Simplify questions and data statements

Last updated: 4 Mar 2007

You will find that the question and data statements are sometimes written in a way which deliberately obscures a fairly simple meaning.

In these cases you will find it useful to simplify the statements or question to make it clearer what information you are provided or what the question you are asked is.

Example problem to simplify

If n is a positive integer, is `(1/10)^n < 0.001`?

  1. `n^3 = 64`
  2. n > 2
  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
  4. EACH statement ALONE is sufficient
  5. Statements (1) and (2) TOGETHER are NOT sufficient

Have a go at this question before reading the explanation below.

Simplify the question

The question in this problem can be simplified.

If n is a positive integer, is `(1/10)^n < 0.001`?

Firstly we can express both sides of the inequality in similar ways because we know that

`0.001 = (1/10)^3`

So we can write the question as

`(1/10)^n < (1/10)^3`

But since the bases for both exponents are the same this can be simplified further to just compare the powers.

`n > 3`

Which means can simplify what looks like quite a complex question to, "If n is a positive integer, is n > 3?"

Simplify the data statements

We can also simplify the first data statement

`n^3 = 64`
If we take cube roots of both sides of the equation we get

n = 4

Statement 2 cannot be simplified further

Solve the problem

Once you have simplified this data sufficiency problem it is easy to solve

Statement 1 tells you n = 4 which is greater than 3 and so is sufficient to answer the question.

Statement 2 tells you that n > 2 which is insufficient to answer the question.

Therefore the answer is A.

Next page: Avoid unnecessary calculations

Comments (3):

  1. If n is larger than 2, and n is an integer. . wouldn't that make it 3 or bigger? Then wouldn't this be enough info to solve question for statement 2?

    Anonymous on 29 Oct 2007 (permalink)

  2. You know that n is an integer and n > 2 and you need to know whether n > 3.

    There are two possibilities n is 3 in which case it IS NOT greater than 3 or n is 4 or more in which case it IS greater than 3.

    Therefore statement 2 is not enough to answer the question.

    joel on 1 Nov 2007 (permalink)

  3. why isnt it n LESS THAN 3, why is it n GREATER THAN 3

    Anonymous on 10 Nov 2007 (permalink)

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