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

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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I completely missed that N was an odd integer... well played GMAT, well played.

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

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 = ?



N = 1111
N - 9 = 1102
C = 1

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

2 different answer. Hence, the statement is Insufficient.




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!

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.

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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