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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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18 Jul 2016, 20:41
Bunuel wrote: If k is an integer and x(x – k) = k + 1, what is the value of x?
(1) x < k (2) x = 3 – k
Kudos for a correct solution. Given: x(xk) = k + 1 x^2  xk k  1 = 0 x^2  1 k(x+1) = 0 (x1)(x+1)  k (x+1) = 0 (x+1)(x1k) = 0  (i) Hence x =  1 or x = 1+k Required: x = ? Statement 1: x < k From this, we can say that ≠ k+1 Hence x can only take the value 1 SUFFICIENT Statement 2: x = 3k On substituting the value of k in the solutions for the equation, we get 3k =  1 and 3k = 1+k Hence k = 4 and k = 1 INSUFFICIENT Correct Option: A A very good question which can trap you in choosing the option C



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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18 Nov 2016, 08:48
Bunuel wrote: If k is an integer and x(x – k) = k + 1, what is the value of x?
(1) x < k (2) x = 3 – k
Kudos for a correct solution. I picked A... x<k so we have few options: 1) x negative k negative xk = negative > x*(xk) = positive. since k+1 must be positive, k must be either zero, or a noninteger. but since we assumed k is negative, then it doesn't work... 2) x positive k positive xk  negative negative * positive = negative it means that k+1 must be negative, meaning that k must be < 1. but we assumed k is positive. doesn't work... 3) we can't assume x positive and k negative, as we are told that x<k 4. x negative k positive xk  negative multiply by x (negative) = positive k+1 is positive. let's test some values: x=1 k=1 1(11) = 1*2 = 2 = 1+1  works x=2 k=1 2(21) = 6 but k=1. so doesn't work we can test more options, but it will not work unless x=1. A is sufficient. 2. x=3k x(x – k) = k + 1 k=3x x(x3+x) = 3x+1 x(2x3) = 4x 2x^2 3x = 4x 2x^2 2x 4 = 0  divide by 2 x^2 x 2 = 0 (x+1)(x2)=0 x=2; x=1 1st option x=2 x = 3 – k 2=3k k=1 x(x – k) = k + 1 = 2(21) = 1+1 2=2 2nd option: x=1 x = 3 – k 1 = 3k k=4 x(x – k) = k + 1 = 2(21) = 1+1 1(14) = 4+1 = 5=5 works 2 outcomes for x  not sufficient. answer is A.



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If k is an integer and x(x – k) = k + 1, what is the value of x?
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18 Nov 2016, 09:11
Bunuel wrote: If k is an integer and x(x – k) = k + 1, what is the value of x?
(1) x < k (2) x = 3 – k
Kudos for a correct solution. From statement 1> x(xk) = k+1 => x^2xkk1 = 0 => x = (k+(k^2+4k+2^2)^1/2)/2 or x = (k (k^2+4k+2^2)^1/2)/2 Since, k^2+4k+2^2 = (k+2)^2 By solving this we get either x= k+1 or x= 1; but x <k, therefore x can't be k+1 Hence, x = 1 => Sufficient From statement 2 > we can solve quadratic for k and get values 2 values for x and k each. Therefore it is insufficient Therefore, answer is A



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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18 Nov 2016, 23:42
(x1)*(x+1)k(x+1)=0
(x+1)*(x1k)=0
x+1=0, x=1 OR x1k=0, x=k+1
St.1 says that second scenario is impossible, so x=1
A



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If k is an integer and x(x – k) = k + 1, what is the value of x?
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31 Mar 2017, 23:27
Bunuel wrote: If k is an integer and x(x – k) = k + 1, what is the value of x?
(1) x < k (2) x = 3 – k
Kudos for a correct solution. correct answer is C statement 1: x(xk)=k+1 x^2xk=k+1 x^21=k+xk (x1)(x+1)(x+1)(k)=0 (x+1)[x1k]=0 this means x=1; or x=k+1 not valid since x<k(given) in sufficient as we cannot say anything about k when x=1 statement 2: putting x=3k given 2 values x=1;k=4 x=2;k=1 insufficient taking both together: x=1;k=4 solution therefore answer should be C give kudos if you liked this explanation



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If k is an integer and x(x – k) = k + 1, what is the value of x?
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31 Mar 2017, 23:35
Engr2012 wrote: Swaroopdev wrote: Hi Bunuel, None of the above solutions show A as the answer, is the OA wrong ? If not, could you please explain the solution ? Thanks. I think everyone is missing out on a very important information.Lets analyse the question: Given equation: x(xk) = k+1 > \(x^2kxk1=0\) >\(x = \frac {k\pm \sqrt{k^24(k1)}}{2}\) Thus you get 2 values of x as =\(\frac {k\pm(k+2)}{2}\) > x = k+1 or x=1 Per statement 1, x<k > x \(\neq\)k+1 > x = 1 . Thus this statement IS SUFFICIENTPer statement 2, x = 3k > susbtituting in the above given equation, you get, k = 4 or 1 > x = 1 or 2. Thus this statement is NOT sufficient. A is the correct answer.This question is a classic "CTrap" question. how can we conclude through statement A when x=1 x<k say x=1 and k=2 then also they satisfy the equation and when x=1 k=2 they also satisfy the equation then how can we find the values where k>x always???????? thus answer is C when x=1 k also takes unique value k=4



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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31 Mar 2017, 23:38
OptimusPrepJanielle wrote: Bunuel wrote: If k is an integer and x(x – k) = k + 1, what is the value of x?
(1) x < k (2) x = 3 – k
Kudos for a correct solution. Given: x(xk) = k + 1 x^2  xk k  1 = 0 x^2  1 k(x+1) = 0 (x1)(x+1)  k (x+1) = 0 (x+1)(x1k) = 0  (i) Hence x =  1 or x = 1+k Required: x = ? Statement 1: x < k From this, we can say that ≠ k+1 Hence x can only take the value 1 SUFFICIENT Statement 2: x = 3k On substituting the value of k in the solutions for the equation, we get 3k =  1 and 3k = 1+k Hence k = 4 and k = 1 INSUFFICIENT Correct Option: A A very good question which can trap you in choosing the option C how can we conclude through statement A when x=1 x<k say x=1 and k=2 then also they satisfy the equation and when x=1 k=2 they also satisfy the equation then how can we find the values where k>x always???????? thus answer is C when x=1 k also takes unique value k=4



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If k is an integer and x(x – k) = k + 1, what is the value of x?
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12 Apr 2017, 00:15
Bunuel, I was wondering about Statement 2. Using x = 3k, we could calculate as follows: (3k) (3kk) = k+1 ==> k^2  5k + 4 = 0 ; k= 4, 1 Using K=4 in the original equation x(xk) = k+1; we get: x^2  4x  5 =0 ==> x= 5 , 1 Using K=1 in the original equation x(xk) = k+1; we get: x^2  x  2 = 0 ==> x = 2 , 1 Since 1 is the only solution of x that satisfies both values of k in the original equation, can we not claim that statement 2 is sufficient?



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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12 Apr 2017, 01:13



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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12 Apr 2017, 02:13
Bunuel wrote: dg88074 wrote: Bunuel, I was wondering about Statement 2. Using x = 3k, we could calculate as follows: (3k) (3kk) = k+1 ==> k^2  5k + 4 = 0 ; k= 4, 1 Using K=4 in the original equation x(xk) = k+1; we get: x^2  4x  5 =0 ==> x= 5 , 1 Using K=1 in the original equation x(xk) = k+1; we get: x^2  x  2 = 0 ==> x = 2 , 1 Since 1 is the only solution of x that satisfies both values of k in the original equation, can we not claim that statement 2 is sufficient? We have: x(x – k) = k + 1 and x = 3 – k. k = 1 and x = 2 OR k = 4 and x = 1. Both sets satisfy the given inequalities. Oh it makes sense now. Thanks a lot Bunuel



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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21 Apr 2017, 15:18
Bunuel wrote: If k is an integer and x(x – k) = k + 1, what is the value of x?
(1) x < k (2) x = 3 – k
Kudos for a correct solution. st1: x^2xk=k+1 (x1)(x+1)=K(x+1) x+1= 0 x=1, k=0 x=k+1( irrelevant since we know k>x) st2: x=3k x=2, k=1 or x=1, k=4 (insufficient on its own) answer is A



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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07 Jul 2017, 05:34
smanujahrc wrote: OptimusPrepJanielle wrote: Bunuel wrote: If k is an integer and x(x – k) = k + 1, what is the value of x?
(1) x < k (2) x = 3 – k
Kudos for a correct solution. Given: x(xk) = k + 1 x^2  xk k  1 = 0 x^2  1 k(x+1) = 0 (x1)(x+1)  k (x+1) = 0 (x+1)(x1k) = 0  (i) Hence x =  1 or x = 1+k Required: x = ? Statement 1: x < k From this, we can say that ≠ k+1 Hence x can only take the value 1 SUFFICIENT Statement 2: x = 3k On substituting the value of k in the solutions for the equation, we get 3k =  1 and 3k = 1+k Hence k = 4 and k = 1 INSUFFICIENT Correct Option: A A very good question which can trap you in choosing the option C how can we conclude through statement A when x=1 x<k say x=1 and k=2 then also they satisfy the equation and when x=1 k=2 they also satisfy the equation then how can we find the values where k>x always???????? thus answer is C when x=1 k also takes unique value k=4 You are given that x=1 OR x=1+k, Statement 1 says that x<k, so how can x=1+k be true? x=1+k will ALWAYS make x>k, thus going against the information mentioned in statement 1. Thus, you MUST reject x=1+k, leaving you with x=1 as the only solution from statement 1. Hence this statement is sufficient.



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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16 Dec 2017, 05:20
Finally some sane question. x(xk) = k+1 => x^2  xk = k+1 => X^21  xk  k = 0 => (x1)(x+1)  k(x+1) = 0 => (x+1((x1k)=0 POssible values x=1, or, x=k+1
(1) x<k. Therefore, the only value is x=1. Sufficient (2) x=3k. Checking two possible values of x, x= k+1 => 3k =k+1 => k=1 & x=2. if x=1, => 3k=1, => k=4, x=1. Both values of x are possible. Ambiguous. Insufficient
Hence A



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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10 Apr 2018, 12:38
Hello, everybody!
I think one of quickest ways to solve it is by using a parabola method and Vieta's formulas ( x1*x2 = c/a; x1 + x2 = b/a).
Case 1:
1) So, we found x1*x2 = k1; and x1 + x2 = k.
Meaning, x1 = k +1, x2 = 1.
2) Our parabola has arms up and two possible xintercepts: x = k1; and x = 1.
If (k1) lays to the right of (1), then k1 > 1. So, k <0. And x<k.
Then, only possible solution is x2 = 1 (because whenever you add 1 to a negative number  it will become bigger, not smaller than it was; meaning x1 does not match the case). Sufficient.
If (k1) lays to the left of (1), then k1 < 1. So,k >0. And x < k.
Then, the only possible solution is x2 = 1 (becuse whenever you add 1 to a positive number  it will become bigger than it was; meaning x1 does not match the case). Sufficient.
Case 2: x = 3k. After soving the equation: k = 4; k = 1. So, 2 choices for x. Not sufficient.



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Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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07 Nov 2018, 09:16
Hi guys,
Im pretty much new to this forum and I'm trying to practice DS questions. Can someone please tell me how to know which one is the correct answer. As I'm able to see pretty much everyone coming up with their own version of the answer. Please help. Thanks.




Re: If k is an integer and x(x – k) = k + 1, what is the value of x? &nbs
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