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If some strips of sticks of lengths 7cm…

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MATHS

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.

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Let the length of the stem = L

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.

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 /

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