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If some strips of sticks of lengths 7cm, 9cm, and 27cm were cut independently from a single stem of a tree without a remainder, find the shortest possible length of that stem.
- A. 197cm
- B. 54cm
- C. 81cm
- D. 189cm
QUICK ANSWER…
D
SOLUTION…
To understand this question properly, we would state it clearly that the stem has a constant length of which:
- 7cm sticks could be cut out of it perfectly without a remainder,
- 9cm sticks could also be cut out of same stem perfectly without a remainder, and
- 27cm sticks could also be cut out of same stem without a remainder
Hence, we are asked to find the least possible length of the stem that will allow any of the length of sticks to be cut out without a remainder.
Let the length of the stem = L
This means the least possible length of the stem is the LCM which is 189cm.
Now for the right answer to the above question:
- Option A is incorrect. 197 does not have any of these numbers as a factor.
- Option B is incorrect. 27 and 9 are factors of 54, but not 7.
- C is incorrect. 27 and 9 are factors of 81, but not 7
- D is the correct answer. 7, 9, and 27 are all factors of 189.
KEY-POINTS…
You may please note these/this:
- Try as much as you can to understand questions before attempting to answer.
- You may quickly get the answer even without solving by testing all the options to find the least option that has all the lengths as a factor.
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/ culled from 2015 JAMB-UTME mathematics past question 50 /
