Exam Hall 2: Eliminate options and dodge unit traps
Often you can throw away two options before doing any arithmetic. Then you only test the rest.
60-second refresher: the basics
The basics, plus percent change, because elimination depends on knowing which way a change goes.
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. What is a percent change? When a value moves from an old value to a new value, the OLD value is the whole (100%), because the change is measured against where you started. A 20% rise on ₹500: 20% of ₹500 = 20 × ₹5 = ₹100, so the new value is ₹600 = 100% + 20% = 120% of the old value. A 20% fall: new value = 100% − 20% = 80% of the old value = ₹400.
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: eliminate, then test
Eliminate first: a price rose 8% to ₹1,350. Which option is the original price?
Show answer
Correct answer: C
Kill 1,458 (too big) and 1,342 (₹8 is far too small for 8%). Test 1,250: 10% of 1,250 = 125 and 2% of 1,250 = 25, so 8% of 1,250 = 100 → 1,250 + 100 = 1,350. ✓
Option A: Wrong direction: The original must be below 1,350 after a rise: eliminate instantly.
Option B: Reversed on the wrong base: 1,350 − 8% of 1,350 uses the wrong base (1,242).
Option D: Percent read as units: Subtracting 8 treats 8% as ₹8.
Hint: Which options are impossible?
Three fast elimination checks
- Direction: after a rise the original is smaller; after a fall it is bigger.
- Size: 8% of about 1,300 is about 100, so a ₹8 change is impossible.
- Back-substitute: multiply the survivor by the multiplier and see if it hits the given number.
Drill 1, solved slowly
Question
A price rose 8% to ₹1,350. What was the original price?
Solution
- What is the question asking?
- ₹1,350 is the value AFTER a 8% rise. It is not 100%.
- We must find the value BEFORE the change: the original price, which is 100%.
- Make it a story
- A gas cylinder now costs ₹1,350 after an 8% price rise. What did it cost before?
- We know / We need
- The 8% is a percent of the original price (the value before).
- So the new price = 100% + 8% = 108% of the original price
- We know: 108% of the original price = ₹1,350
- We need: 100% of the original price = ?
- Step 1: find 1%
- 108% of the original price = ₹1,350, so share ₹1,350 among 108 pieces of 1%.
- 1% of the original price = 1,350 ÷ 108 = ₹12.5
- Step 2: find 100%
- 100% of the original price = 12.5 × 100 = ₹1,250
- See it on a bar
█████████████████████████before = 100% = ₹1,250 (each block = 4% of the original price)█████████████████████████▓▓after = 108% of before = ₹1,350- ▓ = the extra 8% of the original price = ₹100
- Shortcut (only after you understand)
- Before = After × 100 ÷ 108 = 1,350 × 100 ÷ 108 = 1,250
- (Same thing: divide by the multiplier 1.08.)
- Faster way (optional): Eliminate first, then test: 10% of 1,250 = 125 and 2% = 25, so 8% = 100, and 1,250 + 100 = 1,350 ✓.
- Quick check
- 8% of ₹1,250 = ₹100
- 1,250 + 100 = 1,350 ✓
Answer: ₹1,250
Watch out: Most important concept: ₹1,350 is 108% of the original price, not 100%. Do not take 8% of ₹1,350 off: that gives ₹1,242, because it uses the wrong base.
Test your understanding: after a 20% fall, a phone costs ₹9,600. What did it cost before? Eliminate first.
Show answer
Correct answer: C
Eliminate ₹7,680 (smaller than ₹9,600 after a fall) and ₹9,620 (₹20 is far too small for 20%). Then work it out: ₹9,600 = 80% of the old price → 1% = ₹120 → 100% = ₹12,000. Check: 12,000 − 20% of 12,000 = 12,000 − 2,400 = 9,600 ✓.
Option A: Wrong direction: Eliminate: after a FALL the old price must be bigger than ₹9,600. ₹7,680 is another 20% off.
Option B: Wrong base: ₹11,520 adds 20% of ₹9,600. But the 20% was of the OLD price: 20% of 11,520 is 2,304, and 11,520 − 2,304 = 9,216, not 9,600.
Option D: Percent read as rupees: Eliminate: a ₹20 change is far too small for 20% of about ₹10,000 (that is about ₹2,000).
Hint: After a fall, the old price is bigger. ₹9,600 is 80% of it.
Drill 2: units
Unit trap: 45 minutes is what percent of 2.5 hours?
Show answer
Correct answer: A
Same unit first: 45 ÷ 150 × 100 = 30%.
Option B: Unit conversion slip: 45/250 treats 2.5 h as 250 minutes.
Option C: Mixed units: 45/2.5 mixes minutes with hours.
Option D: Base flipped: 150/45 flips the base.
Hint: 1 hour = 60 minutes.
g vs kg, minutes vs hours, paise vs rupees. Convert both numbers to the smaller unit before dividing. Examiners put the unconverted answer in the options on purpose.
Five questions are attached below. Before calculating, cross out at least one option on paper.
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