What is the tens digit of the positive integer n ?

Question

1. The hundreds digit of 10n is 2 .

2. The tens digit of n-9 is 1 .

Alex75PAris · Accepted Answer

let's write n=ABCD, where D units digit, C tens, D hundreds, etc. 
We need to know C

(1) The hundreds digit of 10n is 2
10*n = ABCD0
So, hundreds' digit is C = 2
Sufficient

(2) The tens digit of n-9 is 1
19-9 = 10
20-9 = 11
Not sufficient

MathRevolution · Answer

There is 1 variable (n) in the original condition. In order to match the number of variables and the number of equations, we need 1 equation. Since the condition 1) and 2) each has 1 equation, there is high chance that D is the correct answer.
In case of the condition 1), the tens-digit of n is always 2. The answer is unique and the condition is sufficient.
In case of the condition 2), from n=19 and 21, the tens-digit is 1 and 2. Hence, the answer is not unique and the condition is not sufficient. Thus, the correct answer is A.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Bunuel · Answer

Very similar question from OG for additional practice: if-n-is-a-positive-integer-what-is-the-tens-digit-of-n-144725.html

Konstantin1983 · Answer

Statement 1. This means that n can be 20 or 21 or 22 and so on and then tens digit is 2 always. Sufficient 
Statement 2. n can be 20 or 28 or 120. Hence sufficient. 
Answer D. Wait for official answer

hsbinfy · Answer

A for me what about 19? 19-9=10

varundixitmro2512 · Answer

IMO A

since 19-9 will have tens as 1
and 28-9 will have 1

Megan07 · Answer

1. The hundreds digit of 10n is 2 .
Tens digit will be 2 .
Sufficient

2. The tens digit of n-9 is 1 .
Not Sufficient

Answer A

adiagr · Answer

Statement 1

say n = 325. Ten's digit is 2.

10n = 3250. Here Hundred's digit is 2.

again say n = 25, Ten's digit is 2.

10n = 250. Here Hundred's digit is 2.

We will see that always we will get unique answer.

Statement 1 is sufficient.

Statement 2

say n = 19, then 19-9 = 10. ten's digit of 10 is 1. ten's digit of 19 is also 1

now say n = 22, then 22-9 = 13. ten's digit of 13 is 1. BUT ten's digit of 22 is NOT 1. It is 2.

So not sufficient.

A is the answer.

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What is the tens digit of the positive integer n ?

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