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:

Official Answer and Stats are available only to registered users. Register/Login.

_________________

Encourage me by pressing the KUDOS if you find my post to be helpful.

Help me win "The One Thing You Wish You Knew - GMAT Club Contest" http://gmatclub.com/forum/the-one-thing-you-wish-you-knew-gmat-club-contest-140358.html#p1130989

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als can not be negative. Not sufficient.

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als can not be negative. Not sufficient.

(1)+(2) Since from (1) \(y\geq{2}\), then from (2) \(y=14\). Sufficient.

Answer: C.

Hope it's clear.

Sorry I can't to figure out why y >= 2........

1) 3x^2 - 4 = y-2 and -3x^2 + 4 = y-2 and then ??'

thanks

We are given that \(3|x^2-4|=y-2\). Now, the left hand side in this expression (\(3|x^2-4|\)) is an absolute value, so it cannot be negative, so the right hand side of the expression (\(y-2\)) must also be non-negative: \(y-2\geq{0}\) --> \(y\geq{2}\).

pls point out if i am wrong 1. 3(x^2- 4) = y- 2 and 3(x^2-4)= - (y-2) y=-4 y=-16

from 2 y = 8 y= 14

so e is the answer

from 2 y = 8 - should be y = -8; |3-8| = |-5| = 5 and not 11; |3-(-8)| = |3+8| = 11 y= 14

3(x^2- 4) = y-2 it should be \(3|x^2-4|=y-2\) if \(y-2\geq0\). and 3(x^2-4)= -(y-2) it should be \(3|x^2-4|=-(y-2)\) if \(y-2<0\) but we don't have any information about \(y\). y=-4 y=-16 No justification for these values, we don't know what is the value of \(x.\) Statement (1) is not sufficient.

Statement (2) provides two possible values for \(y\), not sufficient.

Taken together (1) and (2): since \(y-2\) equals an absolute value, it should be non-negative. Only \(y = 14\) is acceptable. Sufficient, therefore answer C.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Bunuel, I understand from statement 1 we get \(y>=2\) , but when we combine both statements together we get \(y>=2\) and \(y=14\). Now how can we just assume y to be 14, because y can also take the value of 2 right . I chose E on this basis .

Bunuel, I understand from statement 1 we get \(y>=2\) , but when we combine both statements together we get \(y>=2\) and \(y=14\). Now how can we just assume y to be 14, because y can also take the value of 2 right . I chose E on this basis .

Thanks TT

That's not correct. Y cannot be 2, otherwise the second equation would not be true. \(|3-2|=11\), \(1=11\) As you can see if we pick 2, the second equation is not verified. If take a look at the explanations above, you'll find out that statement 2 defines two possible vaules for y (-8,14)[ not enough to say the value of y]; and that statement 1 is true only for \(y>=2\), because \(3|x^2-4|=y-2\), the left part is always \(>=0\) (thanks to the abs value), and so the right part must be \(>=0\) too. If we merge those conditions:\(y=-8\) or \(y=14\) with \(y>=2\), the only value that y can have is 14

Hope it's clear now
_________________

It is beyond a doubt that all our knowledge that begins with experience.

I know this is not needed for this problem but can someone show me how to solve 3|x^2 - 4| = y-2 from statement 1? Like what are the equations you could form if you tried to isolate y in this example?

I know this is not needed for this problem but can someone show me how to solve 3|x^2 - 4| = y-2 from statement 1? Like what are the equations you could form if you tried to isolate y in this example?

We have y = \(2+3|x^2-4|\)

Case I: x>2 -->

We can remove the modulus sign as it is and y = \(2+3(x^2-4) = 3x^2-10\)

(1) 3|x^2 – 4| = y – 2 It would take a long time to solve out for the positive and negative cases for x and even if we did I don't believe it would help us get an exact value for y because we would still have two variables to solve for (x, y) with no additional given information.

What we do know is that (y-2) must be ≥0 as it equals an absolute value, so y≥2 INSUFFICIENT

(2) |3 – y| = 11

Two cases:

Positive: y≤3: 3-y=11 ===> -y=8 ===> y=-8 Valid, as -8 falls within the range of ≤3 Negative: y>3: -3+y=11 ===> y=14 Valid, as 14 falls within the range of y>3 INSUFFICIENT - there are two valid solutions for y.

1+2)

What we know y≥2 y=-8 OR y=14

The only solution for y that also satisfies y≥2 is y=14 SUFFICIENT.

Again solving intuitively, and reaching the answer faster.

Picking the statement 2 first as it is the simpler of the two. (2) |3 – y| = 11

we get two values of Y; one +ve(14) and one -ve(-8). Not sufficient.

(1) 3|x^2 – 4| = y – 2 or, y= 3|x^2-4|+2 (RHS expression can never be -ve under any circumstance, since it involves a mod expression and '+2'). Therefore the value of Y is always +ve. But the statement in itself is not sufficient since we don't know the value of x.

Hence combining the two statements we can select the +ve value of Y from statement 2.

No way to determine exact values for x or y. INSUFFICIENT

(2) |3 – y| = 11 y<3 3 - y = 11 y = -8 Valid as -8 falls within the range of y<3 OR y>3 -(3 - y) = 11 -3 + y = 11 y = 14 Valid as y falls within the range or y > 3 Two valid solutions for y INSUFFICIENT

1+2) 3|x^2 – 4| = y – 2 and |3 – y| = 11 We could plug in values of y for the positive and negative cases of 3|x^2 - 4| or we could look at#1 and realize that because y-2 = an absolute value, it must be positive. Between the two solutions for y (-8 and 14) the only one that makes y - 2 positive is y = 14. SUFFICIENT

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(1)+(2) Since from (1) \(y\geq{2}\), then from (2) \(y=14\). Sufficient.

Answer: C.

Hope it's clear.

Hi,

Can I solve statement 1 like this:

3|x^2-4|=y-2

Now since this is an absolute value

I would 1st solve for x

x^2-4=0 x2=4 and x=+/-2 now if I substituent the value of x in the above expression If x= +2 3|x^2-4|=y-2 3|(2)^2-4|=y-2 3|0|=y-2 therefore y=2

now if x=-2 3|x^2-4|=y-2 3|(-2)^2-4|=y-2 3|0|=y-2 and therefore y=2

In both the cases I will get the same value for Y.

Can someone please explain what is wrong with this approach.

We don't know whether x^2-4=0, thus all your further steps are based on that false assumption. If we knew that x^2-4=0, then x^2-4=0=y-2 --> y-2=0 --> y=2.

Also, you can notice that your approach is not correct from the fact that on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. From (2) we have that y is -8 or 14, and if from (1) you get that y is 2 it would mean that the statements clearly contradict.

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...