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# How many positive three-digit integers have an odd digit in both the

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Manager
Joined: 23 Sep 2016
Posts: 94
How many positive three-digit integers have an odd digit in both the  [#permalink]

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10 Oct 2016, 12:32
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2
00:00

Difficulty:

25% (medium)

Question Stats:

75% (00:57) correct 25% (01:17) wrong based on 85 sessions

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How many positive three-digit integers have an odd digit in both the tens and units place?

a) 25
b) 225
c) 250
d) 450
e) 500
Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 533
Location: India
GMAT 1: 780 Q51 V46
Re: How many positive three-digit integers have an odd digit in both the  [#permalink]

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10 Oct 2016, 13:31
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Top Contributor
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Hi SW4,

This is a typical permutation problem where the method of counting comes in very handy.

The following are the steps you need to follow while using the counting method.
1. Make empty spaces and try to fill up the empty spaces one by one
2. If a condition is given, you always find the condition space and fill the condition space first.

Here we need to form a 3 digit number given 2 conditions that the tens and units digit are odd. the digits we can use here are all the digits from 0 to 9 and since nothing is mentioned about the digits being repeated or not, we always consider the with repetition case.

So making 3 empty spaces _ Odd Odd.

The total number of ways of filling the units digit is 5, since we can use any one out of 1,3,5,7 and 9. Similarly the total number of ways of filling the tens digit is 5. Now since the digits can be repeated and we need to have a 3 digit number, we can fill the hundreds digit in 9 ways, since we can use any one out of 1,2,3,4,5,6,7,8,9. We cannot use 0 since we need a 3 digit number.

So the answer here will be 9 * 5 * 5 = 225

Hope this helps!

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Re: How many positive three-digit integers have an odd digit in both the  [#permalink]

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10 Oct 2016, 13:37
SW4 wrote:
How many positive three-digit integers have an odd digit in both the tens and units place?

a) 25
b) 225
c) 250
d) 450
e) 500

There are 10 numbers -
Attachment:

Capture 1.PNG [ 2.03 KiB | Viewed 2416 times ]

The Tens Place can be filled in 5 ways ( 1, 3, 5 , 7 & 9 )
The Units Place can be filled in 5 ways ( 1, 3, 5 , 7 & 9 )
The Hundreth digit can be filled in 9 ways ( 1 ,2 , 3 , 4 ,5 ,6 , 7 , 8 , 9)
Attachment:

Capture.PNG [ 1.88 KiB | Viewed 2413 times ]

So, The total number of ways is 5*5*9 = 225 ways....

Hence Correct answer must be (B) 225

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Abhishek....

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Re: How many positive three-digit integers have an odd digit in both the  [#permalink]

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18 Apr 2018, 11:40
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Re: How many positive three-digit integers have an odd digit in both the &nbs [#permalink] 18 Apr 2018, 11:40
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