GMAT® Practice - Number Theory : DS

Concept: Factors of a number.

The given question is a data sufficiency question from Algebra and requires finding whether a definite solution is possible.

Directions for Data Sufficiency

This data sufficiency problem consists of a question and 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 statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  4. EACH statement ALONE is sufficient to answer the question asked.
  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Numbers

All numbers used are real numbers.

Figures

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

Note

In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Question: What is the value of X, if X and Y are two distinct integers and their product is 30?

  1. X is an odd integer
  2. X > Y

Explanatory Answer

Video explanation will be added soon

What kind of an answer will the question fetch?

The question is a "What is the value" question. Answer has to be a value, a number for 'X'.

When is the data sufficient?

The data is sufficient if we are able to determine a UNIQUE value for 'X' from the information given in the statements.

Do we have any additional information about 'X' or 'Y' from the question stem?

From the question, we know that both X and Y are distinct integers and their product is 30.

30 can be obtained as a product of two distinct integers in the following manner.

Values that satisfy X * Y = 30
S No. Positive X and Y Negative X and Y
1 1 * 30 (-1) * (-30)
2 2 * 15 (-2) * (-15)
3 3 * 10 (-3) * (-10))
4 5 * 6 (-5) * (-6)

Statement 1 Alone: X is an odd integer

From this statement, we know that the value of X is odd.

Therefore, X can be one of the following values: 1, -1, 3, -3, 5, -5.

So, using the information in statement 1 we will not be able to deduce a UNIQUE value for X.

  Statement 1 ALONE is NOT sufficient.

Eliminate choices A and D. Options narrow down to B, C, or E.

Statement 2 Alone: X > Y

From this statement, we know that the value of X > Y.

From the given combinations, X can take more than one value. Here are two possibilities: X could be 10 and Y could be 3. Or X could be 30 and Y could be 1.

Hence, using the information in statement 2, we will not be able to find a UNIQUE value for X.

  Statement 2 ALONE is NOT sufficient.

Eliminate choice B.

Statements Together: X is an odd integer and X > Y

Values of X and Y that satisfy both the conditions are

S No. X is odd and X > Y
1 (-1) * (-30)
2 (-3) * (-10))
3 (-5) * (-6)

More than one value exists for X. Because we are not able to deduce a UNIQUE value for X using the information provided in the two statements together, the given data is NOT sufficient.

  Statements TOGETHER are NOT sufficient.

Choice E is the answer.

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