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Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the
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27 Jun 2017, 07:04

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franz711 wrote:

How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?

a) 9 b) 8 c) 7 d) 6 e) 5

When we check the answer choices (ALWAYS check the answer choices before choosing an approach), we see that all 5 answer choices a small.

In this case, we should consider the straightforward approach of listing and counting 2 x 10^5 = 2 x 100,000 = 200,000 9 x 10^5 = 9 x 100,000 = 900,000

So, we're must consider values between 200,000 and 900,000 The first value whose digits add to 3 is: 200,001 The next one is: 200,010 And: 200,100 201,000 210,000 And there's one more: 300,000

Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the
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26 Jun 2017, 23:55

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1

franz711 wrote:

How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?

a) 9 b) 8 c) 7 d) 6 e) 5

Hi,

Pl post in Correct format

For the sum of digits to be three, two cases.. 1) the first digit is 2, so (3-2) or 1 can take place at any of 5 places after 2.. Example 200001,200010.. So ways = 5 2) 3 in first place, the rest can only be 0.. So 1 way ... 300000

Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the
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27 Jun 2017, 08:04

franz711 wrote:

How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?

a) 9 b) 8 c) 7 d) 6 e) 5

We need to find integers between 200000 and 900000 such that the sum of the digits is 3

For numbers between 200000 and 299999, the first digit is 2. We need one digit to be 1 and the rest to be all 0's The number will be of the form 2 _ _ _ _ _ where one place is 1 and the rest are all 0's. 1 can take any of the 5 places after 2, so there will be 5 integers 210000, 201000, 200100, 200010, and 200001 => 5 integers

Next for numbers starting with the digit 3, all the places need to be 0 for the sum to be 3 Hence only one number is possible 300000 => 1 Integer

For any numbers after 300000, the sum of the digits will be greater than 3.

Hence a total of 6 integers are possible. Answer D

Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the
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27 Jun 2017, 13:13

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How many integers are there between 2 * 10^5 and 9 * 10^5 so that the sum of their digits is 3?

\(2 * 10^5\) = \(200,000\)

\(9 * 10^5\) = \(900,000\)

We need to find number of integers, whose some of digits is 3

First Digit: 200,001

We will get the sum of digits 3 for 5 different places of 1 = 200,001, 200,010, 200,100 201,000, 210,000 = 5 Integers

Next and the only number whose digits sun to 3 is: 300,000 = 1 Integer

Hence, Total Integers \(= 5+1 = 6\)

Hence, Answer is D _________________

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