Class 7 Decomposition: Clues, Ratios and Schedules

Hard problems become easy when broken into layers: number clues, ratio and percentage steps, jobs that wait for others, and elimination puzzles.

Key ideas

Solve layered clues one at a time; each clue shrinks the list of possible answers.

Ratio problems split into steps: find one part, then the share, then any percentage of it.

A job that must wait for others can start only when ALL of them are done; jobs with no waiting rule run at the same time.

The shortest time for all the jobs is the latest finish time, not the sum of every job’s time.

Counting “multiples of a OR b” must not count the multiples of both twice.

In ordering puzzles with no ties, “Y is not taller than X” means X is taller than Y.

Remember

Share in a ratio a : b of N

b part = b ÷ (a + b) × N

Example

boys : girls = 2 : 3 in 40 → 24 girls; 25% of them = 6

Finish time of a job

latest finish of the jobs it waits for + its own time

Multiples of a or b up to N

multiples of a + multiples of b − multiples of both

Example

multiples of 3 or 5 up to 30: 10 + 6 − 2 = 14

Worked example

(a) Rohan, Isha, Sana, Priya each have a different one of: dog, cat, parrot, rabbit. Isha does not have the cat. Sana has the rabbit. Rohan does not have the dog. Priya does not have the parrot. Priya does not have the cat. Who has the parrot?
(b) Rohan is faster than Sana. Arjun is faster than Priya. Rahul is not faster than Priya. Rahul is faster than Rohan. Who is the fastest?

Working: (a) only one way fits every clue: Rohan – cat, Isha – parrot, Sana – rabbit, Priya – dog; (b) the order is Arjun, Priya, Rahul, Rohan, Sana

Answer: (a) Isha; (b) Arjun

Decomposition: Clues, Ratios and Schedules

Key ideas

Remember

Watch out

Worked example