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TANCET 2014 DS 68: Numbers

Directions for Data Sufficiency Question

The question is followed by two statements labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge of mathematics and everyday facts, choose the answer as:

  1. Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
  4. Choice 4 if each statement ALONE is sufficient.
  5. Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.

Question

What is the value of the integer W?

  1. Statement 1: W is a multiple of 3.
  2. Statement 2: 420 < W < 425

  Correct Answer    Choice (3). Statements (1) and (2) TOGETHER are sufficient.


Explanatory Answer - step by step

  • What should we know from the Question Stem?

    Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.

    What kind of an answer will the question fetch?

    The question is "What is the value of the integer W?"

    The answer to the question should be an integer.

    When is the data sufficient?

    If we are able to come up with a UNIQUE value for w, the data is sufficient.

    If we are not able to come up with a UNIQUE value for W, the data is NOT sufficient.

    What additional information do we know about W from the question stem?

    The question stem states that W is an integer. So, we can restrict the set of numbers to include only integers.

  • Statement (1) ALONE

    W is a multiple of 3.

    There are infinite possibilities. We CANNOT find a unique answer for W from statement (1) ALONE.

      Statement (1) ALONE is NOT sufficient.

    If statement (1) ALONE is NOT sufficient, we can eliminate choices 1 and 4.

    Choices narrow down to 2, 3, or 5.

  • Statement (2) ALONE

    420 < W < 425

    Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). Anything said about W in statement (1) should not be used while evaluating statement (2).

    W is an integer and 420 < W < 425

    Therefore, W could be 421 or 422 or 423 or 424.

    Using statement (2) we were NOT able to determine a unique value for W.

      Statement (2) ALONE is NOT sufficient.

    If statement (2) ALONE is NOT sufficient, we can eliminate choice 2 as well.

    Choices narrow down to 3, or 5.

  • Statements Together

    W is a multiple of 3.

    +

    420 < W < 425

    W is an integer, divisible by 3 and should be one of 421, 422, 423 or 424.

    Test of divisibility by 3: Sum of the digits of the number should be divisible by 3.

    Of the numbers shorlisted from statement (2), the only number that is divisible by 3 is 423.

    Using statements (1) and (2) together we were able to determine a unique value for W.

      Hence, choice (3) is the answer.

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