Quantitative Reasoning Core

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Topic 2 in the Qimiyah General Studies paper bundles three reasoning blocks — quantitative, verbal, and analytical — into a single high-weight section. Five formulas carry roughly 60% of the marks: Percentage = (Part/Whole) × 100, Average = Sum ÷ Count, Simple Interest = (P × R × T)/100, Distance = Speed × Time, and Area of rectangle = L × W. Treat ratios as ordered pairs (a:b matches c:d) and percentages as multipliers of the base value. For verbal analogy items, map the relationship (cause-effect, part-whole, function, degree), not surface synonyms. Inductive reasoning items reward pattern detection over arithmetic tricks — scan for position, sign, and alternation rules. Plan ≤45 seconds per MCQ; the block is large and time pressure is the silent killer.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Quantitative Reasoning Core

Quantitative items in Topic 2 cluster into four families. Number operations test integer, fraction, and decimal manipulation with distractors built from careless sign errors. Ratio and proportion requires matching terms in the same order: if a:b = c:d, then ad = bc. Direct proportion scales both sides by the same factor; inverse proportion keeps their product constant (e.g., speed × time = distance for a fixed route). Percentage change is computed as (New − Old)/Old × 100, distinct from percentage-point difference, which subtracts two percentages directly. Profit and loss uses Cost Price (CP) as the base: Profit% = (SP − CP)/CP × 100.

Algebra and Geometry

Linear equations of the form ax + b = c collapse to x = (c − b)/a; word problems translate to equations by assigning the unknown to the quantity asked. Simple Interest accumulates linearly: A = P(1 + RT/100), where R is annual rate in percent and T in years. For geometry, internalise perimeter/area/volume of rectangles, squares, triangles, circles, and cuboids — the volume formula L × W × H traps test-takers who select the surface-area expression 2(LW + LH + WH) for 3D questions.

Verbal and Analytical Reasoning

Vocabulary items use context to disambiguate; analogy items (A:B :: C:?) require identifying the relational operator (synonym, antonym, cause, tool, degree). Reading comprehension passages (≈150 words) yield main-idea, inference, and detail questions — read the stem before the passage. Inductive reasoning presents number/letter sequences; track single-step deltas, alternating signs, and recursive patterns like ×2 + 1.

Key Formulas at a Glance

Concept	Formula	Variables
Percentage	(Part/Whole) × 100	Part, Whole
Average	Sum ÷ n	Sum, n = count
Simple Interest	PRT/100	P = principal, R = %/yr, T = years
Distance	Speed × Time	S, T
Rectangle area	L × W	Length, Width

Typical Question Patterns

Qimiyah Topic 2 items are MCQs in Arabic-translated English with four options. Expect single-step arithmetic, one-equation word problems, one short comprehension passage with three linked questions, and a sequence-completion item. The block contributes about 3% of the total paper but is one of the highest-yield per minute.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge Cases in Quantitative Items

Weighted vs simple mean is the classic trap: the average speed of a round trip is not the arithmetic mean of the two speeds — it equals 2·S₁·S₂/(S₁+S₂) (harmonic mean) because each leg takes a different share of the total time. Percentage-point vs percent-change errors appear in data-interpretation items: a rate rising from 4% to 6% is a 2 percentage-point increase but a 50% relative change. Successive percentages do not add: a 20% rise followed by 10% rise equals 1.20 × 1.10 = 1.32, i.e. 32% net, not 30%. Ratio scaling requires the smallest integer representation only when the problem asks for it; otherwise, any proportional pair is acceptable.

Edge Cases in Verbal and Analytical Items

Analogy items with degree relationships (hot : hotter :: cold : ?) are answered by mapping the grammatical and semantic operator, not by literal translation. Comprehension items frequently include the trap word “EXCEPT” or “NOT” — underline it in the stem. Inductive sequences may use two interleaved sub-sequences (odd-indexed and even-indexed terms follow different rules); test both before committing.

Connections to Adjacent Topics

Topic 2 feeds directly into the science reasoning items (units, rates) and the Islamic-studies quantitative passages (zakat = 2.5%, inheritance fractions). Mastering ratios and percentages here shortens revision time in those cross-topic items.

Common Mistakes

Dividing by the wrong base in profit/loss (use CP, not SP).
Treating a cuboid’s lateral surface as its total surface.
Answering analogy by synonym lookup; the correct operator is often function, part, or cause.
Misreading “most likely” comprehension stems as absolute.

Worked Example

A trader buys 30 items for SR 450 and sells them at SR 18 each. Find profit percent. Total SP = 30 × 18 = SR 540. Profit = 540 − 450 = SR 90. Profit% = 90/450 × 100 = 20%.

Practice Prompts

A sum of SR 5,000 earns simple interest at 6% per year for 3 years. What is the total amount repayable? (Answer: SR 5,900)
Complete the analogy: Pen : Writer :: Scalpel : ? with three plausible distractors and justify the relational operator.

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Quantitative Reasoning Core