In a soap manufacturing scenario, a soap is produced with 11 parts, and creating one soap yields 1 part as scrap. If you accumulate 251 scraps, how many soaps can be made in total?

In a soap manufacturing scenario, a soap is produced with 11 parts, and creating one soap yields 1 part as scrap. If you accumulate 251 scraps, how many soaps can be made in total?

• A. 25
• B. 22
• C. 28
• D. 30

Answer: (A)

Think of scraps as a small currency: it takes 11 scraps to obtain one more soap, and every soap you produce gives you one more scrap. Start with 251 scraps and see how many soaps you can fund initially: 251 divided by 11 is 22, with 9 scraps left over (since 22×11 = 242, and 251 − 242 = 9). Making those 22 soaps yields 22 more scraps, so your total scraps become 9 + 22 = 31. With 31 scraps, you can obtain 2 more soaps (2×11 = 22), leaving 9 scraps. Producing those 2 soaps adds 2 scraps, so scraps total becomes 9 + 2 = 11. Exchange 11 scraps for 1 more soap, which after production adds 1 scrap, leaving 0 scraps before that final scrap is counted. That last soap yields 1 scrap, leaving you with 1 scrap, which isn’t enough for another soap. Total soaps produced = 22 + 2 + 1 = 25.

Think of scraps as a small currency: it takes 11 scraps to obtain one more soap, and every soap you produce gives you one more scrap. Start with 251 scraps and see how many soaps you can fund initially: 251 divided by 11 is 22, with 9 scraps left over (since 22×11 = 242, and 251 − 242 = 9). Making those 22 soaps yields 22 more scraps, so your total scraps become 9 + 22 = 31.

With 31 scraps, you can obtain 2 more soaps (2×11 = 22), leaving 9 scraps. Producing those 2 soaps adds 2 scraps, so scraps total becomes 9 + 2 = 11. Exchange 11 scraps for 1 more soap, which after production adds 1 scrap, leaving 0 scraps before that final scrap is counted. That last soap yields 1 scrap, leaving you with 1 scrap, which isn’t enough for another soap.

Total soaps produced = 22 + 2 + 1 = 25.