A price rises by 20% and then falls by 20%. What is the net change?
Solution:Net change = a + b + ab/100 = 20 − 20 − 400/100 = −4%. So a 4% decrease.
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Two trains 120 m and 180 m long run in opposite directions at 54 km/h and 36 km/h. How long do they take to cross each other?
Solution:Relative speed = 90 km/h = 25 m/s. Distance = 300 m. Time = 300/25 = 12 s.
If x + 1/x = 4, find x² + 1/x².
Solution:Square both sides: x² + 2 + 1/x² = 16, so x² + 1/x² = 14.
Five friends sit in a row. C is in the middle, A is immediately left of C, D immediately right. E is at an end but not next to B. Who is at the other end?
Solution:Positions: _ A C D _. E takes one end; the other end must be B. Since E is not next to B, the arrangement works with B at the far end.
8 teams each play every other team once. How many matches?
Solution:8C2 = 8 × 7 / 2 = 28 matches.
Choose the word closest in meaning to ‘ubiquitous’.
Solution:‘Ubiquitous’ means present or found everywhere.
Pick the odd sentence: (1) The monsoon arrived early. (2) Farmers began sowing in June. (3) Reservoir levels rose. (4) Stock markets closed higher.
Solution:Sentences 1–3 are about the monsoon and farming. Sentence 4 is unrelated.
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