DS-Strategy

[dddanny2006]

Assume we have a question and two statements,and statement 2 has substatements such a x=y+1 or x=y.

Now assuming that individually they are sufficient,I want to know what happens when we combine them.

1.xy!=0 ,Is x>y?

(1)4x=3y
(2)x=y+1 or x=y

If combining st 1 with x=y+1 of statement 2 results in a Yes.And combining statement 1 with x=y results in a No(I dont know in this case if its a No).Whats the result of combining St1 and St2?We have a Yes and a No here..Does the answer still remain to be C?

Please explain this scenario.

Thanks

[Brent@GMATPrepNow]

Assume we have a question and two statements,and statement 2 has substatements such a x=y+1 or x=y.

Now assuming that individually they are sufficient,I want to know what happens when we combine them.

If xy ≠ 0, is x > y?

(1)4x = 3y
(2)x = y + 1 or x = y

If combining st 1 with x=y+1 of statement 2 results in a Yes. And combining statement 1 with x=y results in a No(I dont know in this case if its a No).Whats the result of combining St1 and St2?We have a Yes and a No here..Does the answer still remain to be C?

Please explain this scenario.

Thanks

A common occurrence of an "or" statement is a quadratic equation like x² = 9. Here's we're saying that x = 3 or x = -3. This is similar to your second statement.

So, your first statement is NOT SUFFICIENT since we could have x = 3 and y = 4 (in which case x < y), or we could have x = -3 and y = -4 (in which case x > y)

Your second statement is NOT SUFFICIENT since x = y + 1 tells us that x > y, and x = y tells us that x is not greater than y.

When we combine the statements, we don't get two different answers to the target question. When we combine the statements, the pair 4x=3y and x=y+1 tells us that x = -3 and y = -4, in which case x > y. The pair 4x=3y and x=y tells us that x = y = 0. Since we're told that x ≠ 0 and y ≠ 0, we can ELIMINATE the possibility that x = y, which means it is definitely the case that x > y

Answer: C

Cheers,
Brent

[dddanny2006]

Ok Brent.I got your point.Thanks so much,you've been very helpful throughout.

1.So, 4x = 3y and x=y+1 results in a Yes.What about 4x = 3y and x=ycombo?Do we deem it as Invalid or a result-less situation?

2.What if it wasnt given that xy!=0,the answer would be E right?


3.I am attaching an image here,just a general flowchart.I wanted to know,what happens when we have a Yes and a No situation when combining?


4.Was the problem you solved earlier a Yes/No situation?Or was it that x=y and 4x=3y result-less combinations?



Thanks again Brent.

Assume we have a question and two statements,and statement 2 has substatements such a x=y+1 or x=y.

Now assuming that individually they are sufficient,I want to know what happens when we combine them.

If xy ≠ 0, is x > y?

(1)4x = 3y
(2)x = y + 1 or x = y

If combining st 1 with x=y+1 of statement 2 results in a Yes. And combining statement 1 with x=y results in a No(I dont know in this case if its a No).Whats the result of combining St1 and St2?We have a Yes and a No here..Does the answer still remain to be C?

Please explain this scenario.

Thanks

A common occurrence of an "or" statement is a quadratic equation like x² = 9. Here's we're saying that x = 3 or x = -3. This is similar to your second statement.

So, your first statement is NOT SUFFICIENT since we could have x = 3 and y = 4 (in which case x < y), or we could have x = -3 and y = -4 (in which case x > y)

Your second statement is NOT SUFFICIENT since x = y + 1 tells us that x > y, and x = y tells us that x is not greater than y.

When we combine the statements, we don't get two different answers to the target question. When we combine the statements, the pair 4x=3y and x=y+1 tells us that x = -3 and y = -4, in which case x > y. The pair 4x=3y and x=y tells us that x = y = 0. Since we're told that x ≠ 0 and y ≠ 0, we can ELIMINATE the possibility that x = y, which means it is definitely the case that x > y

Answer: C

Cheers,
Brent

[Brent@GMATPrepNow]

Ok Brent.I got your point.Thanks so much,you've been very helpful.

So, 4x = 3y and x=y+1 result in a Yes.What about 4x = 3y and x=ycombo?Do we deem it as Invalid or a result-less situation?

What if it wasnt given that xy!=0,the answer would be E right?

Thanks again Brent.

The 4x = 3y and x=y combo yields the solution x = 0 and y = 0. Since this solution does not satisfy the given condition that xy ≠ 0, we can rule out the 4x = 3y and x = y combo as a possibility. I guess we could say that the 4x = 3y and x=y combo yields an invalid solution (one that does not adhere to the given conditions).

See my full solution here: https://www.beatthegmat.com/brent-rich-c ... tml#702084

Cheers,
Brent

[dddanny2006]

Is there a way to solve x=y and 4x=3y by substitution or other methods?Or just trial and error?I'd prefer if there was a method.Also,please check your inbox Brent.Its nothing related to any question,just something personal.

Ok Brent.I got your point.Thanks so much,you've been very helpful.

So, 4x = 3y and x=y+1 result in a Yes.What about 4x = 3y and x=ycombo?Do we deem it as Invalid or a result-less situation?

What if it wasnt given that xy!=0,the answer would be E right?

Thanks again Brent.

The 4x = 3y and x=y combo yields the solution x = 0 and y = 0. Since this solution does not satisfy the given condition that xy ≠ 0, we can rule out the 4x = 3y and x = y combo as a possibility. I guess we could say that the 4x = 3y and x=y combo yields an invalid solution (one that does not adhere to the given conditions).

See my full solution here: https://www.beatthegmat.com/brent-rich-c ... tml#702084

Cheers,
Brent

[Brent@GMATPrepNow]

Is there a way to solve x=y and 4x=3y by substitution or other methods?

There are 2 main approaches to solving systems of linear equations:
1) substitution
2) elimination

I'm partial to the elimination method (see https://www.beatthegmat.com/mba/2012/02/ ... limination for more on this approach), but students should be good at both techniques.

1) substitution
Take the equation 4x=3y and replace x with y to get 4y = 3y
Subtract 3y from both sides to get y = 0
If y = 0, then x = 0

2) elimination
Take the equation x = y and multiply both sides by 3 to get 3x = 3y
Now take the equation 4x = 3y and subtract the equation 3x = 3y to get x = 0
If x = 0, then y = 0

In this instance, the 2 equations are relatively simple, so the substitution method may be a bit better.

Cheers,
Brent

[dddanny2006]

Thanks Champ.I wish I had the same brains as you,and could cross the 700 barrier.You tutors are so smart,have mastery over all techniques.Does it come naturally or with hardwork & practice

Is there a way to solve x=y and 4x=3y by substitution or other methods?

There are 2 main approaches to solving systems of linear equations:
1) substitution
2) elimination

I'm partial to the elimination method (see https://www.beatthegmat.com/mba/2012/02/ ... limination for more on this approach), but students should be good at both techniques.

1) substitution
Take the equation 4x=3y and replace x with y to get 4y = 3y
Subtract 3y from both sides to get y = 0
If y = 0, then x = 0

2) elimination
Take the equation x = y and multiply both sides by 3 to get 3x = 3y
Now take the equation 4x = 3y and subtract the equation 3x = 3y to get x = 0
If x = 0, then y = 0

In this instance, the 2 equations are relatively simple, so the substitution method may be a bit better.

Cheers,
Brent

[Mathsbuddy]

Assume we have a question and two statements,and statement 2 has substatements such a x=y+1 or x=y.

Now assuming that individually they are sufficient,I want to know what happens when we combine them.

1.xy!=0 ,Is x>y?

(1)4x=3y
(2)x=y+1 or x=y

If combining st 1 with x=y+1 of statement 2 results in a Yes.And combining statement 1 with x=y results in a No(I dont know in this case if its a No).Whats the result of combining St1 and St2?We have a Yes and a No here..Does the answer still remain to be C?

Please explain this scenario.

Thanks

I think that the methods of looking at sufficiency over-complicate this type of question.
Instead, try this:

(1)4x=3y doesn't tell us anything useful or contradictory to (2a), so ignore it in context with (2a).
(2a)x=y+1 tells us that x>y.
(2b)x=y, substituted into (1) can only mean x = y = 0, but this is banned in the question so ignore.

Therefore the only thing remaining is x > y. True.

Does this help?