A company makes a part that is designed to be 1000 mm long, plus or minus 1%, Which of these lengths would be acceptable? (Select all that apply)
(A) 1100 mm
(B) 1099 mm
(C) 9998 mm
(D) 1020 mm
(E) 998 mm
(F) 1009 mm
The correct Answer and Explanation is:
To solve this problem, we need to determine which lengths fall within the acceptable range for a part that is designed to be 1000 mm long, plus or minus 1%.
Step 1: Determine the acceptable range
The part is supposed to be 1000 mm long, but there’s a tolerance of ±1%. This means the length can vary by 1% of 1000 mm.
1% of 1000 mm is:1%×1000=1100×1000=10 mm1\% \times 1000 = \frac{1}{100} \times 1000 = 10 \text{ mm}1%×1000=1001×1000=10 mm
Thus, the part can be 10 mm longer or shorter than the specified 1000 mm length. Therefore, the acceptable range is:1000 mm−10 mm=990 mm1000 \text{ mm} – 10 \text{ mm} = 990 \text{ mm}1000 mm−10 mm=990 mm 1000 mm+10 mm=1010 mm1000 \text{ mm} + 10 \text{ mm} = 1010 \text{ mm}1000 mm+10 mm=1010 mm
So, the acceptable range is from 990 mm to 1010 mm.
Step 2: Evaluate the options
Let’s examine each option to see if it falls within the acceptable range:
- (A) 1100 mm: This is outside the acceptable range (990 mm – 1010 mm), so it is not acceptable.
- (B) 1099 mm: This is also outside the acceptable range, so it is not acceptable.
- (C) 9998 mm: This appears to be a typo or mistake. If it were 998 mm, that’s outside the range, so it is not acceptable.
- (D) 1020 mm: This is outside the range of 990 mm – 1010 mm, so it is not acceptable.
- (E) 998 mm: This is below the lower bound of 990 mm, so it is not acceptable.
- (F) 1009 mm: This is within the range of 990 mm to 1010 mm, so it is acceptable.
Conclusion
Only (F) 1009 mm falls within the acceptable range of 990 mm to 1010 mm. Therefore, the correct answer is (F).