If some strips of sticks of lengths 7cm…

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:

1. Option A is incorrect. 197 does not have any of these numbers as a factor.
2. Option B is incorrect. 27 and 9 are factors of 54, but not 7.
3. C is incorrect. 27 and 9 are factors of 81, but not 7
4. 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 /