test35 # 15

dunkin77 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 first few integers that have this property are: 324,713, 324,813, 324,913, …. As we can see, this is an arithmetic sequence with common difference of 100. Since the last integer that has this property is 458,513, the number of integers that have this property is:

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

Answer: E

dunkin77 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

Hi,

Can anyone help pls..?

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