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

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

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New post 10 Oct 2016, 13:32
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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
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Re: How many positive three-digit integers have an odd digit in both the  [#permalink]

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New post 10 Oct 2016, 14:31
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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!

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

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New post 10 Oct 2016, 14:37
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
Capture 1.PNG [ 2.03 KiB | Viewed 2158 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
Capture.PNG [ 1.88 KiB | Viewed 2155 times ]

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

Hence Correct answer must be (B) 225

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

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New post 18 Apr 2018, 12:40
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Re: How many positive three-digit integers have an odd digit in both the &nbs [#permalink] 18 Apr 2018, 12:40
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