GMAT Data Sufficiency  Number Theory
Question 10
2. Counter example approach to solve DS 2 concepts
The GMAT DS practice question given below is from Number Properties & Number Theory. Concept tested: Terminating decimals.
Directions
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  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
 Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
 BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
 EACH statement ALONE is sufficient to answer the question asked.
 Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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
Is \\frac{x}{y}\\) a terminating decimal?
 x is a multiple of 2
 y is a multiple of 3
Explanatory Answer

What kind of an answer will the question fetch?
The question is an "Is" question. The answer to an "Is" question is YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get DEFINITE YES or DEFINITE NO as an answer from the information in the statements.
If the statements do not have adequate data to provide a CONCLUSIVE answer and we get YES for some instances and NO for others, data is NOT sufficient.
What is a terminating decimal?
Numbers that have finite number of digits after the decimal point are called terminating or finite decimals. e.g., 2.5, 0.25, 8.
Note: All integers are terminating decimals.Numbers that have infinite digits after the decimal point are called nonterminating or infinite decimals. e.g., \\frac{1}{3}\\) = 0.33333..., \\sqrt{2}\\) = 1.4142...
What is the approach?
Counter Example: We will look for a counter example. i.e., we will look for two examples, both satisfying the information given in the statements  one that gives an answer YES and the other that gives an answer NO.

Statement 1: x is a multiple of 2
No information about y has been provided.
Approach: Let us look for a counter example.
Example: When x = 2 and y = 1, \\frac{x}{y}\\) is terminating. Answer: YES.
Counter Example: When x = 2 and y = 3, \\frac{x}{y}\\) is nonterminating. Answer: NO.
We have found a counter example. Therefore, statement 1 is not providing a DEFINITE answer.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.

Statement 2: y is a multiple of 3
No information about x has been provided.
Approach: Let us look for a counter example
Example: When x = 3 and y = 3, \\frac{x}{y}\\) is terminating. Answer: YES.
Counter Example: When x = 2 and y = 3, \\frac{x}{y}\\) is nonterminating. Answer: NO.
We have found a counter example. Therefore, statement 2 is not providing a DEFINITE answer.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.

Statements Together: x is a multiple of 2 & y is a multiple of 3
Approach: Let us look for a counter example
Example: When x = 6 and y = 3, \\frac{x}{y}\\) is terminating. Answer: YES.
Counter Example: When x = 2 and y = 3, \\frac{x}{y}\\) is nonterminating. Answer: NO.
We have found a counter example. Therefore, despite combining the information in the statements we are not able to find a DEFINITE answer.
Statements TOGETHER are NOT SUFFICIENT.
Choice E is the answer.
More questions from Number Properties & Number Theory
 Missing prime factors in a number
 Counting methods
 What is the divisor?
 Counting Methods : Keystrokes
 What is the value of the divisor?
 Number of divisors
 Number of trailing zeroes
 Find the remainder
 Data Sufficiency : Comparing indices
 GMAT DS : Terminating Decimals
 GMAT DS : Test of divisibility
 GMAT DS : Is y odd?
 GMAT DS : Absolute values
 Data Sufficiency : Remainders
 DS : Positive & negative numbers
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