Negative marking: your score, and when a guess pays
In Tier I each part has 25 questions for 50 marks, so a right answer earns 2 marks, and the SSC notice (para 13.8.2) takes 0.50 marks off for each wrong answer. One wrong answer costs a quarter of a right one. This lesson turns that into numbers you can use in the hall: your score, your score as a percent, and when a guess is worth taking.
Guess first
Guess first: in the 25-question Quant part, Ravi gets 18 right and 5 wrong, and skips 2. What is his score out of 50?
Show answer
Correct answer: B
Right answers: 18 × 2 = 36. Wrong answers: 5 × 0.5 = 2.5 off. Skipped questions: 0. Score = 36 − 2.5 = 33.5.
Option A: 36 counts the right answers and forgets the 0.50 off for each wrong one.
Option C: 31 takes a whole mark off for each wrong answer (36 − 5 = 31); the notice takes 0.50.
Option D: 32.5 also takes 0.50 off for the 2 skipped questions (36 − 7 × 0.5 = 32.5); a skipped question scores 0.
Hint: +2 for each right answer, −0.50 for each wrong one, 0 for a skip.
If you got 33.5, you have the score rule. The rest of the lesson asks the useful question: when is a guess worth it?
An everyday picture
Negative marking works like a samosa seller's day.
Each samosa sold earns ₹2 one right answer
+2 marks
Each samosa thrown away loses ₹0.50 one wrong answer
−0.50 marks
1 sold for every 4 thrown away 1 right in every 5 tries
2 − 4 × 0.5 = 0: no gain, no loss
So a guess pays when it is right more often than 1 time in 5.
See it: what one guess is worth
A blind guess with all four options left: 1 time in 4 it is right, 3 times in 4 it is wrong.
| Outcome | Chance | Marks | Chance × marks |
|---|---|---|---|
| Right | 1/4 | +2 | 1/4 × 2 = 0.5 |
| Wrong | 3/4 | −0.5 | 3/4 × 0.5 = 0.375 off |
| On average | 0.5 − 0.375 = 0.125 |
flowchart TD A["No clear method within your 36 seconds"] --> B["Skip it for now and move on"] B --> C["Near the end of the part, come back"] C --> D["Rule out every option you can"] D --> E["Guess among the rest: even a blind guess gains +0.125 on average"]
The average gain of a guess is chance × 2 − (1 − chance) × 0.5. It is above zero when the chance of being right is more than 1 in 5.
Try it. How many wrong answers cancel the marks of 3 right answers?
Find the rule
With +2 for a right answer and −0.50 for a wrong one, you rule out one of the four options for sure and guess among the other three. What is that guess worth on average?
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Correct answer: A
With 3 options left, the chance of being right is 1/3 and of being wrong 2/3. Average: 1/3 × 2 − 2/3 × 0.5 = ⅔ − ⅓ = ⅓ of a mark.
Option B: +⅔ counts only the right case (1/3 × 2 = ⅔) and forgets the 0.50 lost when wrong.
Option C: +0.125 is a blind guess with all four options; ruling one out raises the chance to 1/3.
Option D: 0 assumes a guess is worth nothing; with one option gone it gains a third of a mark on average.
Hint: Chance right × 2, minus chance wrong × 0.5.
In the 100-question Tier I paper, Meena gets 70 right and 18 wrong, and leaves 12. What percent of the 200 marks does she score?
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Correct answer: B
Score = 70 × 2 − 18 × 0.5 = 140 − 9 = 131. As a percent of 200: 131 ÷ 200 × 100 = 65.5%.
Option A: 70% forgets the 0.50 off for each wrong answer (140 ÷ 200 × 100 = 70).
Option C: 61% takes a whole mark off for each wrong answer ((140 − 18) ÷ 200 × 100 = 61).
Option D: 62.5% also takes 0.50 off for the 12 questions she left ((140 − 30 × 0.5) ÷ 200 × 100 = 62.5).
Hint: Work out the score first, then divide by the 200 marks.
With +2 for a right answer and −0.50 for a wrong one, a guess gains marks on average only when your chance of being right is more than what?
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Correct answer: B
A guess breaks even when chance × 2 = (1 − chance) × 0.5, that is when chance = 0.5 ÷ (2 + 0.5) = 0.2 = 20%, 1 in 5. Above 20% it gains.
Option A: 25% divides the loss by the gain (0.5 ÷ 2 = 0.25); it must be divided by the gain plus the loss.
Option C: 50% thinks a guess must be right more often than wrong, but one right answer outweighs four wrong ones.
Option D: 0% ignores the 0.50 lost on each wrong guess.
Hint: Where do chance × 2 and (1 − chance) × 0.5 become equal?
Name the rule
- Score: 2 × right − 0.5 × wrong. A skipped question scores 0.
- Score as a percent: score ÷ maximum marks × 100 (50 for a part, 200 for the paper).
- A guess on average: chance × 2 − (1 − chance) × 0.5. It gains when the chance is more than 1 in 5.
- Remove options first: with 4 options left a guess is worth +0.125 on average, with 3 left +⅓, with 2 left +0.75.
- Skip first, guess last: leave a question that has no clear method within your time and move on; before the part's time ends, come back, rule out what you can and guess. Even a blind guess gains +0.125 on average.
Because 0.5 ÷ 2 = 1/4: four wrong answers cancel one right answer. That is why a guess that is right even once in four tries still gains a little, and a guess among two options gains a lot.
Worked, half-done, solo
Question
You can rule out two of the four options. What is a guess between the other two worth on average?
Solution
- Find the chances
Two options left: right 1/2 of the time, wrong 1/2 of the time.
- The right case
1/2 × 2 = 1 mark.
- The wrong case
1/2 × 0.5 = 0.25 off.
- Put it together
1 − 0.25 = 0.75 of a mark on average.
Answer: +0.75 marks
Watch out: Counting only the right case gives +1; the 0.25 lost on the wrong half is part of the average.
Now finish one that is half done.
In the Quant part, Kavya gets 20 right and 4 wrong, and skips 1. Her right answers give 20 × 2 = 40 marks. What is her score?
Show answer
Correct answer: A
The wrong answers take 4 × 0.5 = 2 off, and the skip takes nothing: 40 − 2 = 38.
Option B: 40 forgets the 0.50 off for each wrong answer.
Option C: 36 takes a whole mark off for each wrong answer (40 − 4 = 36).
Option D: 37.5 also takes 0.50 off for the skipped question (40 − 5 × 0.5 = 37.5).
Hint: How much do 4 wrong answers take off?
And one on your own.
In the whole Tier I paper, Arjun gets 64 right and 20 wrong. What is his score out of 200?
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Correct answer: B
64 × 2 = 128, and 20 × 0.5 = 10 off: 128 − 10 = 118.
Option A: 128 forgets the 0.50 off for each wrong answer.
Option C: 108 takes a whole mark off for each wrong answer (128 − 20 = 108).
Option D: 158 gives 2 marks for all 84 answers, right or wrong (84 × 2 − 10 = 158).
Hint: Only right answers earn 2 marks.
The traps
- Forgot the minus marks: each wrong answer takes 0.50 off.
- Took a whole mark off: the notice takes 0.50, not 1.
- Took marks off for skips: a skipped question scores 0.
- Divided by the questions, not the marks: a score percent is out of the maximum marks.
- Never guessed: with one or two options ruled out, skipping throws marks away.
Neel ruled out two options on each of 6 questions he could not solve, then skipped all 6 "to be safe". On average, what did skipping cost him?
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Correct answer: A
With two options left, a guess is worth 1/2 × 2 − 1/2 × 0.5 = 0.75 on average, so 6 guesses are worth 6 × 0.75 = 4.5 marks.
Option B: A blank answer scores 0, while each of these guesses was worth +0.75 on average: skipping them gave marks away.
Option C: +1 counts only the right half (1/2 × 2) and forgets the 0.25 lost on the wrong half.
Option D: 12 assumes every guess is right (6 × 2); with two options, about half are wrong.
Hint: What is one guess between two options worth on average?
Mixed check
In the English part, Pooja answers all 25 questions: 19 right and the other 6 wrong. What is her score out of 50?
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Correct answer: B
19 × 2 = 38, and 6 × 0.5 = 3 off: 38 − 3 = 35.
Option A: 38 forgets the 0.50 off for each wrong answer.
Option C: 32 takes a whole mark off for each wrong answer (38 − 6 = 32).
Option D: 47 gives 2 marks for all 25 answers, right or wrong (25 × 2 − 3 = 47).
Hint: +2 for each right answer, −0.50 for each wrong one.
From lesson 11:
On a 1.6 km walk, 600 m have been covered. What percent of the walk is that?
Show answer
Correct answer: B
Same unit first: 1.6 km = 1,600 m. 600 ÷ 1,600 × 100 = 37.5%. Size check: under 100%, as it must be.
Option A: 37,500% divides 600 m by 1.6 km without converting (600 ÷ 1.6 × 100 = 37,500).
Option C: 266⅔% divides the whole by the part (1,600 ÷ 600 × 100 = 266⅔).
Option D: 3.75% is ten times too small: the decimal point slipped one place.
Hint: How many metres are in 1.6 km?
Quick reference
Marks and guesses
- Score
- 2 × right − 0.5 × wrong; a skip scores 0 18 right, 5 wrong: 36 − 2.5 = 33.5
- Score percent
- score ÷ maximum marks × 100 131 of 200: 131 ÷ 200 × 100 = 65.5%
- A guess on average
- chance × 2 − (1 − chance) × 0.5 2 options left: 1 − 0.25 = 0.75
- Break-even
- a guess gains when the chance is more than 0.5 ÷ 2.5 = 1/5 4 options left: 1/4 is more than 1/5
- Skip first, guess last
- move on, come back, rule out options, then guess 3 options left: +⅓ mark on average
Why it works: a wrong answer costs a quarter of a right one, so a guess pays whenever it is right more than once in five tries.
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