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If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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29 Apr 2016, 02:36
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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29 Apr 2016, 02:46
Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Hi, In MODULUS, always be careful of EQUATING two sides.. Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE.. A and B are eliminated.. Now try to substitute remaining choices C. 1 x^2 − 12 = x.. 1^212=1.. 11=1.. NO D. 2 x^2 − 12 = x.. 2^212=2.. 7=2.. NO E. 3 x^2 − 12 = x.. 3^212=3.. 3=3.. YES ans E
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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29 Apr 2016, 12:14
well, a mod here indicates that x is positive. Eliminate a and b immediately. Now, you may substitute values themselves..none of them except E fits the bill.




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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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29 Apr 2016, 03:01
Another easy way and timesaver will be to substitute the values directly in the equation. so A: (4)^212=4 ne 4 => FALSE B: (3)^212=3 ne 3 => FALSE C: (1)^212=11 ne 1 => FALSE D: (2)^212=8 ne 2=> FALSE E: (3)^212=3 eq 3 => TRUE
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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29 Apr 2016, 12:52
Sindbad wrote: Another easy way and timesaver will be to substitute the values directly in the equation. so A: (4)^212=4 ne 4 => FALSE B: (3)^212=3 ne 3 => FALSE C: (1)^212=11 ne 1 => FALSE D: (2)^212=8 ne 2=> FALSE E: (3)^212=3 eq 3 => TRUE Substituting the value works in most of the Problems of GMAT and is a sureshot way... Same opinion , answer will be (E)
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If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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25 Jul 2016, 02:23
Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 \(x^2 − 12 = x\) \(x^2 − 12\)cannot be negative; anything that comes out of mod is always positive so \(x^2 − 12>0\) Out of our options A= 4 B= 3 cannot be the right answer because none of them are greater than 0 Now only Option C=1 or D=2 or E=3 are contenders for right answers. A quick Cursory crude calculation will tell you that E is the right choice \(3^212=3\) \(912=3\) \(3=3\) \(3=3\) ANSWER IS E
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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12 Mar 2018, 05:12
chetan2u wrote: Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Hi, In MODULUS, always be careful of EQUATING two sides.. Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE.. A and B are eliminated.. Now try to substitute remaining choices C. 1 x^2 − 12 = x.. 1^212=1.. 11=1.. NO D. 2 x^2 − 12 = x.. 2^212=2.. 7=2.. NO E. 3 x^2 − 12 = x.. 3^212=3.. 3=3.. YES ans E Hi chetan2u, Though I know the substitution method, but instinctively I went to solve the the equations given. Can you help me how it can be done with critical value method. I am stuck up.
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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12 Mar 2018, 10:36
Abhishek009 wrote: Sindbad wrote: Another easy way and timesaver will be to substitute the values directly in the equation. so A: (4)^212=4 ne 4 => FALSE B: (3)^212=3 ne 3 => FALSE C: (1)^212=11 ne 1 => FALSE D: (2)^212=8 ne 2=> FALSE E: (3)^212=3 eq 3 => TRUE Substituting the value works in most of the Problems of GMAT and is a sureshot way... Same opinion , answer will be (E)Can you tell me the algebraic way? I am stuck up a bit. QZ
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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13 Mar 2018, 16:57
Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Since we see that the left side of the equation must be positive, the right side also must be positive. Thus, A and B cannot be correct since the absolute value of any quantity can’t be negative. Let’s substitute in the remaining answer choices: 1^2  12  = 1 ? We see this is not true. 2^2  12 = 2 ? We see this is not true 3^3  12 = 3 ? We see this is true. Answer: E
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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13 Mar 2018, 18:01
QZ wrote: Abhishek009 wrote: Sindbad wrote: Another easy way and timesaver will be to substitute the values directly in the equation. so A: (4)^212=4 ne 4 => FALSE B: (3)^212=3 ne 3 => FALSE C: (1)^212=11 ne 1 => FALSE D: (2)^212=8 ne 2=> FALSE E: (3)^212=3 eq 3 => TRUE Substituting the value works in most of the Problems of GMAT and is a sureshot way... Same opinion , answer will be (E)Can you tell me the algebraic way? I am stuck up a bit. QZ I'll help. First of all, x is the outcome of an absolute value so x=>0 Then we have to analyze the two possible scenarios of what we have inside the absolute value so that we can eliminate the absolute value: 1. X^212=>0, x^2=>12 So that x=<sqrt(12) or x=>sqrt(12) The only possible scenario according to the constraint that x can take any non negative value is the second one so we can say that x has to be greater than or equal to approximately 3.4 Then we would have the quadratic equation x^2x12=0 with roots x=3 or x=4 we eliminate the first one because x can not take negative values. 2. X^212<0, x^2<12 So that sqrt(12)<x<sqrt(12) Then according to the initial constraint 0<x<3.4 Then we would have the quadratic equation x^2+x12=0 with roots x=3 or x=4 We eliminate the second one because x can not take negative values. So from the first scenario x=4 and from the second one x=3, those are the two solutions for the absolute value equation. I hope it is clear. Regards César Orihuela Posted from my mobile device



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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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20 Mar 2018, 22:05
Thanks Cesar to clarify. Posted from my mobile device
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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28 Apr 2018, 00:08
Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 The algebraic way:
x^2 − 12 = x
Case 1:
x^2  12 = x
x^2  x = 12
x (x  1) = 12
We need two consecutive numbers whose products is 12.
So 4(41) = 12
4*3 = 12
But we don't have "4" in the answer choices.
Case 2:
x^2  12 = x
x^2 + x = 12
x (x + 1) = 12
We need two consecutive numbers whose products is 12.
3 (3 + 1) = 12
3*4 = 12
12 = 12
So x = 3
(E)
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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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23 May 2018, 20:13
chetan2u wrote: Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Hi, In MODULUS, always be careful of EQUATING two sides.. Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE.. A and B are eliminated.. Now try to substitute remaining choices C. 1 x^2 − 12 = x.. 1^212=1.. 11=1.. NO D. 2 x^2 − 12 = x.. 2^212=2.. 7=2.. NO E. 3 x^2 − 12 = x.. 3^212=3.. 3=3.. YES ans E Hello, is there any algebraic way to solve this? can u plz explain Posted from my mobile device



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Re: If x^2 − 12 = x, which of the following could be the value of x? [#permalink]
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23 May 2018, 20:45
AvinashT2303 wrote: chetan2u wrote: Bunuel wrote: If x^2 − 12 = x, which of the following could be the value of x?
A. –4 B. –3 C. 1 D. 2 E. 3 Hi, In MODULUS, always be careful of EQUATING two sides.. Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE.. A and B are eliminated.. Now try to substitute remaining choices C. 1 x^2 − 12 = x.. 1^212=1.. 11=1.. NO D. 2 x^2 − 12 = x.. 2^212=2.. 7=2.. NO E. 3 x^2 − 12 = x.. 3^212=3.. 3=3.. YES ans E Hello, is there any algebraic way to solve this? can u plz explain Posted from my mobile deviceHERE IT IS: https://gmatclub.com/forum/ifx212x ... l#p2052961Please read the complete thread before raising queries. Hope this helps. QZ
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Re: If x^2 − 12 = x, which of the following could be the value of x?
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