Intelligent Math Puzzle – Challenge 92
Intelligent Math Puzzle - Challenge 92 is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.
Some Math puzzles like the following one stumped even the smartest people. Can You Solve It? The solution is also given.
Challenge:
If A and B are integers and (frac{1}{B}=frac{1}{A}-frac{1}{20}) what is the value of A+B?
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The correct answer is 9.
(frac{1}{B} =frac{1}{A} -frac{ 1}{20})
Therefore, A is less than B. Why?
Plug in different values for A.
Let’s begin with 2. If A (= 2 → frac{1}{B} = frac{ 1}{2} – frac{ 1}{20} → frac{ 1}{B} = frac{ 9}{20} → 9B = 20)
B is an integer. Therefore, B cannot be (frac{ 20}{9})
A (= 3 → frac{ 1}{B} = frac{ 1}{3} – frac{ 1}{20} → frac{ 1}{B} = frac{ 17}{60} → 17B = 60)
A (= 4 → frac{ 1}{B} = frac{ 1}{4} – frac{ 1}{20} → frac{ 1}{B} = frac{4}{20} → 4B = 20 → B = 5) Bingo!
A = 4 and B = 5 → A + B = 9The Best Books to Ace Algebra
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