If the mean of x 1 , x 2 , is 7.5 and the mean of x 1 , x 2 , x 3 , is 8, then the value of x 3 ,

The question is garbled in the printed form, but the intended reading is clear: the mean of x1 and x2 is 7.5, and the mean of x1, x2 and x3 is 8. Work with totals, not averages.

Sum of x1 + x2 = 2 × 7.5 = 15. Sum of x1 + x2 + x3 = 3 × 8 = 24. So x3 = 24 − 15 = 9. Option A is correct.

Why the others fail: B (8) and C (7.5) are just the given means repeated, which is the bait the question sets. D (6) would give a three-term sum of 21 and a mean of 7, not 8.

• Core concept: mean multiplied by number of terms gives the sum, and adding a new term shifts the sum by exactly that term.
• Syllabus link: this is basic data handling under quantitative aptitude and CSAT, and it helps when reading averages in government statistical reports.

Trap: Aspirants assume x3 equals the new mean of 8, or average the given means, forgetting to convert averages into totals before subtracting.