Examius
🇵🇰 YPIP · subject
YPIP Quantitative Reasoning Syllabus
Every chapter and topic of Quantitative Reasoning examined in YPIP — 6 chapters, 25 topics, plus 54 flashcards written against it.
Quantitative Reasoning syllabus — full chapter and topic list
Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning in YPIP, not a summary of it.
-
Arithmetic
5 topics- Number System
- HCF and LCM
- Fractions and Decimals
- Simplification
- Square Roots and Cube Roots
-
Ratios and Averages
4 topics- Ratio and Proportion
- Average, Mean, Median and Mode
- Partnership
- Mixtures and Alligations
-
Percentages and Commercial Math
5 topics- Percentage
- Profit and Loss
- Simple Interest
- Compound Interest
- Discount and Markup
-
Time and Work
4 topics- Time and Work
- Pipes and Cisterns
- Time, Speed and Distance
- Problems on Trains
-
Algebra and Equations
3 topics- Linear Equations
- Problems on Ages
- Quadratic Equations
-
Data Interpretation
4 topics- Tables and Charts
- Bar and Line Graphs
- Pie Charts
- Probability and Permutations
Quantitative Reasoning flashcards for YPIP
25 of 54 cards from the Quantitative Reasoning deck — real questions with worked answers.
What are natural numbers, whole numbers, and integers?
Natural numbers: counting numbers 1, 2, 3, ... Whole numbers: natural numbers including 0 (0, 1, 2, ...). Integers: all whole numbers plus their negatives (..., -2, -1, 0, 1, 2, ...).
State the divisibility rules for 3, 4, 8, 9, and 11.
3: sum of digits divisible by 3. 4: last two digits divisible by 4. 8: last three digits divisible by 8. 9: sum of digits divisible by 9. 11: difference between sum of digits in odd and even positions is 0 or divisible by 11.
What is a prime number, and how many even prime numbers exist?
A prime number has exactly two distinct factors: 1 and itself. There is only one even prime number: 2.
What is the relationship between HCF and LCM of two numbers?
HCF x LCM = Product of the two numbers. So Product of two numbers = HCF x LCM.
How do you find the HCF and LCM of fractions?
HCF of fractions = HCF of numerators / LCM of denominators. LCM of fractions = LCM of numerators / HCF of denominators.
What is the difference between HCF (GCD) and LCM?
HCF (Highest Common Factor) is the largest number that divides all given numbers exactly. LCM (Least Common Multiple) is the smallest number that is exactly divisible by all the given numbers.
How do you convert a recurring decimal like 0.\overline{36} (0.363636...) into a fraction?
Write the repeating digits over as many 9s as there are repeating digits. 0.363636... = 36/99 = 4/11.
When comparing fractions with the same numerator, which is larger?
The fraction with the smaller denominator is larger. For example, 3/4 > 3/5 because 4 < 5.
How do you add or subtract fractions with different denominators?
Find the LCM of the denominators, convert each fraction to an equivalent fraction with that common denominator, then add or subtract the numerators.
What is the BODMAS / order of operations rule for simplification?
BODMAS: Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Multiplication and division are done left to right, as are addition and subtraction.
In BODMAS, in what order should brackets be removed?
Innermost first: remove brackets in the order ( ) parentheses, then { } braces, then [ ] square brackets (or by the 'VBODMAS' rule where V is vinculum/bar).
What is a square root, and what is the square root of 0.0064?
A square root of a number x is a value that, when multiplied by itself, gives x. The square root of 0.0064 is 0.08 (since 0.08 x 0.08 = 0.0064).
What is a cube root, and what is the cube root of 0.027?
A cube root of x is a value that, when cubed, gives x. The cube root of 0.027 is 0.3 (since 0.3 x 0.3 x 0.3 = 0.027).
What is the simplest way to find the square root of a perfect square by prime factorization?
Resolve the number into prime factors, group them in pairs, take one factor from each pair, and multiply those factors together.
What is a ratio and how is the ratio a:b expressed as a fraction?
A ratio compares two quantities of the same kind by division. The ratio a:b equals the fraction a/b, where a is the antecedent and b is the consequent.
What does it mean for four quantities to be in proportion?
Four quantities a, b, c, d are in proportion if a:b = c:d, meaning a/b = c/d. This implies the product of extremes equals the product of means: a x d = b x c.
If a:b = 2:3 and b:c = 4:5, what is a:b:c?
Make b common: a:b = 8:12 and b:c = 12:15, so a:b:c = 8:12:15.
What are the mean proportional and third proportional?
Mean proportional between a and b is the square root of (a x b). Third proportional to a and b is the value c where a:b = b:c, so c = b squared / a.
How do you calculate the arithmetic mean (average) of a set of numbers?
Average = (Sum of all observations) / (Number of observations).
What is the median of a data set, and how do you find it?
The median is the middle value when data is arranged in order. For an odd number of values it is the middle one; for an even number it is the average of the two middle values.
What is the mode of a data set?
The mode is the value that occurs most frequently in the data set. A data set can have no mode, one mode, or multiple modes.
What is the empirical relationship between mean, median, and mode?
Mode = 3 x Median - 2 x Mean (approximately, for a moderately skewed distribution).
If the average of n numbers is A and a new number x is added, what is the new average?
New average = (n x A + x) / (n + 1).
In a partnership, how is profit shared when all partners invest for the same time period?
Profit is divided in the ratio of their capital (investment) amounts. If A invests P and B invests Q, profit ratio = P:Q.
How is profit shared in a partnership when partners invest different amounts for different time periods?
Profit is shared in the ratio of (Capital x Time) for each partner. This product is called the monthly/effective equivalent capital.
Planning Quantitative Reasoning for YPIP
Quantitative Reasoning is about 18% of the YPIP syllabus by topic count — 25 of 136 topics, spread over 6 chapters. At roughly 45 minutes per topic plus 12 minutes per sub-topic, a first pass runs to about 20 hours.
The heaviest chapters are Arithmetic (5 topics), Percentages and Commercial Math (5 topics), Ratios and Averages (4 topics) . Front-load those while your energy is high; the short chapters are better revision filler later.
Work top-down: read the chapter, then tick topics off individually rather than marking the whole chapter done. Sub-topics are where silent gaps hide.
Quantitative Reasoning (YPIP) FAQ
What is in the YPIP Quantitative Reasoning syllabus?
Quantitative Reasoning is split into 6 chapters — Arithmetic, Ratios and Averages, Percentages and Commercial Math, Time and Work, Algebra and Equations and Data Interpretation, containing 25 topics and 0 sub-topics in total.
How many chapters are there in Quantitative Reasoning for YPIP?
6 chapters. Quantitative Reasoning accounts for about 18% of the topics in the whole YPIP syllabus (25 of 136).
How long should I spend on Quantitative Reasoning for YPIP?
Budget around 20 hours for a first pass through Quantitative Reasoning — about 45 minutes per topic plus 12 minutes per sub-topic across its 25 topics. Add revision cycles on top.
Are there flashcards for YPIP Quantitative Reasoning?
Yes — a 54-card Quantitative Reasoning deck. Sample cards are printed on this page, and the full deck is free in the Examius app with spaced repetition scheduling.