A man eats 100 grapes in 5 days, each day 6 more than the previous day. How many grapes did he eat on the first day?

A man eats 100 grapes in 5 days, each day 6 more than the previous day. How many grapes did he eat on the first day?

• A. Eight
• B. Five
• C. Ten
• D. Twelve

Answer: (A)

This question tests how an arithmetic progression works when you know the total over several terms and the daily increase. If the first day is x grapes, the five days form x, x+6, x+12, x+18, x+24. The total is 5x plus the sum of the increments: 0+6+12+18+24 = 60. So 5x + 60 = 100, which gives 5x = 40 and x = 8. Therefore, the first day he ate eight grapes.

This question tests how an arithmetic progression works when you know the total over several terms and the daily increase. If the first day is x grapes, the five days form x, x+6, x+12, x+18, x+24. The total is 5x plus the sum of the increments: 0+6+12+18+24 = 60. So 5x + 60 = 100, which gives 5x = 40 and x = 8. Therefore, the first day he ate eight grapes.