I have a question about data sufficiency strategy...

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chieftang: Master | Next Rank: 500 Posts; Posts: 218; Joined: Wed Nov 23, 2011 8:05 pmFollowed by: 4 members; Thanked: 26 times

by chieftang » Thu Dec 08, 2011 11:43 pm

Hi, all. Quick question. Since the two statements can never each be sufficient to answer the target question AND be in conflict with each other, does it mean that the following is a sound strategy?

Suppose we have a problem such as this (I completely made it up) :

What is the value of 2x - 1 ?

(1) 3x^3 - 7x - 9 = 0
(2) 4x - 12 = 0

So, I can easily see that statement #2 is sufficient, but it's not immediately obvious what to do with statement #1. However since I know the solution to statement #2 is 3, can I plug the value 3 in to statement #1 to check if it is a solution to that equation? If it is not a solution to statement #1, then I should be able to conclude that statement 1 must be insufficient because it doesn't have a solution in common with statement 2???

Thanks!

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Source: Beat The GMAT — Data Sufficiency | Thu Dec 08, 2011 11:43 pm

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Fri Dec 09, 2011 3:01 am

NEVER use an info of one statement as an assumption in the other...
If you feel you need to do that... the statement must be insufficient...

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chieftang: Master | Next Rank: 500 Posts; Posts: 218; Joined: Wed Nov 23, 2011 8:05 pmFollowed by: 4 members; Thanked: 26 times

by chieftang » Fri Dec 09, 2011 7:23 am

rijul007 wrote:NEVER use an info of one statement as an assumption in the other...
If you feel you need to do that... the statement must be insufficient...

I know not to carry an assumption over, but what out the specific case above? If you can solve the equation in (2), then doesn't that solution have to work also for (1) in order to not have a conflict?

Valid or Invalid strategy?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Dec 09, 2011 7:56 am

chieftang wrote:
rijul007 wrote:NEVER use an info of one statement as an assumption in the other...
If you feel you need to do that... the statement must be insufficient...
I know not to carry an assumption over, but what out the specific case above? If you can solve the equation in (2), then doesn't that solution have to work also for (1) in order to not have a conflict?

Valid or Invalid strategy?

The two statements can NEVER contradict each other.
If x=3 works in statement 2, then x=3 MUST also work in statement 1.
But x=3 might not be the ONLY solution in statement 1, in which case statement 1 will be INSUFFICIENT.

To illustrate:

What is the value of x?

1. xÂ²-x = 6.
2. 5x-3 = 12.

Statement 2 has one solution: x=3.
SUFFICIENT.

If we plug x=3 into statement 1, we get:
3Â³-3=6.
6=6.
Looks good.
But x=3 is not the ONLY solution in statement 1.
x=-2 also works:
(-2)Â²-(-2)=6
6=6.
Since x=3 is not the ONLY solution in statement 1, statement 1 is INSUFFICIENT, and the correct answer here is B.

There are times, however, when the solution for one statement can help you to PROVE that the other statement also is sufficient.
Check my solutions for the following DS problems:

https://www.beatthegmat.com/the-average- ... 70430.html
https://www.beatthegmat.com/help-me-t15749.html

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Fri Dec 09, 2011 8:07 am

chieftang wrote:
rijul007 wrote:NEVER use an info of one statement as an assumption in the other...
If you feel you need to do that... the statement must be insufficient...
I know not to carry an assumption over, but what out the specific case above? If you can solve the equation in (2), then doesn't that solution have to work also for (1) in order to not have a conflict?

Valid or Invalid strategy?

When you get a question to find a value
its not your job to check wheter a value "works" for a statement
all you should be worried about is whether you can find a value from the given statement
if you cannot.. the statement is insufficient...

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chieftang: Master | Next Rank: 500 Posts; Posts: 218; Joined: Wed Nov 23, 2011 8:05 pmFollowed by: 4 members; Thanked: 26 times

by chieftang » Fri Dec 09, 2011 9:58 am

GMATGuruNY wrote:
chieftang wrote:
rijul007 wrote:NEVER use an info of one statement as an assumption in the other...
If you feel you need to do that... the statement must be insufficient...
I know not to carry an assumption over, but what out the specific case above? If you can solve the equation in (2), then doesn't that solution have to work also for (1) in order to not have a conflict?

Valid or Invalid strategy?
The two statements can NEVER contradict each other.
If x=3 works in statement 2, then x=3 MUST also work in statement 1.
But x=3 might not be the ONLY solution in statement 1, in which case statement 1 will be INSUFFICIENT.

To illustrate:

What is the value of x?

1. xÂ²-x = 6.
2. 5x-3 = 12.

Statement 2 has one solution: x=3.
SUFFICIENT.

If we plug x=3 into statement 1, we get:
3Â³-3=6.
6=6.
Looks good.
But x=3 is not the ONLY solution in statement 1.
x=-2 also works:
(-2)Â²-(-2)=6
6=6.
Since x=3 is not the ONLY solution in statement 1, statement 1 is INSUFFICIENT, and the correct answer here is B.

There are times, however, when the solution for one statement can help you to PROVE that the other statement also is sufficient.
Check my solutions for the following DS problems:

https://www.beatthegmat.com/the-average- ... 70430.html
https://www.beatthegmat.com/help-me-t15749.html

OK, totally agree. My strategy would be to plug x=3 into statement 1, and if it doesn't work, then I would immediately call statement 1 INSUFFICIENT. If it did work, then I can't draw any conclusion.

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chieftang: Master | Next Rank: 500 Posts; Posts: 218; Joined: Wed Nov 23, 2011 8:05 pmFollowed by: 4 members; Thanked: 26 times

by chieftang » Fri Dec 09, 2011 10:01 am

rijul007 wrote:
chieftang wrote:
rijul007 wrote:NEVER use an info of one statement as an assumption in the other...
If you feel you need to do that... the statement must be insufficient...
I know not to carry an assumption over, but what out the specific case above? If you can solve the equation in (2), then doesn't that solution have to work also for (1) in order to not have a conflict?

Valid or Invalid strategy?

When you get a question to find a value
its not your job to check wheter a value "works" for a statement
all you should be worried about is whether you can find a value from the given statement
if you cannot.. the statement is insufficient...

Hmm, I don't think you're following me.

My point is this. Sometimes one statement is very easy to solve and get a value. When possible, you can do this to find sufficiency for THAT statement, and also use that value to TEST FOR sufficiency in other statement. If that value doesn't work in the other statement, then there is an immediate conclusion to be drawn due to the conflict created.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Dec 09, 2011 10:08 am

chieftang wrote:
GMATGuruNY wrote:
chieftang wrote:
rijul007 wrote:NEVER use an info of one statement as an assumption in the other...
If you feel you need to do that... the statement must be insufficient...
I know not to carry an assumption over, but what out the specific case above? If you can solve the equation in (2), then doesn't that solution have to work also for (1) in order to not have a conflict?

Valid or Invalid strategy?
The two statements can NEVER contradict each other.
If x=3 works in statement 2, then x=3 MUST also work in statement 1.
But x=3 might not be the ONLY solution in statement 1, in which case statement 1 will be INSUFFICIENT.

To illustrate:

What is the value of x?

1. xÂ²-x = 6.
2. 5x-3 = 12.

Statement 2 has one solution: x=3.
SUFFICIENT.

If we plug x=3 into statement 1, we get:
3Â³-3=6.
6=6.
Looks good.
But x=3 is not the ONLY solution in statement 1.
x=-2 also works:
(-2)Â²-(-2)=6
6=6.
Since x=3 is not the ONLY solution in statement 1, statement 1 is INSUFFICIENT, and the correct answer here is B.

There are times, however, when the solution for one statement can help you to PROVE that the other statement also is sufficient.
Check my solutions for the following DS problems:

https://www.beatthegmat.com/the-average- ... 70430.html
https://www.beatthegmat.com/help-me-t15749.html
OK, totally agree. My strategy would be to plug x=3 into statement 1, and if it doesn't work, then I would immediately call statement 1 INSUFFICIENT. If it did work, then I can't draw any conclusion.

If you have deemed statement 2 sufficient, but your solution for statement 2 does not work in statement 1, then you should check your work for statement 2.
Perhaps you made an error or overlooked another possible solution in your work for statement 2.
If statement 2 is indeed sufficient -- if it has only one solution -- then that solution MUST satisfy statement 1.

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chieftang: Master | Next Rank: 500 Posts; Posts: 218; Joined: Wed Nov 23, 2011 8:05 pmFollowed by: 4 members; Thanked: 26 times

by chieftang » Fri Dec 09, 2011 11:28 am

GMATGuruNY wrote: If you have deemed statement 2 sufficient, but your solution for statement 2 does not work in statement 1, then you should check your work for statement 2.
Perhaps you made an error or overlooked another possible solution in your work for statement 2.
If statement 2 is indeed sufficient -- if it has only one solution -- then that solution MUST satisfy statement 1.

Exactly. This is what I want to clarify. This can be a useful approach every now and again.

Thanks!

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