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# M01-22

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Math Expert
Joined: 02 Sep 2009
Posts: 43295

Kudos [?]: 139194 [0], given: 12778

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15 Sep 2014, 23:15
Expert's post
21
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BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:13) correct 25% (01:45) wrong based on 152 sessions

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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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139194 [0], given: 12778

Math Expert
Joined: 02 Sep 2009
Posts: 43295

Kudos [?]: 139194 [4], given: 12778

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15 Sep 2014, 23:15
4
KUDOS
Expert's post
7
This post was
BOOKMARKED
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 $$4,585-3,247+1 = 1,339$$.

_________________

Kudos [?]: 139194 [4], given: 12778

Intern
Joined: 21 May 2015
Posts: 18

Kudos [?]: 5 [0], given: 231

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21 Aug 2017, 15:26
I think this is a high-quality question and I agree with explanation.

Kudos [?]: 5 [0], given: 231

Re M01-22   [#permalink] 21 Aug 2017, 15:26
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# M01-22

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