Reading Incomprehension

On Dan Hamermesh‘s always-interesting blog, I read the first sentence of a recent entry:

My grandson will be 13 in 13 months.

I had to read it three times to realize that this was not a clever way of saying that he had a brand new grandson. The “months” at the end of the sentence tied to the second “13,” combined with the word “grandson” (baby image comes to mind) conspired to persuade me that there should have been a “months” following the first “13” as well. How easily the mind — at least, mine — is tricked.

It reminds me of the following very easy math question that a lot of relatively smart people get wrong:

A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?

A. $1.10
B. $0.10
C. $0.05
D. $1.00
E. $0.15

Hint: the answer is not B.



"As a math teacher, I have found it wise not to be too arrogant about getting such problems correct, or about those who misinterpret and get them wrong."

Posted by mathking

How ironic.


That word problem is the type of thing that comes up in meals all the time. The check is $41, my meal was $10 more than I owe $25.50 and you owe $15.50.


If the kid will be 13 in 13 months, that means he's 11 and 11 months old.

Mike B

Just like the "two trains" question this is a classic problem which teach people how and when to employ basic algebra. I actually remembered the strategy, but was too lazy to write it out and instantly thought of B. Makes you wonder if there is a way to separate questions people get wrong due to lazyness vs those they get wrong due to a lack of ability.


x + (1+x) = 1.1

x = (1.1 - 1)/2 = .05


The answer is C, but I also got it wrong the first time. Too many word problems in 8th grade algebra!


my birthday is a little over a year away

Tim Howland

Not only will he be 13 in 13 months, but he's been 11 for 11 months...


The way it is posted, I'd think the grandson would be 13 (years old) in 13 months.

Daniel Reeves

Some people need to read their Elements of Style.

Michael D

I was confounded by the algebra question too. The problem is that you assume the bat cost is $1.00, instead of an additional $1.00.

Ball cost $0.05
Bat cost $1.05 ($1 more)
Total $1.10

Alan Gunn

I had a book once with the title, "How many three-cent stamps in a dozen?" Most people get this wrong, too.

ML Harris

Stunning admission of poor detail reading by the world's leading rogue economist. Goes to show we're all human.

The above question is obviously from a state with no sales tax.


answer is C, two equation x+y=1.10 and x-y=1, two unknowns.


a nickel.

Dubner, this is whay you're the writer and not the economist of the duo.

Incidentally, I always laugh when math students talk about "hating word problems." For the 99.9% of math students who do not go on to be theoretical mathematicians, these are the ONLY kind of problems that matter.


Jose's solution is fine of course, but why use algebra when you don't have to?

Just give the bat a dollar discount. Now the bat and ball cost the same and together they cost 10 cents; that's 5 cents each.


Hmm, I read the phrase correctly the first time. By the time I get to the first '13' ("My grandson will be 13"), I am already thinking 13 years old.

No matter how I spin it in my head, though, it is not a more cute or clever way of saying "My grandson will be 12 next month".


This is why I love this blog. In one simply entry, you managed to raise two persistent problems that arise every day: people's inability to do basic math (even more basic than your word problem), and people's inattention to their use of the English language. Both are annoying at best, and a waste of time at worst (e.g. deciphering the meaning of a sentence in the newspaper or on a blog, or standing behind someone in a checkout line while the cashier tries to do basic addition and subtraction when given an extra nickel to avoid a pocketful of change).


I think what's most interesting is that the grandson in question isn't even close to turning 13, he's close to turning 12.


This day and age you are telling me I can get a bat and a ball for 1.10? No wonder the Price is Right is so difficult for some.