Analytical Problem Solving Flashcards

A rectangle has a perimeter of 36 cm. If the length is twice the width, what is the area of the rectangle?

Answer: 72 sq cm

2(l+w)=36 → l+w=18; l=2w → 3w=18 → w=6, l=12; area=72 sq cm.

In a code language, 'hot sun bright' means 'din tok sul', 'cold wind rain' means 'pax rin mov', and 'hot cold day' means 'din pax vem'. What word means 'hot'?

Answer: din

'Hot' appears in sentences 1 and 3; the word common to 'din tok sul' and 'din pax vem' is 'din'.

A committee of 3 must be chosen from 7 candidates. How many different committees are possible?

Answer: 35

C(7,3) = 7!/(3!×4!) = 35 possible committees.

Five employees — J, K, L, M, N — sit in a row. J must sit next to K, and M cannot sit at either end. How many valid arrangements exist?

Answer: 48

Treat JK as a unit (2 internal arrangements): 4 units arranged in 4! = 24 ways; minus arrangements where M is at an end: 48 valid arrangements remain.

A researcher wants to test whether a new drug reduces blood pressure. She randomly assigns 200 patients to drug or placebo groups and measures results. What type of study is this?

Answer: Randomized controlled trial

Random assignment to treatment and control groups defines a randomized controlled trial, the gold standard for testing causation.

Which number does NOT belong in this group: 16, 25, 36, 48, 64, 81?

Answer: 48

All others are perfect squares (4², 5², 6², 8², 9²); 48 is not a perfect square.

A city's population grows at 10% per year. If the current population is 100,000, what will it be after 2 years?

Answer: 121,000

After year 1: 110,000; after year 2: 110,000 × 1.10 = 121,000 (compound growth).