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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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02 Sep 2015, 00:43
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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
Ans: C
Solution: 1) Option one does not give us any answer if we put the relation x<k into the given equation [Not sufficient]
2) putting x= 3-k we get a quardatic equation which look likes this (3-k)(3-2k)=k+1 After solving it we get k=4,1
Now by putting these two values we get 2 different values of x for each value of k When k= 4 x=5 , -1 and when k= 1 x= 2. ,-1. [Not Sufficient]
By combining both statements we get the value of x =-1 So both statement together are 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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02 Sep 2015, 03:29
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.
Statement one is insufficient as we get more than one value of x.
Statement 2 : substituting x = 3 - k in the equation given in the question. We get k = 1 and k = 4. However, on substitution in x = 3 - k we get two values of x 2 and -1. So insufficient.
When we combine both the statements the only value of x is 2.
So C
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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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Updated on: 15 Apr 2018, 21:07
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
The original condition can be modified as follows. x(x-k) = k+1 ⇔ x^2 - xk = k + 1 ⇔ x^2 - xk - k - 1 = 0 ⇔ x^2 -k(x+1) - 1 = 0 ⇔ (x+1)(x-1) -k(x+1) = 0 ⇔ (x+1)(x-k-1) = 0
Since we have 2 variable (x and y) and 1 equation, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1) Since x < k, x - k - 1 ≠ 0. Thus we have x = -1. Condition 1) is sufficient.
Condition 2) We have two solutions. x = -1, k = 4 x = 2, k = 1 Thus condition 2) is not sufficient.
Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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05 Sep 2015, 12:17
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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.
We know equal number of variables and equations ensures a solution.So I am gonna start to find the value of x from the equation of Statement (2) and x(x+k)=k+1 first Since inequalities of Statement (1)gives no solution
Statement (2) : x=3-k,or k=3-x,now put the value of k to x(x-k)=k+1 as below,
Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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09 Sep 2015, 05:08
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AbdurRakib wrote:
We know equal number of variables and equations ensures a solution.
The statement is red is not 100% correct.
Consider the case:
a+2b = 10 and 2b+4b = 30
You have 2 equations and 2 equations and thus per your statement you should be able to solve for 'a' and 'b'. This is NOT true. You can not solve this system of equations as both the equations are essentially the same wrt the variables involved.
Instead the correct statement should read: We know equal number of variables and DISTINCT equations ensures a solution
Re: If k is an integer and x(x – k) = k + 1, what is the value of x?
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17 Jul 2016, 08:39
Celestial09 wrote:
abhimahna wrote:
Celestial09 wrote:
Hi! I too picked C.
bunuel , chetan4u, empowergmat richi, magoosh mike, veritas.. plz help us on this 1) correct answer and method 2) why answer c is wrong
thanks
I think the explanation as previously stated is the correct explanation for A.
x(x-k)=K+1 => x^2-xk=k+1 => x^2-1=k(x+1)
or (x-1)(x+1)=k(x+1)
you cannot cancel x+1 on both sides directly.
Either we have k=(x-1) or x+1=0 => either x=k+1 or x=-1
Statement 1 says x<k => x <> k+1, thus x=-1, Hence it is sufficient.
Statement 2 says x=3-k => x+k=3. We cannot find out x here, as we don't know the value of K. Hence 2 is insufficient.
Thus, the answer is A.
-- Hit Kudos if you get the answer.
Why can I cancel x+1 on both sides? thanks
This is a trap that many of us get into. Isn't it possible that both sides of the equation are equal just because x was equal to -1, thus making 0 on both the sides.
Always remember, One should NEVER Cancel any common variables unless you are 100% sure about the actual value of that variable.
Let's say if we had 2 common on both sides, then we could have cancelled it as we know that it is NON ZERO Value. But we are not sure what the value of x is, Hence cancellation is NOT ALLOWED.
Hope that helps.
-- Hit Kudos if you get the answer.
_________________
If k is an integer and x(x – k) = k + 1, what is the value of x?
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17 Jul 2016, 08:42
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Celestial09 wrote:
abhimahna wrote:
Celestial09 wrote:
Hi! I too picked C.
bunuel , chetan4u, empowergmat richi, magoosh mike, veritas.. plz help us on this 1) correct answer and method 2) why answer c is wrong
thanks
I think the explanation as previously stated is the correct explanation for A.
x(x-k)=K+1 => x^2-xk=k+1 => x^2-1=k(x+1)
or (x-1)(x+1)=k(x+1)
you cannot cancel x+1 on both sides directly.
Either we have k=(x-1) or x+1=0 => either x=k+1 or x=-1
Statement 1 says x<k => x <> k+1, thus x=-1, Hence it is sufficient.
Statement 2 says x=3-k => x+k=3. We cannot find out x here, as we don't know the value of K. Hence 2 is insufficient.
Thus, the answer is A.
-- Hit Kudos if you get the answer.
Why can I cancel x+1 on both sides? thanks
Because x + 1 can be 0 and we cannot divide by 0.
Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.
Never multiply (or reduce) inequality by variable (or expression with variable) if you don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero. _________________
If k is an integer and x(x – k) = k + 1, what is the value of x?
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17 Jul 2016, 09:11
Celestial09 wrote:
abhimahna wrote:
Celestial09 wrote:
Hi! I too picked C.
bunuel , chetan4u, empowergmat richi, magoosh mike, veritas.. plz help us on this 1) correct answer and method 2) why answer c is wrong
thanks
I think the explanation as previously stated is the correct explanation for A.
x(x-k)=K+1 => x^2-xk=k+1 => x^2-1=k(x+1)
or (x-1)(x+1)=k(x+1)
you cannot cancel x+1 on both sides directly.
Either we have k=(x-1) or x+1=0 => either x=k+1 or x=-1
Statement 1 says x x <> k+1, thus x=-1, Hence it is sufficient.
Statement 2 says x=3-k => x+k=3. We cannot find out x here, as we don't know the value of K. Hence 2 is insufficient.
Thus, the answer is A.
-- Hit Kudos if you get the answer.
Why can I cancel x+1 on both sides? thanks
Another thing to note here is that the given expression in x is a quadratic one . Hence, you will have 2 solutions. By cancelling x+1 you are assuming that x = -1, thus reducing the number of solutions to 1 Instead of 2.
This is an incorrect assumption to make in DS questions as the stem nowhere mentions whether x= -1 is an acceptable solution or not.
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, 06:22
hsbinfy wrote:
A
1)only x=-1 and k=0 suffice.try all values on +v e and -ve side only k=0 and x=-1 suffice .
2)2 values of k
Statement in red above is not complete. x=1 with k=0 also works in the given expression. The only good way to look at is to factorize the given expression and see which of the 2 possible solutions makes most sense.
gmatclubot
Re: If k is an integer and x(x – k) = k + 1, what is the value of x? &nbs
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18 Jul 2016, 06:22
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18% (02:02) correct 
!!
