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Ages & Problems on Numbers · Question 54 of 60

Question 54

MediumOriginal question

The sum of two numbers is 40 and their product is 375. What is the positive difference between them?

Options for question 54

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. (a−b)2=(a+b)2−4ab=1600−1500=100(a - b)^2 = (a + b)^2 - 4ab = 1600 - 1500 = 100.

  2. a−b=100=10a - b = \sqrt{100} = 10. (The numbers are 25 and 15.)

Worth noting

15 and 25 are the numbers themselves. The identity (a−b)2=(a+b)2−4ab(a - b)^2 = (a + b)^2 - 4ab gets the difference without finding them.

Concept
Difference from sum and product
Typical time
60 s
Your time
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