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# If x and y are two points on the number line what is the

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Re: Number Line [#permalink]
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Agreed. It was my mistake. I didn't notice that all possible values of x and y will have a total =12, and that is what the question asks
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Re: If x and y are two points on the number line what is the [#permalink]
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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

Question is asking for x+y

Statement 1 means that (x+y)/2 = 6

Hence x+y = 12

This is sufficient

Statement 2 is obviously not sufficient

Hence A

Cheers!
J
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Re: If x and y are two points on the number line what is the [#permalink]
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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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If x and y are two points on the number line what is the [#permalink]
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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

Cheers,
Brent

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Originally posted by BrentGMATPrepNow on 06 Apr 2019, 07:48.
Last edited by BrentGMATPrepNow on 15 May 2021, 08:26, edited 1 time in total.
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Re: Number Line [#permalink]
Yes, answer is C.

The first statement tells us that the average of X and Y is 6, i.e. (X+Y)/2=6 <=> X+Y=12
I.e. one equation in two unknowns => insufficient

The second equation is yet an equation in to unknowns => insufficient.

Combine the two statements to obtain 2x+3x = 3x = 12 <=> X=4 <=> Y=2*4=8.

So the answer is C.
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If x and y are two points on the number line what is the [#permalink]
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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Re: If x and y are two points on the number line what is the [#permalink]
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.
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Re: If x and y are two points on the number line what is the [#permalink]
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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Re: If x and y are two points on the number line what is the [#permalink]
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

A) Consider cases:
x=5, y=7 => x+y = 12
x=-1, y=13 => x+y = 12
Sufficient

B) x + 2x = 3x = ? => Not sufficient

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Re: If x and y are two points on the number line what is the [#permalink]
Bunuel - If the question asked to solve for x and y , x , y can have multiple solutions. But can you pls explain how to solve for X , Y algebraically?

can i write |6-x|=|6-y| assuming y>x
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Re: If x and y are two points on the number line what is the [#permalink]
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