Problem Solving

swerve wrote: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

The OA is E

Source: GMAT Paper Tests

We want to determine how many integers end in 13
For example, 324713, 324813, 324913, 325013, . . . etc.

Recognize that, for every 100 consecutive integers, only 1 will end in 13.

There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900)
Of those 133,900 integers, 1/100 of them end in 13.

1/10 of 133,900 = 1339, so the correct answer is E

Cheers,
Brent

swerve wrote: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

The OA is E

Source: GMAT Paper Tests

Let's list the first couple of such integers:

324,713; 324,813; 324,913; ...

The last of such an integer is 458,513.

We see that these integers form an arithmetic progression with a common difference of 100. Therefore, the number of integers is:

(458,513 - 324,713)/100 + 1 = 133,800/100 + 1 = 1,338 + 1 = 1,339

Answer: E