Algebra

Inequalities

Easy

A pair of consecutive odd positive integers, both of which are smaller than 19, have a sum that is more than 22. How many such pairs will be there, if we allow a number to be in more than one pair?

✅ Correct Option: 2

Let the numbers be $x$ and $x+2$ .

$x+x+2 > 22$

$2x+2 > 22$

$2x > 20$

$x > 10$

Both numbers are smaller than 19, so $x+2 < 19$ , which means $x < 17$ .

Since $x$ is an odd positive integer, possible values for $x$ are 11, 13, 15.

The pairs are (11, 13), (13, 15), (15, 17).

Total pairs = 3.

2024: Slot 1

Find the sum of the smallest value and the greatest value of $x$ that satisfy the inequality $|5x + 5| - 8 \leq 17$ .

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A pair of consecutive odd positive integers, both of which are smaller than 19, have a sum that is more than 22. How many such pairs will be there, if we allow a number to be in more than one pair?

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