Skip to content

CA Foundation · Quantitative Aptitude · Linear Inequalities

For real x, the inequality (x − 2)(x − 6) < 0 holds. Which statement describes all such x?

The solution is 2 < x < 6. The product (x − 2)(x − 6) is negative only when x lies strictly between the roots, because the factors then have opposite signs. At the roots the product is zero, so the endpoints are excluded.

  1. Ax < 2 or x > 6
  2. B2 < x < 6Correct
  3. Cx < 6 only
  4. D2 ≤ x ≤ 6

Explanation

A product of two factors is negative when the factors have opposite signs. This occurs only when x lies between the roots 2 and 6, so 2 < x < 6. At x = 2 or 6 the product is zero, which is not less than zero, so the endpoints are excluded. The option x < 2 or x > 6 gives a positive product.

Did you get it right without looking?

One question tells you little. A timed set on Linear Inequalities shows your real accuracy, how long you take and where you lose marks.

Practise Linear InequalitiesFree diagnostic mock

More Linear Inequalities questions