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TheUltimateWinner
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 Updated on: 22 Apr 2019, 12:15
Originally posted by TheUltimateWinner on 22 Apr 2019, 09:39.
Last edited by TheUltimateWinner on 22 Apr 2019, 12:15, edited 1 time in total.
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Is \(x> 0?\)

(1) \(4^x= \frac{1}{64}\)
(2) \((-4)^x= -64\)

Source: Wizako

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LevanKhukhunashvili
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 22 Apr 2019, 11:34
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I'm confused

1 stm --> \(4^x\)=4^-3, x=-3 suff
2 stm --> \((-4)^x\)=-\(4^3\), x=3

Do the statements contradict each other?
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TheUltimateWinner
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 22 Apr 2019, 12:27
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AsadAbu
Is \(x> 0?\)

(1) \(4^x= \frac{1}{64}\)
(2) \((-4)^x= -64\)

Source: Wizako
Show more
Hi Bunuel and IanStewart
After posting this question I've realized that both statement contradict each other. But, I have a different question here.

====
The question is YES/NO question.
1) No
2) Yes
====
Suppose, both statement give only YES response in this question! (assuming that x=100 in statement 1 and x=1 in statement 2)------> both gives YES response. My question is:
Is it mandatory that x must be same value (like x=100 in both statement or x=1 in both statement)?
Thanks__

Please locked this topic if it does not help the forum member for being wrong headed question.
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 22 Apr 2019, 13:43
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Levan's solution above is perfect. It's a poor quality question though, and you'll never see a question like it on the real GMAT, because the statements contradict each other.

In real GMAT DS questions, the two statements always need to be logically consistent. In other words, it always needs to be possible for both statements to be true at the same time. So to answer this:

AsadAbu

Suppose, both statement give only YES response in this question! (assuming that x=100 in statement 1 and x=1 in statement 2)------> both gives YES response. My question is:
Is it mandatory that x must be same value (like x=100 in both statement or x=1 in both statement)?
Thanks__
Show more

it will always be true that the statements overlap in at least one solution, at a minimum. So you could see a question like this:

Is x > 0?
1. 20 < x < 30
2. 25 < x < 35

where both statements give a 'yes' answer, even though we can't find a single value for x. These statements are fine, because they overlap: using both, x can take any value between 25 and 30. But you could never see a question like this:

Is x > 0?
1. 20 < x < 30
2. 40 < x < 50

because there are no values of x that work for both statements; they are not logically consistent. Similarly, you can never see a question like this:

Is x > 0?
1. x = 1
2. x = 100

because the two statements cannot both be true. The fact that two statements both give a 'yes' answer to a yes/no DS question does not guarantee that the statements are consistent -- they need to overlap in at least one solution for x in order to be consistent.
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 22 Apr 2019, 13:47
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AsadAbu
AsadAbu
Is \(x> 0?\)

(1) \(4^x= \frac{1}{64}\)
(2) \((-4)^x= -64\)

Source: Wizako
Hi Bunuel and IanStewart
After posting this question I've realized that both statement contradict each other. But, I have a different question here.

====
The question is YES/NO question.
1) No
2) Yes
====
Suppose, both statement give only YES response in this question! (assuming that x=100 in statement 1 and x=1 in statement 2)------> both gives YES response. My question is:
Is it mandatory that x must be same value (like x=100 in both statement or x=1 in both statement)?
Thanks__

Please locked this topic if it does not help the forum member for being wrong headed question.
Show more

Yes. On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. You cannot have a case when you have x = -3 from one statement and x = 3 from another.
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 Updated on: 23 Apr 2019, 12:12
Originally posted by TheUltimateWinner on 22 Apr 2019, 15:57.
Last edited by TheUltimateWinner on 23 Apr 2019, 12:12, edited 2 times in total.
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Thanks IanStewart and Bunuel for your kind feedback.
I've still query on this topic.

IanStewart
But you could never see a question like this:
Is x > 0?
1. 20 < x < 30
2. 40 < x < 50

because there are no values of x that work for both statements; they are not logically consistent.
Show more
Why we are so serious to find the overlapping value from both statements? This one is not the value question; this is the yes/no question. So, should not we be stick with answering the question of value question by just either yes or no?
Suppose, there is a question like:
Is Washington DC the capital of United States?
1) yes
2) yes
Isn't this answer (yes) enough to answer this question? Why do we need an overlapping figure to answer this question, at least here?

Again,
Is x > 0?
1) sometimes yes and sometimes NO (e.g, x=100, x=500, and x=-100)
2) sometimes yes and sometimes NO (e.g, x=100, and x=-50)
Now, if we combine (which directly indicates choice C) both statements, then we get definite YES with one overlapping value.
^^ in this question we're going to establish choice C from the color part

Quote:

If x is an integer, Is x > 0?
1. 20 < x < 30
2. 20 < x < 22
Show more
^^ in this question, we're going to find a definite YES with one overlapping value., too
^^ in this question we're going to establish choice D from the color part
With a definite YES with one overlapping value==> Sometimes this bold part indicates choice C and sometimes this bold part indicates choice D.
But why?
Edited: the part that you did not understand IanStewart. Could you explain a bit now. Thanks__
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 23 Apr 2019, 05:52
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AsadAbu

Why we are so serious to find the overlapping value from both statements?
Show more

You asked me a question in your earlier post about how the two statements overlap. I was merely answering your question.

On a real GMAT question, there's no reason to check that the two statements overlap. They will, but it doesn't help you to confirm that. But for DS Strategy reasons, it can sometimes be helpful to understand that the two statements must be consistent. For example, if a question asks "What is x?" and you analyze Statement 1, and you reach the conclusion that "x=3", and then you analyze Statement 2 and reach the conclusion that "x=4", the answer probably is not D. You've definitely done something wrong, because you haven't found a single solution that works for both statements. You'd want to check your work. And there are other strategy implications, but we discussed those in detail the last time this issue came up, so I won't go over them again.

One other reason it can be helpful to understand that the two statements in DS must be consistent: it gives you a very easy way to recognize low-quality prep materials. I don't know where the question in the OP above is from, but if they don't even understand that DS statements need to be consistent, that would give me very little confidence that they know enough about the test to design worthwhile practice materials. So if you notice a prep company has designed questions with inconsistent statements, you should just throw that material away and move on to better resources.

And I don't understand what you mean by this:

AsadAbu

Quote:
Is x > 0?
1. 20 < x < 30
2. 40 < x < 50
^^ in this question, we're going to find a definite YES with one overlapping value., too
^^ in this question we're going to establish choice D from the color part
With a definite YES with one overlapping value==> Sometimes this bold part indicates choice C and sometimes this bold part indicates choice D.
But why?
Show more

In this question, there is no overlapping value; there is no value x can have if you use both statements together. So this question could never appear on the GMAT, because the statements contradict each other. And there's no reason to even discuss what the 'right' answer is to this question, because it's a badly-designed question that doesn't make logical sense if you elect to combine the statements.
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 24 Apr 2019, 12:32
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AsadAbu
Thanks IanStewart and Bunuel for your kind feedback.
I've still query on this topic.

IanStewart
But you could never see a question like this:
Is x > 0?
1. 20 < x < 30
2. 40 < x < 50

because there are no values of x that work for both statements; they are not logically consistent.
Why we are so serious to find the overlapping value from both statements? This one is not the value question; this is the yes/no question. So, should not we be stick with answering the question of value question by just either yes or no?
Suppose, there is a question like:
Is Washington DC the capital of United States?
1) yes
2) yes
Isn't this answer (yes) enough to answer this question? Why do we need an overlapping figure to answer this question, at least here?

Again,
Is x > 0?
1) sometimes yes and sometimes NO (e.g, x=100, x=500, and x=-100)
2) sometimes yes and sometimes NO (e.g, x=100, and x=-50)
Now, if we combine (which directly indicates choice C) both statements, then we get definite YES with one overlapping value.
^^ in this question we're going to establish choice C from the color part

Quote:

If x is an integer, Is x > 0?
1. 20 < x < 30
2. 20 < x < 22
^^ in this question, we're going to find a definite YES with one overlapping value., too
^^ in this question we're going to establish choice D from the color part
With a definite YES with one overlapping value==> Sometimes this bold part indicates choice C and sometimes this bold part indicates choice D.
But why?
Edited: the part that you did not understand IanStewart. Could you explain a bit now. Thanks__
Show more
Hi Bunuel and IanStewart,
I've edited the previous post. So, could you take a look the edited version, please?
Thanks__
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Is x> 0? 1) 4^x= 1/64 2) (-4)^x= -64 26 Apr 2019, 06:17
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AsadAbu

With a definite YES with one overlapping value==> Sometimes this bold part indicates choice C and sometimes this bold part indicates choice D.
But why?
Show more

Because the number of overlapping solutions is irrelevant until you consider both statements together, and you only need to consider both statements together if neither statement is sufficient alone.

The only point I (and Bunuel) were making is that if you decide to use both statements together, you always will have at least one solution. You can never have zero solutions. But that doesn't mean you should use both statements together. You only do that if you need to, because neither statement is sufficient on its own.

This Question is Locked Due to Poor Quality
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