How many integers are there between 2*10^5 and 9*10^5 so that the sum

Question

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

A. 9
B. 8
C. 7
D. 6
E. 5

BrentGMATPrepNow · Accepted Answer

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:  D

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chetan2u · Answer

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

tapabrata · Answer

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

ydmuley · Answer

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

sashiim20 · Answer

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)... _________________ Please Press "+1 Kudos" to appreciate.

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How many integers are there between 210^5 and 910^5 so that the sum

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