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

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

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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