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Units and tens digits!

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by neeti2711 » Tue Dec 04, 2012 10:56 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

Please suggest the easiest solution!
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by Brent@GMATPrepNow » Tue Dec 04, 2012 11:03 am
neeti2711 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

Please suggest the easiest solution!
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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by puneetkhurana2000 » Mon Dec 10, 2012 12:20 pm
These will be numbers which end in 13.

They will be like 324713, 324813, .....458513.

If you observe carefully only the first four digits are changing, so it is a counter starting from 3247 to 4585. Hence total such digits will be 4585-3247+1 = 1339.

Hope this helps.
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