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Manager  Joined: 05 Oct 2008
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If x and y are two points on the number line what is the  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 51% (01:15) correct 49% (01:42) wrong based on 367 sessions

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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

Originally posted by study on 24 Oct 2009, 00:04.
Last edited by Bunuel on 24 Apr 2012, 05:47, edited 1 time in total.
Edited the question and added the OA
Math Expert V
Joined: 02 Sep 2009
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6
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.

(2) y=2x. Clearly not sufficient

Hope it's clear.
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Director  Joined: 01 Apr 2008
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Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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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.
Manager  Joined: 08 Oct 2009
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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.

Director  Joined: 01 Apr 2008
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Name: Ronak Amin
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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 Intern  Joined: 08 May 2011
Posts: 5
GMAT Date: 04-28-2012
If x and y are two points on the number line what is the  [#permalink]

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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..
SVP  Joined: 06 Sep 2013
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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

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 Manager  Status: Please do not forget to give kudos if you like my post
Joined: 19 Sep 2008
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Re: If x and y are two points on the number line what is the  [#permalink]

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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.
Director  G
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GMAT 1: 770 Q51 V44 GPA: 4
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Re: If x and y are two points on the number line what is the  [#permalink]

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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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Anaira Mitch
Intern  Joined: 08 Apr 2016
Posts: 3
Re: If x and y are two points on the number line what is the  [#permalink]

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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.
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Joined: 12 Sep 2015
Posts: 4134
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

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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Director  V
Joined: 24 Oct 2016
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GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38 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

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

B) x + 2x = 3x = ? => Not sufficient Re: If x and y are two points on the number line what is the   [#permalink] 02 Sep 2019, 15:54
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