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Atheros's avatar

What is two times less than 16?

Asked by Atheros (320points) March 4th, 2012

I just came across this problem, and am not sure what exactly does it mean.
I’m pretty much positive it isn’t 16/2. But then again, is it 16/3 (doesn’t seem logical), or 16/2/2, which equals 16/4?
Or something totally different?

Thank you all!

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26 Answers

zenvelo's avatar

This is why there is innumeracy in the world. It makes no sense, because “times” is multiplication, but “less” is subtraction and division, so the statement is nonsense and any solution can be defended.

I would consider it as 16/2. But you can defend 16/4 easily. If this question was posed by a teacher or a book, I would complain.

filmfann's avatar

Two times less than 16? I would say 8.
Two times more than 8 would be 16.

ragingloli's avatar

The wording of the problem itself is nonsensical.

Atheros's avatar

But couldn’t it also be like 1 x less = 0, and 2 x less = -16?
This question is weird, like @zenvelo said, it doesn’t make sense.

@filmfann If I were asked what’s two times more than 8, I’d say it’s 24 (8 + 2 * 8 = 24). Because I would understand one time more than 8 as 8 + 1 * 8, which is 16.

ragingloli's avatar

2 times more than 8 would be 24.
So you could also say that 2 times less than 16 is 16–16×2, ergo -16

Atheros's avatar

@ragingloli I agree it’s nonsensical, but unfortunately that’s what I run into just too many times.
And to answer @zenvelo , yes this was given to my brother in school.

RocketGuy's avatar

Must be missing a few items (typo).

PhiNotPi's avatar

One interpretation of this question is 2*<16. You can also interpret it as 2*-16 or even 16 – 2* or maybe even that “if 15 is less than 16, then 14 is two times less than 16”.

This is one example of when informal language goes directly against the formal language. Interpreted with the most common version of informal language, “two times less than 16” almost certainly means 16/2=8. When you attempt to interpret it as formal language, it makes no sense whatsoever.

The very nature of informal language means that there is no single correct interpretation, especially when it cannot be interpreted as formal language.

SavoirFaire's avatar

I am also unfamiliar with this kind of problem syntax. The way I parse the question, however, the intended factors are supposed to be “two” and “less than sixteen.” As such, I would say that the answer is “less than 32.” That is:

2 * (<16) = (<32)

I wonder how the problem is actually written, though. Perhaps it looks like this:

2x < 16

If so, the problem you are being asked to solve is not an equation, but an inequality. In such a case, the ”<” takes the place of an ”=” in the problem. The ”x” would also not represent multiplication, but a variable. The logic is very similar, however, and you can see that if two x‘s are less than 16, then one x must be less than 8.

x < 8

Bent's avatar

There appears to be a word missing from the question.

I think it should be “What is two times n less than 16?” in which n is a number less than 16.

For example if n is five, then 16 less 5 is 11 and two times 11 is 22. Written algebraically, you’re solving 2(16-n)

PhiNotPi's avatar

“Two times n less than 16” can also mean 16 – 2n. Since we are dealing with an undefined syntax, it can be interpreted to mean pretty much anything we want.

Bent's avatar

@PhiNotPi you’re right. Either way the question needs re-writing.

PhiNotPi's avatar

@Bent Actually, I think that we are past the incorrectness of the particular statement “two times less than 16”, and we are now faced with the ambiguous nature of language itself.

Brian1946's avatar

I’d say that the question is missing some numerical data.

E.g.: “What is two times less than 16 than 14?” could be asked, and the answer would be 12.

However, it could be asking, “What number is twice as small as 16?”, and the answer is 8, which could be stated as being two times less than 16, because 16 is two times more than 8.

Atheros's avatar

Note to all: there is no typo, and no word missing. Also the question doesn’t include inequalities. So it’s basically “two times less than” + “sixteen”, if you know what I mean.

Also, we got the “correct” answer of this exact problem: 8. I kinda thought that this would be the correct one, because such linguistic errors are (sadly) very common nowadays.

ragingloli's avatar

@Brian1946 “What is two times less than 16 than 14?” could be asked, and the answer would be 12.”
That makes even less sense

Atheros's avatar

@Brian1946 Also, 16 is not two times more than 8. This has been written before.

Brian1946's avatar


I admit it’s a linguistic stretch, but 14 is 2 less than 16, 12 is 4 less than 16, the difference (as expressed by less than) of 4 is twice that of 2.

SavoirFaire's avatar

@Atheros Don’t tell us what it “basically” is. Please give us the exact wording. That might help us out.

Atheros's avatar

@SavoirFaire As it says in the question.
These numbers represent passengers. And the task is: there are 16 passengers on bus no. 1. On bus no. 2 there is two times less passengers than on bus no. 1.
So the question remains: “What is two times less than 16?”

Bent's avatar

@Atheros “16 is not two times more than 8”

Are you using something other than a decimal base here? Or using different meanings than usual for words in this sentence? Because I cannot see how two times 8 can be anything but 16. And I still cannot make sense of the wording in the original question, even with your later explanation.

Can you please provide an algebraic formula for what you are trying to work out?

ragingloli's avatar

There is a difference between (1) two times and (2) two times more.
(1) means 2X
(2) means +2X
“X times” implies a multiplication. “more” implies an addition.

SavoirFaire's avatar

@Atheros Thank you for providing that. Now that I see the question, I can tell that the answer is 8. While the question is poorly worded, parsing it all out suggests that “there is sic two times less passengers” on bus 2 than on bus 1 must be equivalent to “there are twice as many passengers on bus 1 as there are on bus 2.” Once we understand that, the problem becomes:

16/2 = 8

It’s a bizarre English construction, to be sure; but taking all the clues together, I can see what the question is trying to ask. I don’t blame you or your brother for being confused, though. There are certainly more perspicuous ways of posing the question.

ragingloli's avatar

I would still answer with -16

Response moderated (Unhelpful)
RocketGuy's avatar

@Atheros – you should have provided us with the full text of the problem to begin with. I think @SavoirFaire has got it! Many laymen have used “two times less” as being the same as “half as many”. Kind of like when you see a detergent ad for “200% cleaner” actually meaning “half as much dirt remaining”.

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