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

Question

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

Zarrolou · Accepted Answer

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

fozzzy · Answer

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!

mau5 · Answer

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.

Bunuel · Answer

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dave785 · Answer

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

namrata88 · Answer

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

akshayk · Answer

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!

akshayk · Answer

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.

KanishkM · Answer

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

bumpbot · Answer

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

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

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