RudeyboyZ wrote:

askhere wrote:

We are looking at numbers between 10000 and 99999 both inclusive.

There are 90000 numbers.

Now for

10000 : sum of digits is odd;

10001 :sum of digits is even;

10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.

(Exception for the above statement :

When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd

and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)

This means exactly half of the numbers will have odd sum of their digits. i.e 45000

Answer : D

Ambarish

Dear Ambarish,

How were you able to figure out the trend, could you explain this a little in detail...!

sorry for sounding a little stupid.

Warm Regards,

Rudraksh.

Dear Rudraksh,

Its good if you remember in a sequence of consecutive integers : (where the number of "numbers in the sequence" is even. In this case 90000.)

"No: of integers with even sum of digits = No: of integers with odd sum of digits"

This will give you the answer directly as 90000/2 = 45000.

I am happy to elaborate:

In GMAT it is very important that we figure out a pattern so that we can solve it easily.

As I mentioned we were looking for numbers from 10000 to 99999 which gives you a odd sum of digits.

10000 : sum of digits = 1+0+0+0+0 = 1 which is odd

10001 : sum of digits = 1+0+0+0+1 = 2 which is even. As long as you add one to the

units digit the sum of the digits alternates between odd and even.

The exception is when you look at the consecutive numbers where

tens digit gets changed. (You can even check this for hundreds and thousands digits)

For example:

10009: sum of digits = 1+0+0+0+9 = 10 which is

even10010: sum of digits = 1+0+0+1+0 = 2 which is again

even.

So you have two consecutive numbers which gives you sum as

even and destroyed the pattern. But hang on, if you look at

10019: sum of digits = 1+0+0+1+9 = 11 which is

odd10020: sum of digits = 1+0+0+2+0 = 3 which is again

oddSo again you have two consecutive numbers which gives you sum as

odd and compensated for the case in which you got two even sums in succession.

This keeps on repeating and one can see that exactly half the numbers from 10000 to 99999 will be even and the other half odd.

Hope you understood.

Ambarish

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Kindly press Kudos if the explanation is clear.

Thank you

Ambarish