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How many integers between

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How many integers between

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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

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Junior | Next Rank: 30 Posts
Joined
11 Jun 2019
Posted:
13 messages
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The numbers must be of the form ABCD13, where ABCD is any four-digit number between 3247 and 4585 inclusive.
ABCD cannot be 4586, as 458,613>458,600.

Therefore, the total number is 4585 - 3247 + 1 = 1339.

Answer E

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rajeet123 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
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

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rajeet123 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
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

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scott@targettestprep.com



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