1

I am learning word problems for Quantitative reasoning GRE exams. English is not my first language and I wonder if the following expression is ambiguous in English: "Three times the second integer less 4" I interpreted that as 3(x-4), but the solution was 3x-4. Are there any conventions in English language? How do I know that "less 4" refers to the whole expression "three times the second integer" rather than to the expression "the second integer"? I have not had this problem in non-mathematical literature since the relations were possible to be derived from the context, but here it does not seem to be the case.

Improve this question
1
  • 4
    Spoken English (i.e. - the real language) doesn't support brackets, but the intended sense could be indicated by stress/cadence. I writing, the ambiguity could be avoided by using brackets - but I think whoever decided to put this in a test thinking there was a single unambiguously "correct" answer is in the wrong job.
    – FumbleFingers
    Commented Jun 30, 2013 at 20:59

2 Answers 2

Reset to default
3

The convention is to write 3x-4 or 3(x-4). Mathematical notation was invented to reduce this kind of ambiguity.

However, the word quantity is often used to indicate parentheses. I would generally expect 3(x-4) to be pronounced as:

three times the quantity, 'x' minus four
three times the quantity of the second integer minus four

If the word quantity wasn't present, the phrase is ambiguous, but I would assume the phrase should be interpreted as a sequence of symbols precisely as stated, as though no parentheses are present, 3·x-4. In which case, the conventional order of operations takes precedence and multiplication should be performed first.

Improve this answer
2
  • I often hear this same convention used, sometimes without the "the": Three times quantity x minus four.
    – J.R.
    Commented Jun 30, 2013 at 22:44
  • @J.R. I've also heard x minus four quantity times three. Ultimately, this doesn't help reduce ambiguity that much.
    – p.s.w.g
    Commented Jul 1, 2013 at 0:21
0

In the absence of any other indication, I would take it in the sequence given:
(1) "Three times the second integer", then
(2) "less 4".
That would also be the mathematical sequence in the absence of brackets.

While I agree that there is an ambiguity, there is nothing to suggest doing the calculation in anything other than the specified sequence.

Improve this answer

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .