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How many integers between 24,700 and 58,600 have tens digit 3 and unit

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Joined: 26 Dec 2018
Posts: 123
Location: India
How many integers between 24,700 and 58,600 have tens digit 3 and unit  [#permalink]

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New post 30 Dec 2018, 10:15
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Difficulty:

  55% (hard)

Question Stats:

70% (01:09) correct 30% (01:57) wrong based on 53 sessions

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How many integers between 24,700 and 58,600 have tens digit 3 and units digit 7?

A. 339
B. 352
C. 353
D. 630
E. 800

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Re: How many integers between 24,700 and 58,600 have tens digit 3 and unit  [#permalink]

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New post 30 Dec 2018, 12:44
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Approach this question as a Series problem.
Between 24,700 and 58,600, the first integer to have tens digit 3 and units digit 7 is 24737. The next integer satisfying the condition is 24837.
Finally, the last integer between 24,700 and 58,600 satisfying the condition is 58537.

We get an AP series 24737, 24837, 24937, ...........58537
Last term of an AP = a + (n - 1)d, where a = first term, d = common difference, and n = number of terms.
Common difference between consecutive terms is 100
Plug in value in the equation, 58537 = 24737 + (n - 1)100
n = 339
The number of integers between 24,700 and 58,600 have tens digit 3 and units digit 7 is the same as the number of terms in the series, i.e. 339.

Hence, the Correct Answer is A. 339

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Re: How many integers between 24,700 and 58,600 have tens digit 3 and unit  [#permalink]

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New post 12 Jan 2019, 00:24
UB001 wrote:
How many integers between 24,700 and 58,600 have tens digit 3 and units digit 7?

A. 339
B. 352
C. 353
D. 630
E. 800



Don't think too much on this, and use logic..

When can be the tens digit 3 and units digit 7 - when LAST two digits are 37..
so the number is ABC37, where ABC is a 3-digit number between 247 and 586, with 247 inclusive...
Since, only one of the two is inclusive, the number of integers will be straight 586-247=339

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Re: How many integers between 24,700 and 58,600 have tens digit 3 and unit &nbs [#permalink] 12 Jan 2019, 00:24
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