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: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

21 Mar 2011, 23:23

asmit123 wrote:

Is A positive?

1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + 1 is +ve for all x

x^2 - 2x + A >0 x^2-2x +1 +A-1>0 (X-1)^2 -1 >-A A>1-(X-1)^2 (flip the sign) if x is 1/2 A is positive no ... if x is 5 , A>-15 so A could be either positive or negative

2 A x^2 +1>0 Ax^2>-1 A=-1/2 ,x=1 -1/2>-1 true A=1 X=2 4>-1 true.. A could be negative eg (-1/2) or positive ... Insufficient..

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

22 Mar 2011, 02:58

asmit123 wrote:

Is A positive?

1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + 1 is +ve for all x

We need to answer the question "Is A positive?"

Statement 1 says \(x^2 - 2x + A\) is positive for all x. Hence A can only take values that make the expression \(x^2 - 2x + A\) positive for all x.

Now, the term \(x^2-2x\) will be always positive for all x greater than 2. Also, it will always be positive for all x less than zero and it will be zero in case x=0. So for all x greater than or equal to 2 and less than or equal to zero, A can be negative or positive and still the expression can be positive overall depending on magnitude of a and A. So, this does not give us a condition on A.

Lets see when x lies between 0 and 2. In such a case, for both x =0 and x=2, the expression \(x^2-2x\) is zero and hence A needs to be positive. Between x=0 and x=2, the expression remains negative with minimum value of -1 at x=1. Hence, A needs to be greater than +1 to ensure that \(x^2-2x+A\) is greater than zero for all x when x lies between 0 and 2.

So, we have seen that for all x, the expression \(x^2 - 2x + A\) is positive if and only if A is greater than 1 always. Hence we can answer the question "Is A positive?" in affirmative and hence sufficient.

Statement 2 says that \(A*x^2+1\) is always positive for all x. Clearly, \(x^2\) is always positive. So, if A is always positive than \(A*x^2+1\) is always positive. However, \(A*x^2+1\)is always positive also when A=0. Hence, Statement 2) will hold when A is 0 or positive and hence we cannot answer for sure the question "Is A positive?". Hence, insufficient.

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

22 Mar 2011, 19:40

I agree with beyondgmatscore. A has to be positive to satisfy the expression for all values of x.

beyondgmatscore wrote:

asmit123 wrote:

Is A positive?

1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + 1 is +ve for all x

We need to answer the question "Is A positive?"

Statement 1 says \(x^2 - 2x + A\) is positive for all x. Hence A can only take values that make the expression \(x^2 - 2x + A\) positive for all x.

Now, the term \(x^2-2x\) will be always positive for all x greater than 2. Also, it will always be positive for all x less than zero and it will be zero in case x=0. So for all x greater than or equal to 2 and less than or equal to zero, A can be negative or positive and still the expression can be positive overall depending on magnitude of a and A. So, this does not give us a condition on A.

Lets see when x lies between 0 and 2. In such a case, for both x =0 and x=2, the expression \(x^2-2x\) is zero and hence A needs to be positive. Between x=0 and x=2, the expression remains negative with minimum value of -1 at x=1. Hence, A needs to be greater than +1 to ensure that \(x^2-2x+A\) is greater than zero for all x when x lies between 0 and 2.

So, we have seen that for all x, the expression \(x^2 - 2x + A\) is positive if and only if A is greater than 1 always. Hence we can answer the question "Is A positive?" in affirmative and hence sufficient.

Statement 2 says that \(A*x^2+1\) is always positive for all x. Clearly, \(x^2\) is always positive. So, if A is always positive than \(A*x^2+1\) is always positive. However, \(A*x^2+1\)is always positive also when A=0. Hence, Statement 2) will hold when A is 0 or positive and hence we cannot answer for sure the question "Is A positive?". Hence, insufficient.

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

22 Mar 2011, 20:30

beyondgmatscore wrote:

asmit123 wrote:

Is A positive?

1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + 1 is +ve for all x

We need to answer the question "Is A positive?"

Statement 1 says \(x^2 - 2x + A\) is positive for all x. Hence A can only take values that make the expression \(x^2 - 2x + A\) positive for all x.

Now, the term \(x^2-2x\) will be always positive for all x greater than 2. Also, it will always be positive for all x less than zero and it will be zero in case x=0. So for all x greater than or equal to 2 and less than or equal to zero, A can be negative or positive and still the expression can be positive overall depending on magnitude of a and A. So, this does not give us a condition on A.

Lets see when x lies between 0 and 2. In such a case, for both x =0 and x=2, the expression \(x^2-2x\) is zero and hence A needs to be positive. Between x=0 and x=2, the expression remains negative with minimum value of -1 at x=1. Hence, A needs to be greater than +1 to ensure that \(x^2-2x+A\) is greater than zero for all x when x lies between 0 and 2.

So, we have seen that for all x, the expression \(x^2 - 2x + A\) is positive if and only if A is greater than 1 always. Hence we can answer the question "Is A positive?" in affirmative and hence sufficient.

Statement 2 says that \(A*x^2+1\) is always positive for all x. Clearly, \(x^2\) is always positive. So, if A is always positive than \(A*x^2+1\) is always positive. However, \(A*x^2+1\)is always positive also when A=0. Hence, Statement 2) will hold when A is 0 or positive and hence we cannot answer for sure the question "Is A positive?". Hence, insufficient.

Answer is A.

Assume x =5 x^2 - 2x=> 25-10 =15 for x^2 - 2x + A to be positive A can be either positive no or negative no if A= -1 (Statement A is still valid x^2 - 2x + A>0) if A=1 (Statement A is still valid x^2 - 2x + A>0) A can be either positive no or negative no ..So How could you say A>0 ....Am I missing something ?

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

22 Mar 2011, 22:34

Onell wrote:

beyondgmatscore wrote:

asmit123 wrote:

Is A positive?

1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + 1 is +ve for all x

We need to answer the question "Is A positive?"

Statement 1 says \(x^2 - 2x + A\) is positive for all x. Hence A can only take values that make the expression \(x^2 - 2x + A\) positive for all x.

Now, the term \(x^2-2x\) will be always positive for all x greater than 2. Also, it will always be positive for all x less than zero and it will be zero in case x=0. So for all x greater than or equal to 2 and less than or equal to zero, A can be negative or positive and still the expression can be positive overall depending on magnitude of a and A. So, this does not give us a condition on A.

Lets see when x lies between 0 and 2. In such a case, for both x =0 and x=2, the expression \(x^2-2x\) is zero and hence A needs to be positive. Between x=0 and x=2, the expression remains negative with minimum value of -1 at x=1. Hence, A needs to be greater than +1 to ensure that \(x^2-2x+A\) is greater than zero for all x when x lies between 0 and 2.

So, we have seen that for all x, the expression \(x^2 - 2x + A\) is positive if and only if A is greater than 1 always. Hence we can answer the question "Is A positive?" in affirmative and hence sufficient.

Statement 2 says that \(A*x^2+1\) is always positive for all x. Clearly, \(x^2\) is always positive. So, if A is always positive than \(A*x^2+1\) is always positive. However, \(A*x^2+1\)is always positive also when A=0. Hence, Statement 2) will hold when A is 0 or positive and hence we cannot answer for sure the question "Is A positive?". Hence, insufficient.

Answer is A.

Assume x =5 x^2 - 2x=> 25-10 =15 for x^2 - 2x + A to be positive A can be either positive no or negative no if A= -1 (Statement A is still valid x^2 - 2x + A>0) if A=1 (Statement A is still valid x^2 - 2x + A>0) A can be either positive no or negative no ..So How could you say A>0 ....Am I missing something ?

Onell - you are right in deducing that for x=5 A can be either positive or negative. In fact, if you see my response, I have reached a similar conclusion as well. However, we need the value of A for which the expression \(x^2 - 2x + A\)is positive for ALL x. As I explained earlier, for x between 0 and 2, this can be true only if A is greater than 1. So, \(x^2 - 2x + A\) is positive for ALL x only when A is greater than 1. For some x, it can be positive even when A is negative, but it is positive for ALL x if and only if A is greater than +1.

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

07 Apr 2011, 09:57

The first statement can be solved with some calculus. Differentiating x^2 - 2x + A yields 2x - 2. If we assume 2x - 2 = 0 and x = 1, we know that the quadratic curve is at its minimum (lowest value possible) when x = 1.

Therefore, substituting x = 1 into x^2 - 2x + A, we get -1 + A. This is the lowest value possible and since -1 + A > 0 (always positive), A > 1 and always positive.

So it's sufficient.

I'm inclined to say the second statement is true as well. If A < 0, the quadratic curve will have a maximum, which means it will definitely go negative, hence contradicting the statement ("(A*x^2) + 1 is +ve for all x "). The only way to make it always positive is if A > 0.

So I personally think the answer should be D.

I don't have any software to plot graphs right now, but if anyone fancies plotting quadratic graphs they might be able to show this.

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

07 Apr 2011, 22:54

1

This post received KUDOS

oster wrote:

The first statement can be solved with some calculus. Differentiating x^2 - 2x + A yields 2x - 2. If we assume 2x - 2 = 0 and x = 1, we know that the quadratic curve is at its minimum (lowest value possible) when x = 1.

Therefore, substituting x = 1 into x^2 - 2x + A, we get -1 + A. This is the lowest value possible and since -1 + A > 0 (always positive), A > 1 and always positive.

So it's sufficient.

I'm inclined to say the second statement is true as well. If A < 0, the quadratic curve will have a maximum, which means it will definitely go negative, hence contradicting the statement ("(A*x^2) + 1 is +ve for all x "). The only way to make it always positive is if A > 0.

So I personally think the answer should be D.

I don't have any software to plot graphs right now, but if anyone fancies plotting quadratic graphs they might be able to show this.

Your reasoning for the second statement is incorrect. The only way to make it always positive is if A > 0 OR A = 0. As, at A=0, the value of expression is 1 - always positive. So, A can be zero or positive and hence insufficient.

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

08 Apr 2011, 02:52

beyondgmatscore wrote:

Your reasoning for the second statement is incorrect. The only way to make it always positive is if A > 0 OR A = 0. As, at A=0, the value of expression is 1 - always positive. So, A can be zero or positive and hence insufficient.

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

08 Apr 2011, 07:28

Expert's post

asmit123 wrote:

Is A positive?

1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + 1 is +ve for all x

I've posted about this question a couple of times. Many people solve this backwards and arrive at the wrong answer (those test takers relying on 'number picking' strategies almost always answer this question incorrectly). The important word in each of the two statements is 'all'. In Statement 1, x^2 - 2x + A is positive not just for some value of x; it must be positive for EVERY value of x. In particular, it's positive when x=0, so substituting x=0, we learn instantly that A is positive and Statement 1 is sufficient.

Statement 2 is also almost sufficient. It is only insufficient because of a technicality: it's possible that A=0.

So the answer is A. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: Is A positive? 1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + [#permalink]

Show Tags

26 Nov 2014, 15:22

asmit123 wrote:

Is A positive?

1. x^2 - 2x + A is +ve for all x 2. (A*x^2) + 1 is +ve for all x

from statement 1: \(x^2-2x+A > 0\), adding and subtracting 1,\(x^2-2x+1+A-1 > 0\), this reduces to \((x-1)^2+A-1 > 0\), the least value of \((x-1)^2\) is 0, substitute this value in the expression to get the least value of A. 0 + A -1 > , this implies A>1 so sufficient From statement 2: A can take any value for the expression to be positive, NSF

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...