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If x and y Represent Number on The Number Line, is x + y = 0 GMAT Data Sufficiency

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Question: If x and y represent number on the number line, is x + y = 0?

(1) Distance between x and 0 is the same as distance between y and 0.
(2) |x-y| = |x| +|y|

  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.

Correct Answer: C

Solution and Explanation:
Approach Solution 1:

The problem statement cites that if x and y represent a number on the number line, it is required to find whether x + y = 0.

Statement 1 alone:

Distance between x and 0 is the same as the distance between y and 0.
Let’s assume x = 4 and y = -4.
Therefore, the distance between x and 0 and y and 0 are the same, i.e, 4.
and x+y = 0
Let’s assume x = 4 and y = 4. The distance between x and 0 and y and 0 are the same, i.e, However, x+y = 8.
Therefore, statement 1 alone is INSUFFICIENT.

Statement 2 alone:

|x-y| = |x| +|y|
x and y are of different signs.
However, there is no information about the values of X and Y.
Therefore, statement 2 alone is INSUFFICIENT.
By combining both statements, we get:
x and y are of opposite signs and the distance is the same.
Therefore, x+y = 0
Hence, both statements together are SUFFICIENT.

Correct Answer: C

Approach Solution 2:

The problem statement suggests that if x and y represent a number on the number line, it asked to find whether x + y = 0.

Statement 1 alone: Distance between x and 0 is the same as distance between y and 0.

Therefore we can say, |x|=|y|
If x and y hold identical signs then x+y is not 0
If x and y hold the opposite signs then x+y is 0

Statement 2 alone:

|x-y|=|x|+|y|
which indicates that x and y holds opposite signs.
If |x|=|y|, then x+y is 0.
If |x|≠|y|, then x+y≠0

By merging both statements
x and y are equal in magnitude and have opposite signs.
Therefore, x+y=0
Hence, both statements together are Sufficient.

Correct Answer: C

Approach Solution 3:

The problem statement indicates that if x and y represent a number on the number line, it asked to find whether x + y = 0.

Statement 1: Distance between x and 0 is the same as distance between y and 0.

Therefore it implies, |x|=|y|
If x and y have similar signs then x+y is not 0
If x and y have opposite signs then x+y is 0
Hence, insufficient.

Statement 2: |x-y| = |x| +|y|

Let's assume x = 5 and y = -4.
Therefore, we get,
|5 - (-4)| = |5| + |- 4|
=> |9| = 5 + 4
=> 9 = 9.
Hence, it shows x + y = 1.
On the other hand, if x and y do have equal magnitude as well as opposite signs
If x = 5 and y = -5,

we will get, x + y = 0.
Therefore, from statement 2, we can say Yes or No. Thus, making statement 2 insufficient.

By combining both statements, we get:
x and y are of opposite signs and the distance is the same.
Hence we can say, x+y = 0
Hence, both statements together are SUFFICIENT.

Correct Answer: C

“If x and y represent number on the number line, is x + y = 0”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2019". The GMAT Quant section comprises a total of 31 questions. GMAT Data Sufficiency questions emerge with a problem statement that is followed by two factual statements. GMAT data sufficiency consists of 15 questions which are two-fifths of the entire 31 GMAT quant questions.

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*The article might have information for the previous academic years, please refer the official website of the exam.

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