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I have to disagree with C. The answer to the question must be A.

If x and y are two points on the number line what is the value of x + y?

(1) 6 is halfway between x and y. On the GMAT we often see such statement and it can ALWAYS be expressed algebraically as \(6=\frac{x+y}{2}\) --> \(x+y=12\). Remember we are asked to determine the value of \(x+y\) not \(x\) and \(y\). Sufficient.

stmt 1: x and y can be anything...(4,8) (5,7)....(-12,24). stmt 2: y = 2x, again we can have (4,8) (5,10)...since 6 is not necessarily the midpoint of the line segment under consideration.

combining, 6+c = y = 2x, 6-c=x adding these two equations, we get 12 = 3x => x = 4, y=8. This is the only possibility that satisfies both conditions.

However, if stmt 2 was something like: |y| = |2x|, then answer would have been E.

If x and y are two points on the number line what is the
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23 Apr 2012, 22:20

If x and y are points on the number line, what is the value of x + y ? (1) 6 is halfway between x and y. (2) y = 2x

Ans: A When we say 6 is midway between x and y it means among x and y one number is 6 + m and other is 6 - m thus sum of x and y is (6+m)+(6-m) thus 12 irrespective of the value of m..

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20 Sep 2014, 18:22

Question is asking X+Y =>

isn't below always 12? ==< answer should be A. stmt 1: x and y can be anything...(4,8) (5,7)....(-12,24).

Economist wrote:

IMO C.

stmt 1: x and y can be anything...(4,8) (5,7)....(-12,24). stmt 2: y = 2x, again we can have (4,8) (5,10)...since 6 is not necessarily the midpoint of the line segment under consideration.

combining, 6+c = y = 2x, 6-c=x adding these two equations, we get 12 = 3x => x = 4, y=8. This is the only possibility that satisfies both conditions.

However, if stmt 2 was something like: |y| = |2x|, then answer would have been E.

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13 Feb 2017, 18:52

Whenever see a statement about AVERAGES (of which 'halfway' is one), you should automatically associate averages with SUMS. in other words, if you ever see a statement about an average, you should immediately translate that statement into the language of sums. to do so, just use the following equation: average = sum / # of data points or, equivalently, sum = (average) x (# of data points)

statement (1): this tells you that 6 is the average of x and y (or, (x + y)/2 = 6). therefore, sum of x + y = (average)(# of data points) = 6 x 2 = 12. you can also do good old fashioned algebra to get this result: multiply both sides of (x + y)/2 = 6 by 2 to yield x + y = 12. in fact, that's probably easier on this problem, but it's important that you learn the average/sum formula so that you can apply it effortlessly to other situations (such as sums of 10, 20, or more numbers) on which an algebraic solution would be awkward or just plain impossible in a reasonable amount of time.

in any case, x + y = 12, so this is sufficient.

statement (2): clearly insufficient by itself, since x and y could be huge (1 million and 2 million) or tiny (0.0001 and 0.0002).

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21 Feb 2017, 02:06

anairamitch1804 wrote:

Whenever see a statement about AVERAGES (of which 'halfway' is one), you should automatically associate averages with SUMS. in other words, if you ever see a statement about an average, you should immediately translate that statement into the language of sums. to do so, just use the following equation: average = sum / # of data points or, equivalently, sum = (average) x (# of data points)

statement (1): this tells you that 6 is the average of x and y (or, (x + y)/2 = 6). therefore, sum of x + y = (average)(# of data points) = 6 x 2 = 12. you can also do good old fashioned algebra to get this result: multiply both sides of (x + y)/2 = 6 by 2 to yield x + y = 12. in fact, that's probably easier on this problem, but it's important that you learn the average/sum formula so that you can apply it effortlessly to other situations (such as sums of 10, 20, or more numbers) on which an algebraic solution would be awkward or just plain impossible in a reasonable amount of time.

in any case, x + y = 12, so this is sufficient.

statement (2): clearly insufficient by itself, since x and y could be huge (1 million and 2 million) or tiny (0.0001 and 0.0002).

Hence A.

anairamitch1804 wrote:

Whenever see a statement about AVERAGES (of which 'halfway' is one), you should automatically associate averages with SUMS. in other words, if you ever see a statement about an average, you should immediately translate that statement into the language of sums. to do so, just use the following equation: average = sum / # of data points or, equivalently, sum = (average) x (# of data points)

statement (1): this tells you that 6 is the average of x and y (or, (x + y)/2 = 6). therefore, sum of x + y = (average)(# of data points) = 6 x 2 = 12. you can also do good old fashioned algebra to get this result: multiply both sides of (x + y)/2 = 6 by 2 to yield x + y = 12. in fact, that's probably easier on this problem, but it's important that you learn the average/sum formula so that you can apply it effortlessly to other situations (such as sums of 10, 20, or more numbers) on which an algebraic solution would be awkward or just plain impossible in a reasonable amount of time.

in any case, x + y = 12, so this is sufficient.

statement (2): clearly insufficient by itself, since x and y could be huge (1 million and 2 million) or tiny (0.0001 and 0.0002).

Hence A.

What if x=-5 and y = 22 the sum is 17. If x= -10 and y = 32 the sum is 22. Statement never said that the numbers are +ve. Also the stat 1 and 2 speak only about alzebra not about absolute distance. Please help. I think the answer is C as it gives unique solution ie 4 and 8.

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06 Apr 2019, 07:48

Top Contributor

study wrote:

If x and y are two points on the number line what is the value of x + y?

(1) 6 is halfway between x and y

(2) y = 2x

Target question:What is the value of x + y?

Statement 1: 6 is halfway between x and y. KEY CONCEPT: The average (arithmetic mean) of 2 numbers is HALFWAY between those 2 numbers. For example, the average of 1 and 9 is 5. Notice that 5 is HALFWAY between 1 and 9.

So, statement is telling us that 6 is the average of x and y In other words, (x + y)/2 = 6 This means x + y = 12 The answer to the target question is x + y = 12 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y = 2x There are infinitely many values of x and y that satisfy statement 2. Here are two: Case a: x = 1 and y = 2. In this case, the answer to the target question is x + y = 1 + 2 = 3 Case b: x = 3 and y = 6. In this case, the answer to the target question is x + y = 3 + 6 = 9 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT