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Conceptual question

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Conceptual question [#permalink] New post 11 Aug 2012, 07:17
Hi,
I have a conceptual question about variables. In the GMAT, "x" (or, "y", whatever) or represents a unique unknown number, right?
For example:
If they say x^2=4, what is the value of x? Then the possible solutions are 2 or -2. But because x represents an unknown number can be ONLY one of those solutions, right? So, in this case, we don't know what the value of x is. We cannot answer the question.
Another example:
If they say |x-2|>4, is x>5? Then again we have two possible solutions x>6 or x<-2. Again, we cannot answer the question because or x>6 OR x>-2. CANNOT BE BOTH, right?
In summary, the possible solutions of a variable are the possible values of that variable, but ONLY one of them is its true value. The possible solutions are NOT the values that variable have. In other words, a variable has a UNIQUE unknown value, so we have to find it among the possible solutions we find. A variable doesn't have multiple values.
Otherwise, in a DS question:
What is x?
(1) x^2 = 4
This clue is insufficient because they want a single value for x. The variable has a unique unknown value.

Sorry for this dumb question, but the other day I read a different concept of variable (very different from what I learned in high school) and that confused me. :s That book said that a variable is something that can be replaced for any number of a set of numbers. In other words, a variable has multiple values at the same time. :s
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Re: Conceptual question [#permalink] New post 11 Aug 2012, 08:08
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danzig wrote:
Hi,
I have a conceptual question about variables. In the GMAT, "x" (or, "y", whatever) or represents a unique unknown number, right?
For example:
If they say x^2=4, what is the value of x? Then the possible solutions are 2 or -2. But because x represents an unknown number can be ONLY one of those solutions, right? So, in this case, we don't know what the value of x is. We cannot answer the question.
Another example:
If they say |x-2|>4, is x>5? Then again we have two possible solutions x>6 or x<-2. Again, we cannot answer the question because or x>6 OR x>-2. CANNOT BE BOTH, right?
In summary, the possible solutions of a variable are the possible values of that variable, but ONLY one of them is its true value. The possible solutions are NOT the values that variable have. In other words, a variable has a UNIQUE value, so we have to find it among the possible solutions we find. A variable doesn't have multiple values.

Sorry for this dumb question, but the other day I read a different concept of variable (very different from what I learned in high school) and that confused me. :s That book said that a variable is something that can be replaced for any number of a set of numbers. In other words, a variable has multiple values at the same time. :s


I beg to differ
A variable by its name says it can take many values.
Here i will take you on a tour of algebra as that will make it easier.
When we plot a graph of x v/s Y we get many values of x for many values of Y and vice versa and the reason we need variables is because their are more than one value which satisfies the equation its when we start imposing conditions on the variables that its range and domain start shrinking.
The equation Y = x has infinite solutions Yes x and Y both take infinite values. x haas no definitr value right now nether do Y but when we fix either of this then the other will have a unique value
Now Y = x for all x >0 .. now x and Y can be only positive
Y = x for all x (0,5) now x can only be in between 0 and 5
Y - x for all x (0.5 , 1.5) and X belongs to Z now x can only be 1


When we talk of a function X^2 =2 here what is important for x is that it haas to satisfy this equation ! weather it is 2 or -2 it satisfies the equation we cant say it is one of these values neither we say that x is both 2 and -2 what we say is x can only be 2 or -2 for this equation to be true.

I will recommend that you go through a text on functions and variables by probably Thomas Finey.
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Re: Conceptual question [#permalink] New post 11 Aug 2012, 09:35
mandyrhtdm wrote:
danzig wrote:
Hi,
I have a conceptual question about variables. In the GMAT, "x" (or, "y", whatever) or represents a unique unknown number, right?
For example:
If they say x^2=4, what is the value of x? Then the possible solutions are 2 or -2. But because x represents an unknown number can be ONLY one of those solutions, right? So, in this case, we don't know what the value of x is. We cannot answer the question.
Another example:
If they say |x-2|>4, is x>5? Then again we have two possible solutions x>6 or x<-2. Again, we cannot answer the question because or x>6 OR x>-2. CANNOT BE BOTH, right?
In summary, the possible solutions of a variable are the possible values of that variable, but ONLY one of them is its true value. The possible solutions are NOT the values that variable have. In other words, a variable has a UNIQUE value, so we have to find it among the possible solutions we find. A variable doesn't have multiple values.

Sorry for this dumb question, but the other day I read a different concept of variable (very different from what I learned in high school) and that confused me. :s That book said that a variable is something that can be replaced for any number of a set of numbers. In other words, a variable has multiple values at the same time. :s


I beg to differ
A variable by its name says it can take many values.
Here i will take you on a tour of algebra as that will make it easier.
When we plot a graph of x v/s Y we get many values of x for many values of Y and vice versa and the reason we need variables is because their are more than one value which satisfies the equation its when we start imposing conditions on the variables that its range and domain start shrinking.
The equation Y = x has infinite solutions Yes x and Y both take infinite values. x haas no definitr value right now nether do Y but when we fix either of this then the other will have a unique value
Now Y = x for all x >0 .. now x and Y can be only positive
Y = x for all x (0,5) now x can only be in between 0 and 5
Y - x for all x (0.5 , 1.5) and X belongs to Z now x can only be 1


When we talk of a function X^2 =2 here what is important for x is that it haas to satisfy this equation ! weather it is 2 or -2 it satisfies the equation we cant say it is one of these values neither we say that x is both 2 and -2 what we say is x can only be 2 or -2 for this equation to be true.

I will recommend that you go through a text on functions and variables by probably Thomas Finey.


I agree with you in almost everything. However, as you have said, x can only be 2 or -2. In that sense it has a UNIQUE value that we don't know yet; there is not enough information to answer what x is. That's why when the GMAT says in a DS question:
What is the value of x? :
(1) x^2=4"
The clue (1) is insufficient. They want a UNIQUE value (2 OR -2, one of them).
Otherwise, why would it be insufficient?
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Re: Conceptual question [#permalink] New post 11 Aug 2012, 18:58
metallicafan wrote:
mandyrhtdm wrote:
danzig wrote:
Hi,
I have a conceptual question about variables. In the GMAT, "x" (or, "y", whatever) or represents a unique unknown number, right?
For example:
If they say x^2=4, what is the value of x? Then the possible solutions are 2 or -2. But because x represents an unknown number can be ONLY one of those solutions, right? So, in this case, we don't know what the value of x is. We cannot answer the question.
Another example:
If they say |x-2|>4, is x>5? Then again we have two possible solutions x>6 or x<-2. Again, we cannot answer the question because or x>6 OR x>-2. CANNOT BE BOTH, right?
In summary, the possible solutions of a variable are the possible values of that variable, but ONLY one of them is its true value. The possible solutions are NOT the values that variable have. In other words, a variable has a UNIQUE value, so we have to find it among the possible solutions we find. A variable doesn't have multiple values.

Sorry for this dumb question, but the other day I read a different concept of variable (very different from what I learned in high school) and that confused me. :s That book said that a variable is something that can be replaced for any number of a set of numbers. In other words, a variable has multiple values at the same time. :s


I beg to differ
A variable by its name says it can take many values.
Here i will take you on a tour of algebra as that will make it easier.
When we plot a graph of x v/s Y we get many values of x for many values of Y and vice versa and the reason we need variables is because their are more than one value which satisfies the equation its when we start imposing conditions on the variables that its range and domain start shrinking.
The equation Y = x has infinite solutions Yes x and Y both take infinite values. x haas no definitr value right now nether do Y but when we fix either of this then the other will have a unique value
Now Y = x for all x >0 .. now x and Y can be only positive
Y = x for all x (0,5) now x can only be in between 0 and 5
Y - x for all x (0.5 , 1.5) and X belongs to Z now x can only be 1


When we talk of a function X^2 =2 here what is important for x is that it haas to satisfy this equation ! weather it is 2 or -2 it satisfies the equation we cant say it is one of these values neither we say that x is both 2 and -2 what we say is x can only be 2 or -2 for this equation to be true.

I will recommend that you go through a text on functions and variables by probably Thomas Finey.


I agree with you in almost everything. However, as you have said, x can only be 2 or -2. In that sense it has a UNIQUE value that we don't know yet; there is not enough information to answer what x is. That's why when the GMAT says in a DS question:
What is the value of x? :
(1) x^2=4"
The clue (1) is insufficient. They want a UNIQUE value (2 OR -2, one of them).
Otherwise, why would it be insufficient?



That is the difference between an GMAT problem! for all discussions related to GMAT yes, the conditions should give us a Unique value as that is being asked in the question. But like in many real life problems and applications of mathematics an equation has millions of solutions and all such solutions are valid and has a different interpretation.
Lets say for example the motion of a pendulum, if some one asks you when will a pendulum bob currently in motion come back to its mean position, what will you say ? It will come back to mean position after every time period and that will be infinite n o. of times. but if he asks you when will it be in its mean position second time we can tell him that exact and unique answer.

In actual world of physics all the solutions are valid and have some information to give regarding the equation which they satisfy.
But as long as we are preparing only about GMAT, we shouldn't worry about it all. Get a unique answer and move on.
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Re: Conceptual question [#permalink] New post 19 Aug 2012, 01:30
danzig wrote:

in a DS question:
What is x?
(1) x^2 = 4
This clue is insufficient because they want a single value for x. The variable has a unique unknown value.


Yes, in Data Sufficiency on the GMAT, if a question asks for the value of x, you *only* have enough information if you can get *one and only one* value for x. If, from a statement, you get two solutions for x, and those solutions agree with all the information provided in the question itself, the statement is not sufficient.

danzig wrote:

Another example:
If they say |x-2|>4, is x>5? Then again we have two possible solutions x>6 or x<-2. Again, we cannot answer the question because or x>6 OR x>-2. CANNOT BE BOTH, right?


This question is a bit different from the previous one. First, this is a yes/no DS question, and not a question which asks for a value. We have enough information in a yes/no DS question if we can be 100% certain the answer to the question is 'yes', or, in rare cases, 100% certain the answer to the question is 'no'. If the answer might be 'yes' and might be 'no', the information is not sufficient.

So in the question above, you do not have "two possible solutions" here for x when you look at the inequality |x-2| > 4. You have an infinite number of possible solutions for x; x can be any number less than -2 or any number greater than 6. "x" still stands for some single value; x is not a range of values. So using that information, we can't be certain of the answer to the question "Is x > 5?" Maybe x is equal to -17, or to -99, and the answer is 'no'. Or maybe x is equal to 55, or to 313, and the answer is 'yes'. So the information is not sufficient. If we had a second statement that told us 'x > 0', then the two statements together would be sufficient, since combining them, it would need to be true that x > 6. Notice though that we still have no way to tell what the value of x actually is.
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Re: Conceptual question [#permalink] New post 10 Sep 2012, 13:49
danzig wrote:
Hi,
I have a conceptual question about variables. In the GMAT, "x" (or, "y", whatever) or represents a unique unknown number, right?
For example:
If they say x^2=4, what is the value of x? Then the possible solutions are 2 or -2. But because x represents an unknown number can be ONLY one of those solutions, right? So, in this case, we don't know what the value of x is. We cannot answer the question.
Another example:
If they say |x-2|>4, is x>5? Then again we have two possible solutions x>6 or x<-2. Again, we cannot answer the question because or x>6 OR x>-2. CANNOT BE BOTH, right?
In summary, the possible solutions of a variable are the possible values of that variable, but ONLY one of them is its true value. The possible solutions are NOT the values that variable have. In other words, a variable has a UNIQUE unknown value, so we have to find it among the possible solutions we find. A variable doesn't have multiple values.
Otherwise, in a DS question:
What is x?
(1) x^2 = 4
This clue is insufficient because they want a single value for x. The variable has a unique unknown value.

Sorry for this dumb question, but the other day I read a different concept of variable (very different from what I learned in high school) and that confused me. :s That book said that a variable is something that can be replaced for any number of a set of numbers. In other words, a variable has multiple values at the same time. :s



You're absolutely right. This is a condition of all DS question that we get one and only value using the statements.

I would like to quote OG12 in this regard. Hope it will clear your doubt completely.

"6.1 Test-Taking Strategies

4. Answer the question asked.
For example, if the question asks, “What is the value of y ?” for an answer statement to be
sufficient, you must be able to find one and only one value for y. Being able to determine
minimum or maximum values for an answer (e.g., y = x + 2) is not sufficient, because such
answers constitute a range of values rather than the specific value of y."

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Re: Conceptual question [#permalink] New post 10 Sep 2012, 21:54
Expert's post
danzig wrote:
Hi,
I have a conceptual question about variables. In the GMAT, "x" (or, "y", whatever) or represents a unique unknown number, right?
For example:
If they say x^2=4, what is the value of x? Then the possible solutions are 2 or -2. But because x represents an unknown number can be ONLY one of those solutions, right? So, in this case, we don't know what the value of x is. We cannot answer the question.
Another example:
If they say |x-2|>4, is x>5? Then again we have two possible solutions x>6 or x<-2. Again, we cannot answer the question because or x>6 OR x>-2. CANNOT BE BOTH, right?
In summary, the possible solutions of a variable are the possible values of that variable, but ONLY one of them is its true value. The possible solutions are NOT the values that variable have. In other words, a variable has a UNIQUE unknown value, so we have to find it among the possible solutions we find. A variable doesn't have multiple values.
Otherwise, in a DS question:
What is x?
(1) x^2 = 4
This clue is insufficient because they want a single value for x. The variable has a unique unknown value.

Sorry for this dumb question, but the other day I read a different concept of variable (very different from what I learned in high school) and that confused me. :s That book said that a variable is something that can be replaced for any number of a set of numbers. In other words, a variable has multiple values at the same time. :s


Conceptually speaking, a variable is an unknown. It can take any given value or a set of values. Why do we use variables?

Say, I ask you the following question: Which number when added to 10 gives me 12?
You: I don't know. Let me find out. Let that number be x.
10 + x = 12
So x = 2
You found a unique value for the number I wanted. Great!

Say, now I ask you another question: Which number is 2 units away from 0 on the number line?
You: I don't know. Let me find out. Let that number be x.
mod x = 2
x = 2 or -2
Here x can take 2 values.

x can take any number of values depending on the restrictions we apply.

When dealing with DS questions in GMAT, you have to answer the question asked and nothing more.

Question: What is the value of x?
Here, x stands for one unique value. They are asking you to give a value to the unknown. You should be able to give that value. If you get 2 or more, you do not have sufficient data to arrive at a single value and hence, you cannot answer the question. e.g. I ask you: what is your name? If you tell me that it is either 'Danny' or 'Zig Ziglar', you haven't answered my question. You need to give me only one name.

Question: Is x greater than 0?
Here, they are not asking for the value of x. Their question is whether x MUST be positive under the given restrictions. I don't care about the actual value(s) x can take. e.g. I ask you: is your name 'Danny'? You only have to say yes or no. You don't need to tell me your name. If you say no, you have answered by question satisfactorily.
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Re: Conceptual question   [#permalink] 10 Sep 2012, 21:54
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