Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If k is an integer and x(x – k) = k + 1, what is the value of x? [#permalink]

Show Tags

01 Sep 2015, 23:43

1

This post received KUDOS

2

This post was BOOKMARKED

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
_________________

-------------------------------------------------------------------- The Mind is Everything, What we Think we Become. Kudos will encourage many others, like me. Please Give Kudos !! Thanks

Re: If k is an integer and x(x – k) = k + 1, what is the value of x? [#permalink]

Show Tags

02 Sep 2015, 02:29

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
_________________

Kindly support by giving Kudos, if my post helped you!

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

If k is an integer and x(x ? k) = k + 1, what is the value of x?

(1) x < k (2) x = 3 ? k

In the original condition we have 2 variable (x,k) and 1 equation (x(x-k)=k+1) and in order to match the number of variables and equations we need 1 more equation. Since there is 1 each in 1) and 2), D is likely the answer. In case of 1), x<k is not sufficient while in case of 2), substituting x=3-k gives us (3-k)(3-k-k)=k+1, (3-k)(3-2k)=k+1, 2k^2-9k+9=k+1, 2k^2-10k+8=0, k^2-5k+4=0, (k-4)(k-1)=0 k=1,4 therefore it is not unique. thus it is not sufficient. Using both 1) and 2) gives us unique answer k=4, x=-1, and therefore is sufficient.

Re: If k is an integer and x(x – k) = k + 1, what is the value of x? [#permalink]

Show Tags

05 Sep 2015, 11:17

1

This post received KUDOS

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? [#permalink]

Show Tags

09 Sep 2015, 04:08

1

This post received KUDOS

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? [#permalink]

Show Tags

17 Jul 2016, 07:39

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.
_________________

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? [#permalink]

Show Tags

17 Jul 2016, 08:11

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? [#permalink]

Show Tags

18 Jul 2016, 05:22

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.