GMAT Quantitative Reasoning: Data Sufficiency Example Problem #2

 

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This week we will turn our attention to a GMAT Data Sufficiency question. Because the instructions regarding Data Sufficiency questions are highly specific we have included them.

GMAT Data Sufficiency Instructions: Each of the data sufficiency questions below consist 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 statement plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise) you are to fill in oval:

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

 

If x is an integer, is (54 + 27)/x an integer: 

  1. 6 ≤ x ≤ 81
  2. X is a multiple of 3.

 

It’s important not to make assumptions with data sufficiency problems. Plugging in numbers is a good way to check for consistency. Remember that a statement is not sufficient unless it always gives a consistent answer.

Now, let’s look at this problem. An integer is a whole positive or negative number.  Any decimal or fraction that can’t be reduced to a whole number is not an integer. Therefore, for the expression to be an integer you must be able to divide 81 evenly divided by x.  To simplify this statement, first add the two numbers in the denominator. 54 added to 27 is 81. This sum of 81 will be divided by x.  Now, look at each statement separately.

This expression means that x is some integer from 6 to 81. With a problem of this type, it helps to plug in numbers. To make things simple, let’s start by dividing 81 by the highest and lowest possible numbers, which are 6 and 81.  If x is 81, then the expression will be an integer.

81/81 = 1

If x is 6, the expression will not be an integer.

81/6 = 13.5

The fraction 6/80 cannot be reduced to a whole number. Again, the question is whether 81/x is an integer. Since there is not a consistent answer to the question, the first statement is not sufficient.

If x is a multiple of 3, it is a number that can be evenly divided by 3. Again, it helps to plug in numbers. One possible value of x would be 3. This results in an integer.

81/3 = 27

It might be tempting at this point to conclude that the statement is sufficient. However, remember that another possible value of x is 6. This does not result in an integer.

81/6 = 13.5

The second statement is not sufficient because there is not a consistent answer.

Now, try combining both statements together. This would mean that x was a multiple of 3 from 6 to 81. Once again, you can plugin numbers. Luckily, we’ve already tried 81 and 6, two values that are both multiples of 3. We found that in one case we got an integer, in the other we did not. Once again, we are left with inconsistent answers. This means that our final answer is (E), the statements together are not sufficient.

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