Arithmetic : Properties of NOS.

anirudhbhalotia wrote:If n is a positive integer, what is the tens digit of n?

1. The hundreds digit of 10n is 6.
2. The tens digit of n+1 is 7.

Say, n = ...cba, where a is the units, b is the tens and c is the hundreds digit of n. We need to determine b.

Statement 1: The hundreds digit of 10n is 6.
10n = ...cba0 => Hundreds digit of 10n is b.
Hence, b = 6

Sufficient

Statement 2: The tens digit of n+1 is 7.
(n + 1) = (...cba + 1)
Now, if a < 9, then tens digit of (n + 1) will be b => b = 7
and, if a = 9, then tens digit of (n + 1) will be (b + 1) => b = (7 - 1) = 6

Not sufficient

The correct answer is A.

anirudhbhalotia wrote:If n is a positive integer, what is the tens digit of n?

1. The hundreds digit of 10n is 6.
2. The tens digit of n+1 is 7.

Target question: What is the tens digit of n?

Statement 1: The hundreds digit of 10n is 6
Notice what happens when we multiply any positive integer by 10:
34 x 10 = 340
60 x 10 = 600
128 x 10 = 1280
54629 x 10 = 546290
The tens digit in the original number becomes the hundreds digit in the new number.

So, if we're told that the hundreds digit of 10n is 6, then we know that the tens digit in n must be 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The tens digit of n+1 is 7
There are several values of n that meet this condition. Here are two:
case a: n=69 in which case the tens digit of n is 6
case b: n=74 in which case the tens digit of n is 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

anirudhbhalotia wrote:If n is a positive integer, what is the tens digit of n?

1. The hundreds digit of 10n is 6.
2. The tens digit of n+1 is 7.

OA - A

We are given that n is a positive integer, and we must determine the tens digit of n.

Statement One Alone:

The hundreds digit of 10n is 6.

In order for the hundreds digit of 10n to be 6, the tens digit of n must be 6.

For example, if n = 60, then 10n = 600; and if n = 169, 10n =1,690.

We see that whenever we multiply a positive integer (at least two digits) by 10, the original tens digit will be the hundreds digit of the resulting integer. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

If you are wondering why n has to be at least two digits, note that if n is only one digit, such as n = 7, there will be no hundreds digit when we multiply 7 by 10 to get 70. Statement one specifically states that the hundreds digit of 10n is 6, so we can ignore all single-digit numbers in our consideration.

Statement Two Alone:

The tens digit of n+1 is 7.

Using the information in statement two we see that n could have a tens digit of 6 (for example, n = 69), or n could also have a tens digit of 7 (for example, n = 70). Thus, statement two is not sufficient to answer the question.

Answer: A