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Director  Joined: 29 Nov 2012
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If n is a four-digit positive integer, then what is the tens  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 42% (02:06) correct 58% (02:02) wrong based on 187 sessions

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If n is a four-digit positive odd integer, then what is the tens digit of n?

1) the tens digit of n-9 is 0
2) the tens digit of n+9 is 2
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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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If n is a four-digit positive odd integer, then what is the tens digit of n?

1) the tens digit of n-9 is 0
N is in the range XX09 to XX18, but since it's odd the possible values are XX09,XX11,... till XX17
Not sufficient

2) the tens digit of n+9 is 2
N is in the range XX11 to XX20, but we are told that N is odd so the range is reduced: from XX11 to XX19.
The tens digit is always 1, sufficient
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Director  Joined: 29 Nov 2012
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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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Zarrolou wrote:
If n is a four-digit positive odd integer, then what is the tens digit of n?

1) the tens digit of n-9 is 0
N is in the range XX09 to XX18, but since it's odd the possible values are XX09,XX11,... till XX17
Not sufficient

2) the tens digit of n+9 is 2
N is in the range XX11 to XX20, but we are told that N is odd so the range is reduced: from XX11 to XX19.
The tens digit is always 1, sufficient

its given that the number is odd so the last digit can be 1,3,5,7 or 9 so there are few cases where we don't have to test the value but great explanation!
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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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fozzzy wrote:
If n is a four-digit positive odd integer, then what is the tens digit of n?

1) the tens digit of n-9 is 0
2) the tens digit of n+9 is 2

From F.S 1 , for n = XX17,the tens digit of n-9 is 0,the tens digit of n is 1; for XX09,the tens digit of n-9 is 0, the tens digit of n is 0. Insufficient.

From F. S 2, we know that the units digit of n will atleast be 1(as n is odd). Thus, XXX1+9,gives tens digit of 2. Thus, the tens digit of n has to be 1.Sufficient.

B.
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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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I completely missed that N was an odd integer... well played GMAT, well played.
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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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Can someone please explain me the answer ?how is the range calculated?
Thanks
Namrata
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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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namrata88 wrote:
Can someone please explain me the answer ?how is the range calculated?
Thanks
Namrata

Quote:
If n is a four-digit positive odd integer, then what is the tens digit of n?

We are given that N is a Four Digit Integer.
N = ABCD
where A,B,C,D are representing the digits of the FOUR digit ODD number N.
We need the find a unique value for C = ?

Quote:
1) the tens digit of n-9 is 0

N = 1111
N - 9 = 1102
C = 1

But N = 1109
N - 9 = 1100
C = 0

2 different answer. Hence, the statement is Insufficient.

Quote:
2) the tens digit of n+9 is 2

N = ABCD = Odd
=> N = 1111
N + 9 = 1120
C = 2

N = 1119
N + 9 = 1128
C = 2

=> For the 4 digit odd integer, the value of the ten's digit denoted by C will always be 1.
B is sufficient, and is the answer.

Hope this helps!
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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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namrata88 wrote:
Can someone please explain me the answer ?how is the range calculated?
Thanks
Namrata

Also, in terms of the range, you can try to use smaller numbers for the statements to understand what they mean.

For e.g.

Statement 1 - Ten's digit is 0 when N is subtracted by 9.

The maximum value of N can be 18, but since N is odd, the maximum value it can take is 17.
As 17 - 9 = 08
Here the ten's digit after subtraction is 0.
Minimum Value of N = 9
As 9 - 9 = 0 => Ten's digit will also be 0.

If we take N = 19, then N - 9 = 10
Here the ten's digit after subtraction is 1, and it breaks the statement. The statement is a fact, so this value is OUT of range.

Statement 2 - Ten's digit is 2 when 9 is added to N.
We cannot say N = 20, as N is odd.
So the maximum value of N = 19
And 19 + 9 = 28
The minimum value of N can be 11, as we need the ten's digit to be 2 when we add 9 to it.

Now try using this concept in a 4 digit odd number, and you'll figure it out.
Hope this helps.
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Re: If n is a four-digit positive integer, then what is the tens  [#permalink]

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fozzzy wrote:
If n is a four-digit positive odd integer, then what is the tens digit of n?

1) the tens digit of n-9 is 0
2) the tens digit of n+9 is 2

n is a 4 digit ODD I => _ _ _ _

Now lets see what can we do

from 1) 1209-9 = 1200 or 1217-9 = 1208

We get 2 values for ten's digit

from 2) 1219+9 = 1228, addition with 9 to give 2, will always have a 1 as ten's digit

B
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: If n is a four-digit positive integer, then what is the tens   [#permalink] 18 Feb 2019, 09:54
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