CA Foundation · Quantitative Aptitude · Linear Inequalities
If x is an integer satisfying both |3x - 4| < 8 and 2x - 1 ≥ 1, what is the sum of all possible values of x?
The sum is 6. The absolute value condition gives -4/3 < x < 4, and the second inequality gives x ≥ 1. The integers satisfying both are 1, 2 and 3, because 4 is excluded by the strict inequality, so they add up to 6.
- A6Correct
- B10
- C5
- D3
Explanation
|3x - 4| < 8 means -8 < 3x - 4 < 8, so -4/3 < x < 4. The second condition gives 2x ≥ 2, so x ≥ 1. Together 1 ≤ x < 4, so x = 1, 2, 3 and the sum is 6. A sum of 10 wrongly includes x = 4, and 3 is just the count of solutions or the largest value.
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