SRMJEEE Aptitude Syllabus

Aptitude syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Aptitude in SRMJEEE, not a summary of it.

1. 1

   Quantitative Aptitude

   4 topics

   • Number System and Arithmetic
     • HCF, LCM and divisibility
     • Percentages, profit and loss
   • Ratio, Proportion and Averages
     • Ratio and proportion
     • Mixtures and alligation
   • Time, Speed, Work and Distance
     • Time and work
     • Speed, distance and time
   • Simple and Compound Interest
     • Interest calculations
2. 2

   Logical Reasoning

   4 topics

   • Series and Pattern Recognition
     • Number and letter series
   • Coding-Decoding
     • Letter and number coding
   • Blood Relations and Directions
     • Family tree problems
     • Direction sense test
   • Syllogisms and Statements
     • Logical deductions
3. 3

   Data Interpretation and Analytical Reasoning

   3 topics

   • Data Interpretation
     • Tables, bar and pie charts
     • Line graphs
   • Seating Arrangement and Puzzles
     • Linear and circular arrangements
   • Clocks and Calendars
     • Clock angle and calendar problems

Aptitude flashcards for SRMJEEE

23 of 50 cards from the Aptitude deck — real questions with worked answers.

1. What are the divisibility rules for 3 and 9?

   A number is divisible by $3$ if the sum of its digits is divisible by $3$; it is divisible by $9$ if the digit sum is divisible by $9$.

2. State the divisibility rules for 4 and 8.

   Divisible by $4$ if the number formed by the last two digits is divisible by $4$; divisible by $8$ if the number formed by the last three digits is divisible by $8$.

3. What is the divisibility rule for 11?

   A number is divisible by $11$ if the difference between the sum of digits in odd positions and the sum of digits in even positions is $0$ or a multiple of $11$.

4. What is the sum of the first $n$ natural numbers, and the sum of their squares?

   $$\sum_{k=1}^{n} k = \frac{n(n+1)}{2}, \qquad \sum_{k=1}^{n} k^{2} = \frac{n(n+1)(2n+1)}{6}$$

5. What is the sum of the cubes of the first $n$ natural numbers?

   $$\sum_{k=1}^{n} k^{3} = \left[\frac{n(n+1)}{2}\right]^{2}$$

6. How is a number expressed in terms of divisor, quotient and remainder?

   $$\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}, \quad 0 \leq \text{Remainder} < \text{Divisor}$$

7. How do you find the number of divisors of a number $N$ from its prime factorization?

   If $N = p_{1}^{a_{1}} \cdot p_{2}^{a_{2}} \cdots p_{k}^{a_{k}}$, then the number of divisors is $(a_{1}+1)(a_{2}+1)\cdots(a_{k}+1)$.

8. What is the fundamental relationship between the HCF and LCM of two numbers?

   $$\text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b$$

9. How do you find the HCF and LCM from prime factorizations?

   HCF is the product of common prime factors raised to their lowest powers; LCM is the product of all prime factors raised to their highest powers.

10. How do you find the HCF and LCM of fractions?

    $$\text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}}, \quad \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}}$$

11. What number, when divided by $a$, $b$, $c$, leaves the same remainder $r$ each time?

    It is of the form $k \cdot \text{LCM}(a,b,c) + r$. The smallest such number greater than $r$ is $\text{LCM}(a,b,c) + r$.

12. How do you convert a fraction to a percentage and vice versa?

    To get a percentage, multiply the fraction by $100$: $\frac{a}{b} \times 100\%$. To convert a percentage to a fraction, divide by $100$: $x\% = \frac{x}{100}$.

13. If a quantity increases by $x\%$ and then decreases by $x\%$, what is the net change?

    There is a net decrease of $\frac{x^{2}}{100}\%$ of the original value.

14. What is the formula for percentage change between two values?

    $$\text{Percentage change} = \frac{\text{New value} - \text{Old value}}{\text{Old value}} \times 100\%$$

15. Define profit percent and loss percent in terms of cost price (CP) and selling price (SP).

    $$\text{Profit}\% = \frac{SP - CP}{CP} \times 100, \qquad \text{Loss}\% = \frac{CP - SP}{CP} \times 100$$

16. How do you find SP given CP and a gain or loss percent?

    $$SP = CP \times \frac{100 + \text{Gain}\%}{100} \quad \text{or} \quad SP = CP \times \frac{100 - \text{Loss}\%}{100}$$

17. What is the relationship between marked price (MP), discount and selling price?

    $$SP = MP \times \frac{100 - \text{Discount}\%}{100}$$ where discount is calculated on the marked price.

18. If two articles are sold at the same SP, one at $x\%$ profit and the other at $x\%$ loss, what is the overall result?

    There is always an overall loss of $\frac{x^{2}}{100}\%$.

19. Define the ratio $a:b$ and what it means to say two ratios are in proportion.

    A ratio $a:b = \frac{a}{b}$ compares two quantities. Four quantities are in proportion if $a:b = c:d$, i.e. $\frac{a}{b} = \frac{c}{d}$, which gives $ad = bc$.

20. In the proportion $a:b = c:d$, what are the means, extremes and the product rule?

    $a$ and $d$ are the extremes, $b$ and $c$ are the means. Product of extremes equals product of means: $ad = bc$.

21. Define mean proportional and third proportional.

    Mean proportional between $a$ and $b$ is $\sqrt{ab}$. The third proportional to $a$ and $b$ is $\frac{b^{2}}{a}$ (where $a:b = b:x$).

22. What is the formula for the average (arithmetic mean) of $n$ quantities?

    $$\text{Average} = \frac{\text{Sum of all quantities}}{\text{Number of quantities}} = \frac{1}{n}\sum_{i=1}^{n} x_{i}$$

23. What is the average of the first $n$ natural numbers and of $n$ consecutive numbers?

    Average of the first $n$ natural numbers is $\frac{n+1}{2}$. The average of any set of consecutive numbers equals the average of the first and last terms.

See more Aptitude flashcards →

Planning Aptitude for SRMJEEE

Aptitude (SRMJEEE) FAQ