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

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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

Source: GMAT Paper Tests

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Vincen wrote:
Thu Apr 15, 2021 10:39 am
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

Source: GMAT Paper Tests
A nice rule says: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 324,700 to 458,600 = 458,600 - 324,700 + 1 = 133901
ASIDE: We can safely round this number 133900 (you'll see why shortly)

Now let's look at how frequently we have a 1 in the tens digit and 3 in the units digit.
Integers from 1 to 100: 13 (1 integer)
Integers from 101 to 200: 113 (1 integer)
Integers from 201 to 300: 213 (1 integer)
Integers from 301 to 400: 313 (1 integer)
.
.
.
As we can see, for every 100 integers, there's 1 integer with a 1 in the tens digit and 3 in the units digit.
In other words, 1/100 of all integers have a 1 in the tens digit and 3 in the units digit.

So, among the 133900 integers in question 1/100 of them meet the given condition.
(1/100)(133900) = 1339

Answer: E

Cheers,
Brent
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