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What is the value of x ? 1. x^4 = |x| 2. x^2 \gt xSource: GMAT Club Tests - hardest GMAT questions
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ventivish wrote: What is the value of x ?
1. x^4 = |x|
2. x^2 \gt x 1: x = -1 or 0 or 1. i. if x is +ve, x^4 = x x^4 - x = 0 x (x^3 - 1) = 0 x = 0, and x^3 = 1 or x = 1. ii: if x is -ve, x^4 = -x x^4 + x = 0 x (x^3 + 1) = 0 x = 0, and x^3 = -1 or x = -1. so not suff... 2: x could be anything other than 0 and a +ve fraction. x^2 > x x^2 - x > 0 x (x-1) > 0 if x is a +ve (x-1) is also a +ve. i: x > 0 .......... not possible. ii: x - 1 > 0 x >1 ............... possible. so x > 1. if x is a -ve (x-1) is also a -ve. i: x < 0 .............. possible. ii: x < 1 ............... not possible. so x <0. 1&2: x has to be -1. so C.
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The graphs of y=x^4 and y=|x| 1ntersect each other at three points (-1,1), (0,0) and (1,1), then A is wrong. Any x<0 or x>1 satisfies the inequality x^2>x, then B is wrong.
Both statements together uniquely determine the value x=-1, so C is the answer.
Last edited by nvgroshar on 31 Dec 2009, 15:21, edited 1 time in total.
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ANS:E from both statement we can conclude only x>1 not a single value.
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It should be C. I thought it E though 
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1 is not sufficient - x could be 0 or 1, -1 2 X^2>X which means x(x-1)>0 x>1 or x<0 Combine 1 and 2, x=-1 Answer is C
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When combine both the stmt, we get x = -1, so IMO Ans should be C.
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ventivish wrote: What is the value of x ? 1. x^4 = |x| 2. x^2 \gt xSource: GMAT Club Tests - hardest GMAT questions stmt1L x^4 = x or x^4 = -x x(x^3-1)=0 or x(x^3+1) =0 so x = 0, -1,1 stmt2: x^2 > x => x(x-1)>0 insuff combine both. x <>0 or 1 so x is -1 hence c is the answer
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What is the value of x ?
1. x^4 = |x|
X can equal 1 or -1 or 0 (IS)
2. x^2 > x
x(x-1)>0 (IS)
Both: You can conclude that X is -1 using st.2 to validate it.
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C
From option A, x can be 0 or 1 or -1.
From option B , x can be any negative integer. And it can be any negative fraction value.
Using both we can deduce x value as -1.
Hence the option is c.
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x= -1, excellent explanation were given above.
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I concur with the OA. Stmt 1 tells you it is +1 or -1 Stmt 2 tells you it is an integer Combining the two stmts you can tell that the only possible fit is -1. Therefore, it is C.
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1. Not sufficient
When x is +ve x = 1
When x is -ve x = -1
2. Not sufficient
x<0 or x>1
together we have x = -1. Sufficient.
Answer is C.
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ventivish wrote: What is the value of x ? 1. x^4 = |x| 2. x^2 \gt xSource: GMAT Club Tests - hardest GMAT questions This one is interesting as the answer is different if you do not know that its a GMAT question. From statement 1, on squaring both sides we get x^8 = x^2 or x^2*(x^6-1) = 0so, x = 0 or x^6 = 1. Now x^6 = 1 has six roots and the six sixth roots of unity are ±1, and (±1 ± i√3)/2. My confusion arose because i considered the complex roots as well and hence my initial reaction was that answer is E. I guess on GMAT you can go along with only real roots and in that case, answer is indeed C.
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Answer C (by taking option 1+ 2).
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Bunuel wrote: ventivish wrote: What is the value of x ? 1. x^4 = |x| 2. x^2 \gt xSource: GMAT Club Tests - hardest GMAT questions (1) x^4 = |x|. This statement implies that x=-1, x=0, or x=1. Not sufficient. (2) x^2> x. Rearrange and factor out x to get x(x-1)>0. The roots are x=0 and x=1, " >" sign means that the given inequality holds true for: x<0 and x>1. Not sufficient. (1)+(2) The only value of x from (1) which is in the range from (2) is x=-1. Sufficient. Answer: C. Bunuel/Karishma I dont understand the following: The roots are x=0 and x=1, " >" sign means that the given inequality holds true for: x<0 and x>1. shouldn't x(x-1)>0 mean that x>0 or (x-1)>0 ? Please explain why it means x<0 ?
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