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# How many 7-digit numbers are having sum of digits ODD?

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How many 7-digit numbers are having sum of digits ODD?  [#permalink]

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13 Oct 2018, 09:59
9
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:21) correct 46% (02:19) wrong based on 66 sessions

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How many 7-digit numbers are having sum of digits ODD?
A) 3505000
B) 4350200
C) 4500000
D) 4520500
E) 5502000

Weekly Quant Quiz #4 Ques 1

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Re: How many 7-digit numbers are having sum of digits ODD?  [#permalink]

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13 Oct 2018, 10:13
8
smallest 7 digit number=1000000
greatest=9999999.
total 7 digit number=9999999-1000000+1=90000000
So now out of 9000000,half have sum as odd and half has sum as even.So 4500000 are having sum as odd.
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Re: How many 7-digit numbers are having sum of digits ODD?  [#permalink]

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13 Oct 2018, 10:05
According to me the answer should be (C). Please find my solution attached.

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Re: How many 7-digit numbers are having sum of digits ODD?  [#permalink]

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13 Oct 2018, 10:13
How many 7-digit numbers are having sum of digits ODD?
A) 3505000
B) 4350200
C) 4500000
D) 4520500
E) 5502000
OA: C
a 7 digit number : _ _ _ _ _ _ 7th'

first digit : {1,2,3,4,5,6,7,8,9} - 9 values
2nd,3rd,4th,5th,6th : {0,1,2,3,4,5,6,7,8,9} - 10 values
the 7th digit takes set of { 1,3,5,7,9} - 5 values , all odd numbers

total no of values you can get with these : 9*(10^5)*5 = 4500000
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Re: How many 7-digit numbers are having sum of digits ODD?  [#permalink]

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13 Oct 2018, 10:21
How many 7-digit numbers are having sum of digits ODD?
A) 3505000
B) 4350200
C) 4500000
D) 4520500
E) 5502000
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Re: How many 7-digit numbers are having sum of digits ODD?  [#permalink]

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Updated on: 13 Oct 2018, 12:04
Total number of 7 digit integers 9999999-999999=9,000,000
Half of them have even sum and other odd sum.
( can ve verified in any consecutive series if even number of terms---
say... 11,12,13, 14 ===> 4 terms ....2 even sum & 2 odd sum
again 11,12,13......20 ==>10 terms ....5 even sum & 5 odd sum)
Hence, Odd sum = 9,000,000/2= 4,500,000
Ans C.
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Please let me know if I am going in wrong direction.
Thanks in appreciation.

Originally posted by u1983 on 13 Oct 2018, 10:22.
Last edited by u1983 on 13 Oct 2018, 12:04, edited 1 time in total.
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Re: How many 7-digit numbers are having sum of digits ODD?  [#permalink]

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13 Oct 2018, 11:01
total count of 7 digit number =9999999-1000000+1=9000000...so every alternate number in the set will have a sum even or odd,so half the 7 digit numbers would have odd sum hence 9000000/2=4500000.Hence answer C
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Re: How many 7-digit numbers are having sum of digits ODD?  [#permalink]

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28 Oct 2018, 03:40
7 digit numbers are from 1000000 to 9999999.

First we need to find the total number of terms from 1000000 to 9999999.

(Last term - first term) +1 => (9999999 - 1000000) + 1 => 8999999 + 1 => 9000000

We know there are 5 odd integers and 5 even integers in every 10 numbers.

So we divide 9000000/2 = 4500000

Hence C
Re: How many 7-digit numbers are having sum of digits ODD?   [#permalink] 28 Oct 2018, 03:40
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