If A+1/(B+1/(C+1/(D+1/E))) = 1331/1000 what is the value of A*B*C*D*E?
2025
If A+1/(B+1/(C+1/(D+1/E))) = 1331/1000
what is the value of A*B*C*D*E?
- A.
486
- B.
648
- C.
846
- D.
864
Attempted by 418 students.
Show answer & explanation
Correct answer: C
Given: A + 1/(B + 1/(C + 1/(D + 1/E))) = 1331/1000
Step 1: Extract A by taking the integer part of 1331/1000. Since 1331/1000 = 1 + 331/1000, we have A = 1.
Step 2: The remaining fraction is 331/1000, so take its reciprocal to find B + 1/(...): 1000/331 = 3 + 7/331, hence B = 3.
Step 3: Invert the fractional part 7/331: 331/7 = 47 + 2/7, so C = 47.
Step 4: Invert 2/7: 7/2 = 3 + 1/2, so D = 3 and the remaining part is 1/2.
Step 5: From 1/2 = 1/E, we get E = 2.
Now multiply the integers: 1 * 3 * 47 * 3 * 2 = 846.
Answer: 846