integers in digit places

[guest612]

the question asks:

How many integers between 324,700 and 458,600 have tens digit 1 and units digit 3?

A) 10,300
B) 10,030
C) 1,353
D) 1,352
E) 1,339

Answer: E) 1,339.

I got to that number by subtracting 458,600-324,000 to calculate the value in between and resulted in the correct answer E) 1339. But they are just numbers to me and I don't quite get the concept behind calculating the tens digit 1 and units digit 3. Can you please help explain this?

Thank you so much.

[RonPurewal]

please cite a source for this problem.

if you don't cite a source and/or if the source is one of our banned sources, we will summarily delete this thread within a few days.

thanks

[guest612]

hi ron! it's test code (ets) #37, section 1 #8.

[RonPurewal]

the question asks:

How many integers between 324,700 and 458,600 have tens digit 1 and units digit 3?

A) 10,300
B) 10,030
C) 1,353
D) 1,352
E) 1,339

Answer: E) 1,339.

I got to that number by subtracting 458,600-324,000 to calculate the value in between and resulted in the correct answer E) 1339. But they are just numbers to me and I don't quite get the concept behind calculating the tens digit 1 and units digit 3. Can you please help explain this?

Thank you so much.

first off, i'll assume you meant to type 324,700.

with most problems like this, you can gain considerable insight by simply listing all the possibilities until you get what's going on; this one is no exception.
the possibilities are:
324,713
324,813
324,913
325,013
...
...
458,413
458,513
if you ignore the boldfaced thirteens, you'll see that this question is just a really roundabout, annoying way of asking how many integers are in the list 3247, 3248, 3249, ..., 4585.
using the 'add one before you're done' rule, that happens to be 4585 - 3247 + 1, which happens, by coincidence perhaps, to be the same as 4586 - 3247 (the subtraction you did, once the zeroes are lopped off the ends).

in any case, here's the principal lesson you should take here: don't stare at problems. if a problem deals with a list of numbers, don't delay; just start listing the numbers and get going, and a pattern will probably emerge.