Number System and Simplification
Number System and Simplification
Part-II General Studies carries 40 questions, and Elementary Mathematics is one of its five equal parts — so expect about 8 maths questions. Number system and simplification usually supply 1 to 2 of them. The questions are short, single-step and class 6-8 level, but you get roughly 60 seconds each.
Types of Numbers You Must Recognise
Every number question starts with correct classification. Learn these five labels and half the paper becomes readable.
| Type | Meaning | Example |
|---|---|---|
| Natural (N) | Counting numbers from 1 | 1, 2, 3, 4 |
| Whole (W) | Natural numbers plus zero | 0, 1, 2, 3 |
| Integer (Z) | Positive, negative and zero | -3, -1, 0, 5 |
| Rational (Q) | Can be written as p/q, q ≠ 0 | 3/4, 0.25, -7 |
| Irrational | Never ends, never repeats | √2, π |
| Prime | Exactly two factors | 2, 3, 5, 7, 11 |
| Composite | More than two factors | 4, 6, 8, 9 |
Two facts get asked directly: 1 is neither prime nor composite, and 2 is the only even prime number.
Divisibility Rules That Save Time
Never do long division in the exam hall. Test the digits instead.
| Divisible by | Rule | Quick check |
|---|---|---|
| 2 | Last digit is even | 4386 → yes |
| 3 | Digit sum divisible by 3 | 4386 → 21 → yes |
| 4 | Last two digits divisible by 4 | 4386 → 86 → no |
| 5 | Ends in 0 or 5 | 4385 → yes |
| 6 | Divisible by both 2 and 3 | 4386 → yes |
| 8 | Last three digits divisible by 8 | 5128 → 128 → yes |
| 9 | Digit sum divisible by 9 | 4383 → 18 → yes |
| 11 | (Odd-place sum) − (even-place sum) = 0 or 11k | 2915 → (2+1)−(9+5) = −11 → yes |
BODMAS: The Order of Simplification
Simplification questions are pure order-of-operations tests. The rule is fixed.
B → O (of) → D → M → A → S
The trap is that division and multiplication share one rank, and so do addition and subtraction. When they appear together you move left to right, not D before M.
✗ 24 ÷ 6 × 2 = 24 ÷ 12 = 2 | ✓ 24 ÷ 6 × 2 = 4 × 2 = 8
Worked example: 12 + 6 ÷ 3 × 2 − 4 = 12 + 2 × 2 − 4 = 12 + 4 − 4 = 12.
BODMAS में भाग और गुणा बराबर हैं — जो पहले आए वही पहले होगा।
Place Value, Face Value and Unit Digit
Face value is the digit itself. Place value is the digit multiplied by its position. In 5,847 the face value of 8 is 8 but its place value is 800.
For unit-digit questions, only the last digit of each number matters. In 47 × 63 the unit digit is the unit digit of 7 × 3 = 21, which is 1. Powers repeat in a cycle of four: 2¹=2, 2²=4, 2³=8, 2⁴=6, then it starts again.
TRE pointer: Elementary Mathematics gives you roughly 8 of the 40 Part-II questions, and Part-II counts towards your merit — unlike the Prarambhik paper. The common trap here is a simplification chain with a negative sign in the middle. Remember the new pattern too: there are five options A to E, and if you want to skip a question you must mark option E. Leaving the row blank still costs you −1/3.
60-Second Recap
- Elementary Maths ≈ 8 questions inside the 40-question Part-II, and Part-II is merit-counting.
- 1 is neither prime nor composite; 2 is the only even prime.
- Digit sum for 3 and 9; last two digits for 4; last three for 8; alternate-sum for 11.
- In BODMAS, D and M rank equal — solve left to right. Same for A and S.
- Unit digit of a product depends only on the unit digits; powers of 2 cycle in fours.
- Skipping a question needs option E, otherwise you still lose 1/3 mark.
Frequently Asked Questions
How many maths questions come in BPSC TRE 4.0 Part-II?
Part-II General Studies has 40 questions built from five areas — Elementary Mathematics, General Awareness, General Science, Indian National Movement and Geography. That works out to roughly 8 maths questions. These marks count towards your final merit, so the section is worth real preparation time.
Is 1 a prime number?
No. A prime number must have exactly two distinct factors, 1 and itself. The number 1 has only one factor, so it is neither prime nor composite. This single line is asked directly in teaching exams, usually inside a statement-based question with three or four claims.
What is the correct order in BODMAS?
Bracket, Of, Division, Multiplication, Addition, Subtraction. The catch is that division and multiplication carry equal priority, and so do addition and subtraction. When two equal-rank operations sit side by side, you solve strictly from left to right rather than following the letter order.
Does leaving a question blank cost marks in TRE 4.0?
Yes. Each paper offers five options, A to E. If you do not want to attempt a question you must darken option E. A completely blank row is treated as an unanswered question and still attracts the same one-third negative mark, so E is compulsory, not optional.