If n is a positive integer with k digits. What is the value of n?

Question

(1) k = 1
(2) n = k

vitaliyGMAT · Answer

(1) k = 1

We have a set of one digit numbers where n can be any of the {1, 2, 3, 4, 5, 6, 7, 8, 9}. Not sufficient.

(2) n = k

If k=1 ----> n=1 We have one digit number that should have only one digit. Consistent.
If k=2 ----> n=2 We have one digit number that should have two digits (k=2). Inconsistent.
If k=3 ----> n=3 Again one digit number that should have three digits according to k=3. Inconsistent.

There is no need to proceed, the logic is the same. We have only one working option when n=k=1. Sufficient.

Answer B.

komals06 · Answer

can anyone explain please Statement 2 and why ans is B when st 2 is both consistent and inconsistent

CrackverbalGMAT · Answer

From the question data, we know that n is a positive integer which is dependent on k for the number of digits.

For example, if k = 1, we can say that n is a single digit positive integer. Similarly, if k=2, we can say that n is a 2-digit positive integer and so on. 
Now that we are clear about this, let us try to answer the question. We are supposed to find a unique value of n here.

Using statement I alone, we know k =1. This only means that n is a single digit positive integer. It could be any of the integers from 1 through 9. So, this data is insufficient.
Answer options A and D can be eliminated; possible answer options are B, C and E.

Using statement II alone, we know that the value of positive integer n should be equal to k. This is possible only when k = 1. When k = 1, we can say n is a single digit integer whose value equals that of k i.e. n = k = 1.

Should we worry about k being 2 or more? Absolutely not! Look at this:
If k = 2, n should be a two digit integer but it’s value should be equal to k. Can that happen? Impossible. 
The same analogy holds true for k = 3, 4, …….
This means that the only value of k that satisfies the condition given in statement II is k=1. This is a unique answer. So, this data is sufficient!
The correct answer option is B.

The trap answer here is C. If you don’t go that extra mile to analyse the second statement alone and figure out that k can only take one value, you will end up believing that statement II is insufficient and combine it with statement I and obtain the answer as C. But as we demonstrated, combining the statements is clearly not necessary.

Hope this helps!

daniformic · Answer

(1) k = 1

n can be 1, 2, 3, 4, 5, 6, 7, 8, 9 -> NS

(2) n = k

If k=1 -> n=1: one digit number OK
If k=2 -> n=2: two digit number but n=2 Not possible
If k=3 -> n=3: three digit number but n=3 Not possible
...

Answer -> B

If n is a positive integer with k digits. What is the value of n?

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GMAT Data Sufficiency (DS) Questions

If n is a positive integer with k digits. What is the value of n?

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