GMAT question - If k is not equal to... - Review

Type: Data Sufficiency

Difficulty: 5 star rating

If mathematical expression, is mathematical expression?

  1. mathematical expression
  2. mathematical expression
  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

Explanation

Simplify the question

If mathematical expression 0, 1, or -1...

This part of the question is just to stop the pathological cases which result in a division by zero (which is undefined).

...is mathematical expression?

mathematical expression is greater than zero if and only if mathematical expression, so the question is actually asking if mathematical expression is positive.

Is statement (1) sufficient?

Statement (1) tells us that mathematical expression which means that mathematical expression.

This tells us that mathematical expression, but mathematical expression could still be greater than 0, e.g. 0.5, or less than 0, e.g. -2 and so statement (1) is not sufficient to answer the question.

Is statement (1) sufficient?

Statement (1) tells us that mathematical expression which means that mathematical expression.

This tells us that mathematical expression, but mathematical expression could still be greater than 0, e.g. 2, or less than 0, e.g. -0.5 and so statement (2) is not sufficient to answer the question.

Select an answer

Since neither statement on its own is sufficient to answer the question the answer could be C (Together) or E (Neither).

Putting both statements together gives us

mathematical expression

This is still not sufficient to tell us whether mathematical expression is positive or not.

Therefore the correct answer is E (Neither).

Comments (9):

  1. I got B as the answer.

    If (1/k+1) is greater than 0 implies k is greater than 0
    since for any value of k less than 0 the inequality is not satisfied.

    Therefore for all values of k greater than 0, 1/k should also be greater than 0

    I hope I didnt miss any step above. Please correct me if I am wrong.

    Anonymous on 29 Nov 2007 (permalink)

  2. k doesn't have to be an integer

    If k = -0.5, the inequality is satisfied and equals 2

    asherei1 on 11 Aug 2008 (permalink)

  3. but aren't we supposed to assume that all numbers given would be integers?

    dsfafaass on 14 Nov 2008 (permalink)

  4. You should assume all numbers in the GMAT are real numbers unless the question tells you otherwise, see our properties of numbers tutorial for more details.

    joel on 15 Nov 2008 (permalink)

  5. How did you get -1 < k < 1 ?
    In the statement above it says k > 1 (because 1-k > 0)
    In the subsequent statement it says k > -1 (because 1+k > 0)
    why isn't this -1 > k > 1

    Thank-you.

    sguk on 24 Dec 2008 (permalink)

  6. My apologies there was a typo in the explanation of the question, which I have now fixed.

    Statement 1 tells us that k < 1 and statement 2 tells us that k > -1, so -1 < k < 1.

    joel on 24 Dec 2008 (permalink)

  7. Thanks for the question. I understand fully

    lets on 7 Feb 2009 (permalink)

  8. According to me it is not mentioned any where that what is K?
    is it integer,rational, irrational no?
    It is neither mentioned in question nor in any of the clues.
    Now solving 1st statement K<1>1.
    but not the number. So, option 5 is right.

    ersweta on 2 Mar 2009 (permalink)

  9. "You should assume that all answers in the GMAT are real numbers unless you are told otherwise", from properties of numbers tutorial.

    joel on 3 Mar 2009 (permalink)

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