Data Sufficiency

If a and b are positive integers, and a× 10^5 = b × 10^n what is the value of n ?

(1) a = 100b

(2) a+b= 5050.

Although the answer is A, I posted it for the reason below:
According to what I solved, St2: We can solve for n. It just gives two different values, 7 and 3. That is why st2 is insufficient. In KAP, it says that using st2, n cannot be solved ( it is not possible to solve for n). I think that it is not true. Please correct me, if I am wrong.

a x 10^5 = b x 10^n

To find: "n"

Statement 1:
a = 100b
a x 10^5 = b x 10^n
100b x 10^5 = b x 10^n
we can solve and get "n"
SUFFICIENT

Statement 2:
a + b = 5050
(5050 - b) x 10^5 = b x 10^n
5050x10^5 = b (10^n + 10^5)
b = 5050 x 10^5 / (10^n + 10^5)
we can have different values of "n"
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]

tanvis1120 wrote: Although the answer is A, I posted it for the reason below:
According to what I solved, St2: We can solve for n. It just gives two different values, 7 and 3. That is why st2 is insufficient. In KAP, it says that using st2, n cannot be solved ( it is not possible to solve for n). I think that it is not true. Please correct me, if I am wrong.

Statement 2:
According to me, "n" can have many multiple values...
a + b = 5050
(5050 - b) x 10^5 = b x 10^n
5050x10^5 = b (10^n + 10^5)
b = 5050 x 10^5 / (10^n + 10^5)
If n=1, b = 5050 x 10^5 ( 100010) = approx 5050
If n=2, b = 5050 x 10^5 ( 100100) = approx 5050 but different than n=1
correspondingly value of "a" will change.
and so on
INSUFFICIENT

tanvis1120 wrote:If a and b are positive integers, and a× 10^5 = b × 10^n what is the value of n ?

(1) a = 100b

(2) a+b= 5050.

Statement 1: a = 100b
Substituting a = 100b into a × 10� = b × 10^n, we get:
100b * 10� = b * 10^n
100 * 10� = 10^n
10� = 10^n
n=7.
SUFFICIENT.

Statement 2: a+b = 5050
Case 1: a=5000 and b=50
Plugging these values into a × 10� = b × 10^n, we get:
5000 × 10� = 50 × 10^n
100 * 10� = 10^n
10� = 10^n
n=7.

Case 2: a=50 and b=5000
Plugging these values into a × 10� = b × 10^n, we get:
50 × 10� = 5000 × 10^n
10� = 100 * 10^n
10³ = 10^n
n=3.

Since n can take on different values, INSUFFICIENT.

The correct answer is A.

Note the following:
It is not required that the value of n be an integer.
In statement 2, the following case also is possible:

Case 3: a=5049 and b=1
Plugging these values into a × 10� = b × 10^n, we get:
5049 × 10� = 1 × 10^n
504,900,000 = 10^n.
Here, the value of n would be a non-integer.

Implication:
In statement 2, n could take on MANY different values.

Thanks All.
So, I was correct. It is possible to solve for n but n will have multiple values. So, the answer in one of the Kap lan tests was not correctly framed as it said that using statement 2, value of n cannot be solved.

You and Kaplan are both right! It is possible to solve for n in the sense that you can find some valid values, but it is not possible (given that statement) to find a UNIQUE value of n, which is what you need to "solve" a question in Data Sufficiency.

tanvis1120 wrote:Thanks All.
So, I was correct. It is possible to solve for n but n will have multiple values. So, the answer in one of the Kap lan tests was not correctly framed as it said that using statement 2, value of n cannot be solved.