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Can two statements in DS contradict each other ?

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Source: — Data Sufficiency |
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by shankar.ashwin » Wed Sep 21, 2011 6:53 am
If you are able to definitively answer a YES or a NO using these statements alone, you answer should be 'D', i.e both statements alone is sufficient to answer the question, though the answer may not be the same.

But that said, choices for DS in GMAT usually result in the same answer, atleast from what I have seen.
But yes, if you encounter such a situation, D would be the answer because you can still answer the question using two option used separately (AS mentioned in instructions for DS)
bijoyajj wrote:Say statement 1, says YES for a y/n DS prob AND
statement 2 , says NO...?
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by Brent@GMATPrepNow » Wed Sep 21, 2011 6:57 am
bijoyajj wrote:Say statement 1, says YES for a y/n DS prob AND
statement 2 , says NO...?
No, the statements cannot contradict each other.

In fact I have a free video lesson that shows how this fact can help us avoid careless mistakes.
It's video lesson #10 (Useful Contradictions) at https://www.gmatprepnow.com/module/gmat-data-sufficiency

Cheers,
Brent
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by shankar.ashwin » Wed Sep 21, 2011 7:01 am
Brent, for some reason your video links do not open. Could you pls check
Brent@GMATPrepNow wrote:
bijoyajj wrote:Say statement 1, says YES for a y/n DS prob AND
statement 2 , says NO...?
No, the statements cannot contradict each other.

In fact I have a free video lesson that shows how this fact can help us avoid careless mistakes.
It's video lesson #10 (Useful Contradictions) at https://www.gmatprepnow.com/module/gmat-data-sufficiency

Cheers,
Brent
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by Brent@GMATPrepNow » Wed Sep 21, 2011 7:02 am
For example, let's say that we are asked to determine the value of x.
If this were the case, you would never see the following statements:
(1) x+2=5
(2) x-3=7
In one case x=3, and in the other case x=10
As such, these contradicting statements would never appear in an actual GMAT question.

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by Brent@GMATPrepNow » Wed Sep 21, 2011 7:06 am
shankar.ashwin wrote:Brent, for some reason your video links do not open. Could you pls check
Are you certain? I just checked and it opens for Chrome, IE8 and Firefox.
Do you have an up-to-date browser?

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by shankar.ashwin » Wed Sep 21, 2011 7:27 am
Brent@GMATPrepNow wrote:
shankar.ashwin wrote:Brent, for some reason your video links do not open. Could you pls check
Are you certain? I just checked and it opens for Chrome, IE8 and Firefox.
Do you have an up-to-date browser?

Cheers,
Brent
I tried all browsers, not sure if the issue is with PC.

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by Brent@GMATPrepNow » Wed Sep 21, 2011 7:32 am
shankar.ashwin wrote: I tried all browsers, not sure if the issue is with PC.
It must be - our server is up and running.

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by bijoyajj » Sat Sep 24, 2011 1:59 am
Brent@GMATPrepNow wrote:For example, let's say that we are asked to determine the value of x.
If this were the case, you would never see the following statements:
(1) x+2=5
(2) x-3=7
In one case x=3, and in the other case x=10
As such, these contradicting statements would never appear in an actual GMAT question.

Cheers,
Brent
So it means we can directly substitute value from one equation into the second and see if it satisfies. If not, then 2nd option can be neglected.. Lets say in your example, option two is a complicated equation which takes time to solve using the usual way. then since we know the value of x from first option, i would substitute and see if the case suffice.. Am i making sense?
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by Brent@GMATPrepNow » Sat Sep 24, 2011 5:59 am
bijoyajj wrote:
So it means we can directly substitute value from one equation into the second and see if it satisfies. If not, then 2nd option can be neglected.. Lets say in your example, option two is a complicated equation which takes time to solve using the usual way. then since we know the value of x from first option, i would substitute and see if the case suffice.. Am i making sense?
I'm not certain that I totally understand what you're saying.
If you have a DS question involving equations and a statement yields one unique value of x, say x=3, then x=3 must also satisfy the second equation. Of course, it may be the case that the second equation has 2 (or more) solutions, but one of those solutions must be x=3 (if x=3 is the only solution to the first equation)

Consider this example.

What is the value of x?
(1) x+1= 4
(2) x^2 - 5x + 6 = 0

Here, we can see that statement 1 is sufficient (since x=3)
If we plug x=3 into statement 2, we see that it is a solution here, but this doesn't tell us anything about whether or not statement 2 is sufficient since equation x^2 - 5x + 6 = 0 could have two different solutions (which it does). So, we'd still have to solve the second equation in this question.

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by bijoyajj » Sat Sep 24, 2011 9:45 am
Brent@GMATPrepNow wrote: Consider this example.

What is the value of x?
(1) x+1= 4
(2) x^2 - 5x + 6 = 0

Here, we can see that statement 1 is sufficient (since x=3)
If we plug x=3 into statement 2, we see that it is a solution here, but this doesn't tell us anything about whether or not statement 2 is sufficient since equation x^2 - 5x + 6 = 0 could have two different solutions (which it does). So, we'd still have to solve the second equation in this question.

Cheers,
Brent
What i meant is, if we substitute the value in the second statement and if its not a solution then we can right away say that statement 2 is not sufficient.. In your example when we can plug in x=3 and if its not a solution, then we can move forward stating statement as insufficient..
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by Brent@GMATPrepNow » Sat Sep 24, 2011 11:33 am
bijoyajj wrote: What i meant is, if we substitute the value in the second statement and if its not a solution then we can right away say that statement 2 is not sufficient.. In your example when we can plug in x=3 and if its not a solution, then we can move forward stating statement as insufficient..
I'd have to see an example of such a question. I don't think it's possible to have a scenario that you describe (where there's only one solution to the first equation)

I can think of an example where there are 2 solutions to the first equation and we plug one one of the solutions into the second equation, but even this doesn't yield the results that you speak of.

Example:
What is the value of x?
(1) x^2 = 9
(2) x^2 - 5x + 6 = 0

From statement 1, we get x=3 or x=-3
When we plug x= -3 into the second equation it doesn't work. So what can we conclude about the sufficiency of statement without trying to actually solve the equation? Not much.
In this example, we see that statement 2 is not sufficient on its own.

Compare those results to the results of this similar question:

What is the value of x?
(1) x^2 = 9
(2) x + 1 = 4

From statement 1, we get x=3 or x=-3
When we plug x= -3 into the second equation it doesn't work. So what can we conclude about the sufficiency of statement without trying to actually solve the equation? Not much.
In this example, we see that statement 2 is sufficient on its own.

Given these results, I don't think we can create a general rule concerning plugging results from one statement into the other statement.

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Brent
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by bijoyajj » Sun Sep 25, 2011 12:01 am
What is the value of x?
(1) x^2 = 16
(2) x + 1 = 4

Lets start solving from statement 2.. it explicitly gives the value of x as 3..Hence sufficient.

Statement (1).. Instead of start solving the equation, since we know value is 3, we substitute and see if the equation holds good.. here equation fails.. hence no need to solve it and we can say it insufficient..

Lets take another example..

What is the value of x?
(1) Square root (9x^3+5*x+4) = 2
(2) x + 1 = 3

Statement 2:- sufficient and x =2
Statement 1:- we plug in x=2 , so root(72+10+4)some amount, which is not equal to 2.. hence insufficient.. (if x=2 is a root of the equation then we would av to solve it )

We might av had spend time solving the equation in other case.. like squaring and solving..


If this method is fine, then it would be pretty usefull for the probs in which one equation is simple and other is pretty complex.
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by Brent@GMATPrepNow » Sun Sep 25, 2011 6:01 am
bijoyajj wrote:What is the value of x?
(1) x^2 = 16
(2) x + 1 = 4

Lets start solving from statement 2.. it explicitly gives the value of x as 3..Hence sufficient.

Statement (1).. Instead of start solving the equation, since we know value is 3, we substitute and see if the equation holds good.. here equation fails.. hence no need to solve it and we can say it insufficient..

Lets take another example..

What is the value of x?
(1) Square root (9x^3+5*x+4) = 2
(2) x + 1 = 3

Statement 2:- sufficient and x =2
Statement 1:- we plug in x=2 , so root(72+10+4)some amount, which is not equal to 2.. hence insufficient.. (if x=2 is a root of the equation then we would av to solve it )

We might av had spend time solving the equation in other case.. like squaring and solving..


If this method is fine, then it would be pretty usefull for the probs in which one equation is simple and other is pretty complex.
Hi bijoyajj,

You're right in that this method would be useful for DS questions where one equation is simple and other is complex, However, the two questions you provided would never appear on the GMAT because the statements in each contradict each other. In fact, I'm quite positive that the scenario that you would apply your method to cannot exist.

Your first example:
What is the value of x?
(1) x^2 = 16
(2) x + 1 = 4
Here, statement 2 tells us that x must equal 3, but statement 1 essentially tells us that x does not equal 3.
Since these two statements contradict each other, they could never appear together on the GMAT.


Now it would be possible to have a question like this:
What is the value of x?
(1) x^2 = 9
(2) x + 1 = 4
Here, statement 2 tells us that x must equal 3, and statement 1 tells us that x could equal 3 or negative 3.
Since these two statements do not contradict each other, they could appear together on the GMAT. However, your method would not apply here.

Aside: the correct answer here is B


Your second example:
What is the value of x?
(1) Square root (9x^3+5*x+4) = 2
(2) x + 1 = 3
Here, statement 2 tells us that x must equal 2, but statement 1 tells us that x must equal 0.
Since these two statements contradict each other, they could never appear together on the GMAT.

Cheers,
Brent
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by bijoyajj » Sun Sep 25, 2011 10:45 am
If we just modify the first statement as Square root (9x^3-4*x+4) = 2,the we would av got 3 solutions (0,-2/3,2/3)..hence statement 1 insufficient :-).. May be gmat won't test this way.. thanks Brent for helping me out..[/img]
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