖 Step-by-Step Solution & Conceptual Rationale:
To find the two numbers, we can work the long division method for finding the G.C.M. (or H.C.F.) backward, starting from the final step:

Step 3 (Last Step):
Last Divisor = 41, Quotient = 2, Remainder = 0
Dividend = \((41 \times 2) + 0 =\) 82
(This dividend becomes the divisor for the previous step)

Step 2:Divisor = 82, Quotient = 4, Remainder = 41
Dividend = \((82 \times 4) + 41 = 328 + 41 =\) 369
(This is our first number, and it becomes the divisor for the step before it)

Step 1:Divisor = 369, Quotient = 2, Remainder = 82
Dividend = \((369 \times 2) + 82 = 738 + 82 =\) 820
(This is our second number)

The two numbers are 820 and 369.
Sample Question 3
HCF Medium • Quantitative Aptitude Test
Highest common factor of 28, 56, 40 is:
A 4
B 10
C 8
D 14
✓ Correct Answer: A - 4
📖 Step-by-Step Solution & Conceptual Rationale:
Factors: 28(4,7),56(4,14),40(4,10). 4 is the largest shared divisor.
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