In my thinking:

  • 3 times a is increased by b:
    This is a SVO sentence. The subject is "3 times a", the verb is "is increased" and the object is "by b". Therefore the correct form in math is 3a+b
  • 3 times a increased by b:
    This is a shorten form of "3 times a, which is increased by b". The subject is "3", the verb is "times" and the object is "a increased by 3" or "a, which is increased by 3". Mathematically, it is 3(a+b)

But my teacher and the rest of my GRE class don't agree with this. They opine that these sentences are the same, and the correct is 3a+b. What do you think?

This is the origin question:

When 3 times a number n is increased by 7, the result is at most 4 times the number decreased by 1

  • Is your class conducted in English? The spoken version of 3a+b for native speakers is "Three times a plus b". One of the problems with using "increased" in such contexts is there's something decidedly odd about increasing/reducing an "intermediate" result (because that intermediate value doesn't really "exist" except briefly within the calculation process). It's like increment/decrement operands in many programming languages, which can only be applied to actual values held within named variables, not nameless intermediate results. – FumbleFingers Oct 27 '14 at 17:33
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    This question appears to be off-topic because it is about the inherent ambiguity of compound expressions where in mathematical notation either brackets or the BODMAS convention would resolve the ambiguity. Neither such device is part of English. – FumbleFingers Oct 27 '14 at 18:23
  • @FumbleFingers: no, it's not. If the problem is about the order of operations, I would have asked in Mathematics.SE. This question is about how to make a correct expression from the English words. – Ooker Oct 27 '14 at 18:30
  • BODMAS/PEMDAS convention would definitely resolve the issue. Three times A plus B is 3A+B. s/plus/increased by/ and the situation remains. See also this question and its duplicate. – SrJoven Oct 27 '14 at 19:44
  • @SrJoven: this question is not about how to read (or speak) a mathematical expression, it is how to interpret a phrase to a mathematical expression. – Ooker Oct 27 '14 at 19:49

If you wish to communicate a mathematical expression clearly and concisely, don't use either of those forms. Both are ambiguous:

3 times a is increased by b may mean

a+(3b), since a is increased by b three times
(3a)+b, since 3a is increased by b

3 times a increased by b may mean

3(a+b), since a is increased by b and multiplied by three
(3a)+b, since 3a is increased by b

Instead, use phrasing like “b is added to three a” or “b added to three a” for (3a)+b, or “three times the quantity a plus b” for 3(a+b), etc.

| improve this answer | |
  • I don't want to be rude, sorry if you feel any inconvenience. But are you a native speaker? Are your sure about this? – Ooker Oct 27 '14 at 17:55
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    I would never interpret 3 times a is increased by b as a+(3b). – 200_success Oct 27 '14 at 17:58
  • I'm still not clear what the question is getting at, but +1 because everything in this answer is perfectly correct, and whoever downvoted it is either a sloppy thinker or not a native speaker. – FumbleFingers Oct 27 '14 at 18:04
  • @FumbleFingers: I'm sorry that my question is not clear. Can you point out where it should be improved? – Ooker Oct 27 '14 at 18:14
  • Ooker, I'm a native speaker of central-US English. Note that some of the interpretations I listed would not be available if commas (or pauses when speaking) were used to prioritize operations. – James Waldby - jwpat7 Oct 27 '14 at 18:45

Mathematically and grammatically, if I assume increase means plus..

then in your words,

  • 3a+b= 3 times a is increased by b or 3 times a increased by b
  • 3(a+b)= 3a+3b..3 times a is increased by 3 times b or 3 times a increased by 3 times b.
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  • So you mean that "3 times a increased by b" is 3a+b? – Ooker Oct 27 '14 at 17:38
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    @Ooker: I think this question would have been better asked on English Language Learners. Native speakers don't normally use increase the way you have. – FumbleFingers Oct 27 '14 at 17:46
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    @FumbleFingers: I don't use this way either. This is a GRE pre-test. So (I think), it must be the normal way. – Ooker Oct 27 '14 at 17:48
  • @Ooker: Your recent edit slightly changes things. Not that your new final line makes much sense to me (it's only true if n <= 8). – FumbleFingers Oct 27 '14 at 18:00
  • @FumbleFingers: Which edit makes change? I just add an origin question and I don't think I have changed the information. – Ooker Oct 27 '14 at 18:13

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