(UPDATE on Aug. 5 with MOE’s confirmation in the last section of the article.)
Never had I been so eager in trying to find out a woman’s age.
A few days ago, I was posed a question. Tom is 10 years old. Amy is three times older than Tom. How old is Amy?
It seems to be a very simple question but there’s a lot of disagreement in Amy’s age.
There are two camps of thoughts. The first team thinks Amy must be 30 years old. Another group says Amy should be 40. To be absolutely sure, we approached a reporter, a news editor, a scientist, a trader, an English teacher, a Maths tutor and four Maths school teachers.
The six non-Maths teachers unanimously understood that the answer is 30 and the four Maths teachers said the answer is 40.
It is interesting to see the difference between how the English teacher and news editors think from a linguistic point of view and how the Mathematicians view this from their perspective.
Camp 1: Why 30
The first school of thought thinks “three times older than” is equivalent to “three times as old as” so the way to derive Amy’s age is 10×3.
Many Maths questions on international websites are also in this camp (see examples below).
Camp 2: Why 40
If the question is “Mary is 30 years older than Tom,” the solution is: 10+30=40.
Going by this logic, Mary is “three times older than Tom,” so it is 10+(10×3)=40
Where the Confusion Arises
A professor from Ausberg College says this:
“If B is three times as much as A, then B is two times more than A – not three times more than A. The essential feature is the difference is between ‘as much as’ and ‘more than’. ‘As much as’ indicates a ratio; ‘more than’ indicates a difference. ‘More than ’means ‘added onto the base’.”
For other comparative adjectives, like “times older than”, “times faster than”, “times bigger than”, “times longer than”, the interpretation is less clear cut.
What to do if this happens during the examinations
If it does appear in your examinations, one teacher suggests showing both answers to show your thought process, creativity and critical thinking.
We decided to seek the authority’s view on the matter and wrote an e-mail to the Ministry of Education. Fortunately, MOE confirmed that this is no longer in the current syllabus.
“We do not use such language in our current syllabus,” Ruth Teng, the curriculum planning officer for Maths said in an e-mail reply to our queries on Aug. 5.
It’s great the MOE has acknowledged the amiguity of our question and spared our children such questions. Kudos to them for the wise move and good luck to all of you for future Maths exams.
This article was written jointly by Wallace and Wei. Wallace is a trader, while Wei is a reporter. We have recently started a Facebook site to help PSLE queries. Like us here http://facebook.com/studyroomjr
“bigger /greater than”