from question we can we can say that x^2 = 1;
so answer should be d.
Exponents: Is it true that x > 0 ?
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Source: Beat The GMAT — Data Sufficiency |
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nikhilagrawal
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dnairo1981
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Here's what I have
C
1) x = x^2-2
or.... 0 = x^2-x-2
0 = (x-2) (x-1)
x = 2 or x = -1 ........Not Suff.
2) 2x<X^5
0<x^5-2X
0<(x) (X^4 - 2)
0<x
2<X^4..........Not Suff.
C) Since 2<X^4..........
Only 2^4>0....................Suff.
(-1)^4 < 0
Please correct me if I'm wrong on this...
C
1) x = x^2-2
or.... 0 = x^2-x-2
0 = (x-2) (x-1)
x = 2 or x = -1 ........Not Suff.
2) 2x<X^5
0<x^5-2X
0<(x) (X^4 - 2)
0<x
2<X^4..........Not Suff.
C) Since 2<X^4..........
Only 2^4>0....................Suff.
(-1)^4 < 0
Please correct me if I'm wrong on this...
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dnairo1981
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For Prob. 1
1) x = x^2-2
or.... 0 = x^2-x-2
0 = (x-2) (x-1)
x = 2 or x = -1 ........Not Suff.
I meant 0 = (x-2) (x+1)....Not 0 = (x-2) (x-1)
1) x = x^2-2
or.... 0 = x^2-x-2
0 = (x-2) (x-1)
x = 2 or x = -1 ........Not Suff.
I meant 0 = (x-2) (x+1)....Not 0 = (x-2) (x-1)
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gmattester
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parallel_chase
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The answer should be D.
x^n=x^n * x^2
x^2 = 1
x = +1 or -1
Statement I
x=x^2 - 2
if x =-1
x = -1
if x=1
x=-1
Sufficient.
Statement II
2x < x^5
if x =-1
-2 < -1
if x=1
2<1 which is not possible.
Therefore x=-1
Sufficient.
Hence D is the answer
x^n=x^n * x^2
x^2 = 1
x = +1 or -1
Statement I
x=x^2 - 2
if x =-1
x = -1
if x=1
x=-1
Sufficient.
Statement II
2x < x^5
if x =-1
-2 < -1
if x=1
2<1 which is not possible.
Therefore x=-1
Sufficient.
Hence D is the answer
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II
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OA is D.
This is testing your knowledge of exponents ... and how well you know your exponent rules.
Remember the rule for exponents:
An exponent expression with a base of 0 will always yield 0, regardless of the exponent
And exponent expression with a base of 1 will always yield 1, regardless of the exponent.
So if you are told that x^6 = x^7 = x^15, so x must be 0 or 1.
If you are told x^6 = x^8 = x^10, x could be 0, 1, or -1 (note even exponents here)
Lets take a look at the Q-stem:
x^n = x^n+2
What is this telling us.
This is telling ust that x could be 0, 1, or -1.
0^n will always = 0^n+2
1^n will always = 1^n+2
(-1)^n will always = (-1)^n+2 (Note: if n is even, then n+2 is also even. If n is odd, then n+2 is also odd.)
So from the Q-stem we know that the possible values of x are 0, 1, -1.
(1) x = x^2 - 2
=> 0 = x^2 + x - 2
=> 0 = (x+1)(x-2)
So x = -1 or x = 2.
We know from Q-stem that x could be 0, 1, or -1.
x = 2 is not in this list. Only -1 is. so (1) is SUFF.
(2) 2x < x^5
We use the possible values for x from q-stem (0, 1, -1) and plug them into this inequality, to see which will make this inequality true.
Lets try -1:
2(-1) < (-1)^5
-2 < -1
this is true so x could be -1
Lets try 0:
2(0) < (0)^5
0 < 0
this is NOT true, so x cannot be 0
Lets try 1:
2(1) < 1^5
2 < 1
this is NOT true, so x cannot be 1.
Only poss value of x is -1. So (2) is SUFF.
Hence answer D.
I think if you remember the exponent rules ... then it sets you off on the right foundation in answering this question.
I was really interested in finding out alternative ways in solving this question. Did anyone use a different approach in solving this ?
Thanks.
This is testing your knowledge of exponents ... and how well you know your exponent rules.
Remember the rule for exponents:
An exponent expression with a base of 0 will always yield 0, regardless of the exponent
And exponent expression with a base of 1 will always yield 1, regardless of the exponent.
So if you are told that x^6 = x^7 = x^15, so x must be 0 or 1.
If you are told x^6 = x^8 = x^10, x could be 0, 1, or -1 (note even exponents here)
Lets take a look at the Q-stem:
x^n = x^n+2
What is this telling us.
This is telling ust that x could be 0, 1, or -1.
0^n will always = 0^n+2
1^n will always = 1^n+2
(-1)^n will always = (-1)^n+2 (Note: if n is even, then n+2 is also even. If n is odd, then n+2 is also odd.)
So from the Q-stem we know that the possible values of x are 0, 1, -1.
(1) x = x^2 - 2
=> 0 = x^2 + x - 2
=> 0 = (x+1)(x-2)
So x = -1 or x = 2.
We know from Q-stem that x could be 0, 1, or -1.
x = 2 is not in this list. Only -1 is. so (1) is SUFF.
(2) 2x < x^5
We use the possible values for x from q-stem (0, 1, -1) and plug them into this inequality, to see which will make this inequality true.
Lets try -1:
2(-1) < (-1)^5
-2 < -1
this is true so x could be -1
Lets try 0:
2(0) < (0)^5
0 < 0
this is NOT true, so x cannot be 0
Lets try 1:
2(1) < 1^5
2 < 1
this is NOT true, so x cannot be 1.
Only poss value of x is -1. So (2) is SUFF.
Hence answer D.
I think if you remember the exponent rules ... then it sets you off on the right foundation in answering this question.
I was really interested in finding out alternative ways in solving this question. Did anyone use a different approach in solving this ?
Thanks.
-
II
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Good question.pepeprepa wrote:Are you sure for this one ? "0^n will always = 0^n+2"
if n=0 0^0=1 and 0^2=0
My understanding is that ... Where x is not equal to 0. x^0 will always be 1. E.g. 6^0 = 1
However ... putting aside exponent rules for one minute ... lets consider what 0^0. The base here is 0 ... this mean there is nothing there in the first place ... so how can we get 1 from 0 !
Maybe someone else has a better explanation on this point.
Thanks.
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II
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yes ... I think sometimes you have to take a step back from all the math rules and apply some common sense to these types of items.pepeprepa wrote:You are right 0^0 does not exist.. I have vague remembers that we used it during our classes, perhaps kind of tips for some situations, but we cannot state that 0^0 that's WRONG.
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pepeprepa
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It is a convention, I don't think you can see it with good sens. You can consider it in some context/formula (so it can be logical) but you cannot state it in some other contexts... You need to know when you can use it, for gmat it is useless.
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Ian Stewart
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0^0 is normally considered 'undefined', in the same way that 6/0 or sqrt(-5) are undefined. There is no common sense way to arrive at a definition- if x is not zero, x^0 is always equal to 1, while 0^x is always equal to 0, so what 'common sense' answer could we have for 0^0 ?
That said, some mathematicians prefer to define 0^0 as being equal to 1. On the GMAT, I've never seen a question that required you to know these technicalities, and as you'll notice with the question above, it doesn't matter whether you include zero or not- you get the same answer either way.
That said, some mathematicians prefer to define 0^0 as being equal to 1. On the GMAT, I've never seen a question that required you to know these technicalities, and as you'll notice with the question above, it doesn't matter whether you include zero or not- you get the same answer either way.
