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Ages & Problems on Numbers · Question 25 of 60

Question 25

HardOriginal question

The product of Nisha's age 3 years ago and her age 3 years from now is 160. What is her present age?

Options for question 25

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Let her present age be xx. Then (x−3)(x+3)=160(x - 3)(x + 3) = 160.

  2. x2−9=160x^2 - 9 = 160, so x2=169x^2 = 169.

  3. x=13x = 13 (an age cannot be negative).

  4. Check: 10×16=16010 \times 16 = 160.

Worth noting

10 and 16 are her ages 3 years ago and 3 years ahead. The product of (x−3)(x - 3) and (x+3)(x + 3) is x2−9x^2 - 9, a quick identity that saves solving a full quadratic.

Concept
Quadratic from a product of past and future ages
Typical time
100 s
Your time
—
The rule this testsProblems on ages
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Ten questions from Ages & Problems on Numbers, at your own pace.

Practise this chapter →

Ten questions from Ages & Problems on Numbers, at your own pace.