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How many integers are there between 2 x 10^5 and 9 X 10^5 so that the

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How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

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New post Updated on: 26 Jun 2017, 23:10
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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

Originally posted by franz711 on 26 Jun 2017, 22:45.
Last edited by Bunuel on 26 Jun 2017, 23:10, edited 2 times in total.
Renamed the topic.
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Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

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New post 27 Jun 2017, 06:04
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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

TOTAL = 6
Answer:

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Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

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New post 26 Jun 2017, 22:55
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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


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

Total 5+1=6
D
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Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

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

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New post 27 Jun 2017, 12:13
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1
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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How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

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New post 29 Jun 2017, 00:02
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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


\(2 * 10^5 = 200000\)

\(9 * 10^5 = 900000\)

From the given set of integers, sum of digits to be 3 would be; \(2 + 1 = 3\). and \(3 + 0 = 3\).

Numbers would be ;

\(200001,200010,200100,201000,210000 = 5\) integers.

\(300000 =1\) integer.

Total number of integers with sum of digits \(3 = 5 + 1 = 6\). Answer (D)...

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Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

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Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the &nbs [#permalink] 17 Sep 2018, 04:39
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