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M01-22

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M01-22 [#permalink]

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Kudos [?]: 129081 [0], given: 12194

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New post 16 Sep 2014, 00:15
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Official Solution:

How many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit?

A. 1,339
B. 1,352
C. 1,353
D. 10,030
E. 10,300


Approach #1:

There is one number in each hundred with 2 in the tens digit and 1 in the units digit: 21, 121, 221, 321, ...

The difference between 324,700 and 458,600 is \(458,600-324,700=133,900\) - one number per each hundred gives \(\frac{133,900}{100}=1,339\) numbers.

Approach #2:

Look at the series of all numbers ending with 21 within the given range.
  • 324,721
  • 324,821
  • .....
  • 458,421
  • 458,521

Following the series, we can see that only the first four numbers are changing. Instead of counting the numbers ending in 21 in the given range (324,700 to 458,600), simplify and only count the numbers in the range of 3,247 to 4,585. Therefore, the number of integers ending in 21 within the range is \(4,585-3,247+1 = 1,339\).


Answer: A
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Re M01-22 [#permalink]

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New post 21 Aug 2017, 16:26
I think this is a high-quality question and I agree with explanation.

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Re M01-22   [#permalink] 21 Aug 2017, 16:26
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