Exam Hall 3: Negative marking maths and a skip rule
Is guessing worth it at −0.50? Work it out once, then decide your rule before exam day.
60-second refresher: the basics
The basics, plus what your score means as a percent.
1. What is a percent? "Per cent" means per hundred. 35% means 35 out of every 100. Think of ₹100 as 100 coins of ₹1. If you spend 35 of the coins, you spent 35 out of 100, which is 35% of your money. On a 100-square grid each square is 1%, so 35% is 35 shaded squares:
███████████████████████████████████·································································
Text version: 35 of the 100 squares are shaded (35%); 65 are not (65%).
2. What does "of" mean? "Of" tells you which thing the percent is taken from. "35% of ₹200" means: cut ₹200 into 100 equal pieces (each piece is ₹200 ÷ 100 = ₹2) and take 35 pieces: 35 × ₹2 = ₹70.
3. Whole and part. The number after "of" is the whole: all of it, 100%. A part is a piece of the whole. The rest is what is left: whole − part, which is (100 − percent)%. In the example: whole ₹200, part ₹70 (35%), rest ₹130 (65%).
4. The one tool you will use in every question: find 1% first. 1% of anything = that thing ÷ 100. From 1% you can build any percent (multiply by the percent) or get back to the whole (multiply by 100). Try it now: 1% of ₹300 = 300 ÷ 100 = ₹3, so 35% of ₹300 = 35 × 3 = ₹105.
5. A score as a percent. Your marks are the part; the total marks of the section are the whole. 30 marks out of 50 = 30 ÷ 50 × 100 = 60% of the section's marks.
Words to know
- Percent (%)
- out of every 100 35% = 35 out of 100
- Whole
- the number after 'of' = 100% ₹200 in '35% of ₹200'
- Part
- a piece of the whole ₹70 = 35% of ₹200
- Rest
- whole − part ₹130 = 65% of ₹200
- 1%
- whole ÷ 100 1% of ₹200 = ₹2
Drill 1: the expected mark
A blind guess on a CHSL question (+2 right, −0.5 wrong, 4 options): what is the expected mark?
Show answer
Correct answer: B
Expected mark = P(right) × 2 − P(wrong) × 0.5. With 4 options: 0.125. After removing two options: ½ × 2 − ½ × 0.5 = 0.75.
Option A: Assumed it cancels: The penalty is smaller than a quarter of the reward, so it is slightly positive.
Option C: Used one outcome: −0.5 is the loss only when wrong.
Option D: Ignored negative marking: +0.5 counts the 25% win but forgets the 75% losses.
Hint: Weight each outcome by its chance.
| Options left | Chance right | Expected mark |
|---|---|---|
| 4 | 1/4 | +0.125 |
| 3 | 1/3 | +0.333 |
| 2 | 1/2 | +0.750 |
Even a blind guess is slightly positive here, but each guess costs time you could spend on a question you can solve. Removing options is what makes a guess worth taking.
- First pass: answer everything you can solve in about 30 seconds.
- If a question passes 45 seconds with no clear method, mark it and move on.
- Second pass: return to marked questions. Guess only after you have removed at least one option.
- Never leave the section timer with solvable questions unseen.
Drill 2: speed line
Speed line: +15% then −15%. Net change?
Show answer
Correct answer: D
1.15 × 0.85 = 0.9775 → −2.25%.
Option A: Assumed it cancels: Equal changes never cancel.
Option B: Sign error: Opposite directions give a negative cross term.
Option C: Arithmetic slip: 15²/100 = 2.25, not 1.5.
Hint: x²/100 with x = 15.
Your score as a percent, solved slowly
Question
You score 27.5 marks out of 50. What percent is that?
Solution
- What is the question asking?
- 50 marks is the whole (100%). 27.5 marks is a part of it.
- We must say how big the part is, counted in hundredths of 50 marks.
- Make it a story
- In the 25-question Quant part (2 marks each, 50 marks) you get 15 right and 5 wrong. Net marks = 15 × 2 − 5 × 0.5 = 30 − 2.5 = 27.5.
- We know / We need
- We know: 100% of the 50 Quant marks = 50 marks, and the part = 27.5 marks
- We need: 27.5 marks = ?% of the 50 Quant marks
- Step 1: find 1% of the whole
- 1% of the 50 Quant marks = 50 ÷ 100 = 0.5 marks
- Step 2: count how many 1% pieces fit in the part
- 27.5 ÷ 0.5 = 55 pieces of 1%
- So 27.5 marks = 55% of the 50 Quant marks
- See it on a bar
███████████░░░░░░░░░each block = 5% of the 50 Quant marks = 2.5 marks- █ 55% = 27.5 marks (your net marks)
- ░ 45% = 22.5 marks (marks not scored)
- Whole bar = 100% = 50 marks
- Shortcut (only after you understand)
- Percent = Part ÷ Whole × 100 = 27.5 ÷ 50 × 100 = 55%, so 27.5 is 55% of 50
- Quick check
- 55% of 50 marks = 50 × 55 ÷ 100 = 27.5 marks ✓
Answer: 55%
Watch out: Most important concept: Divide by the WHOLE (50), not by the part. The part 27.5 is smaller than the whole, so the answer must be below 100%.
Test your understanding: in the 50-mark Quant part you get 16 right (+2 each) and 4 wrong (−0.50 each). What percent of the 50 marks do you score?
Show answer
Correct answer: A
Step 1: net marks = 16 × 2 − 4 × 0.5 = 32 − 2 = 30. Step 2: 1% of the 50 marks = 0.5, so 30 ÷ 0.5 = 60 → 60%. Check: 60% of 50 = 30 ✓.
Option B: Forgot negative marks: 64% = 32 out of 50 forgets the −2 for the 4 wrong answers.
Option C: Wrong whole: 80% = 16 out of 20 attempted questions. The question asks about marks out of 50.
Option D: Wrong penalty: 56% = 28 out of 50 takes 1 mark per wrong answer. The penalty is 0.50 per wrong answer.
Hint: Net marks first, then compare with 50.
Five questions are attached below. Apply your skip rule as you go.
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