GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 16:03 GMAT Club Daily Prep

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

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.  What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Joined: 20 Apr 2010
Posts: 169
Schools: ISB, HEC, Said
What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

2
5 00:00

Difficulty:   55% (hard)

Question Stats: 56% (01:30) correct 44% (02:01) wrong based on 200 sessions

HideShow timer Statistics

What is the value of y?

(1) 3|x^2 - 4| = y - 2

(2) |3 - y| = 11

Originally posted by prashantbacchewar on 29 Sep 2010, 08:33.
Last edited by Bunuel on 30 May 2019, 01:38, edited 2 times in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

7
What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) As 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.

(2) $$|3 - y| = 11$$:

$$y<3$$ --> $$3-y=11$$ --> $$y=-8$$;
$$y\geq{3}$$ --> $$-3+y=11$$ --> $$y=14$$.

Two values for $$y$$. Not sufficient.

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

_________________
General Discussion
Retired Moderator B
Joined: 05 Jul 2006
Posts: 1439
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

1
prashantbacchewar wrote:
What is the value of y?

(1) 3|x^2 – 4| = y – 2

(2) |3 – y| = 11

from 1

equation with 2 unknown we can only deduct that y-2> 0 ie: y>2

from 2

y has to have 2 values +ve and -ve..........insuff

both

y>2 , then from 2 y has the +ve value.

C
Retired Moderator Joined: 03 Aug 2010
Posts: 174
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

Bunuel wrote:
What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) As 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.

(2) $$|3 - y| = 11$$:

$$y<3$$ --> $$3-y=11$$ --> $$y=-8$$;
$$y\geq{3}$$ --> $$-3+y=11$$ --> $$y=14$$.

Two values for $$y$$. Not sufficient.

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

Hey, pls explain the reasoning of LHS

LHS is absolute value which is never negative, hence RHS als can not be negative.???
_________________
http://www.gmatpill.com/gmat-practice-test/

Amazing Platform
Manager  Joined: 01 Oct 2010
Posts: 63
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

hirendhanak wrote:
Bunuel wrote:
What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) As 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.

(2) $$|3 - y| = 11$$:

$$y<3$$ --> $$3-y=11$$ --> $$y=-8$$;
$$y\geq{3}$$ --> $$-3+y=11$$ --> $$y=14$$.

Two values for $$y$$. Not sufficient.

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

Hey, pls explain the reasoning of LHS

LHS is absolute value which is never negative, hence RHS als can not be negative.???

what values you can put for x?
if you put x = 2, left hand side becomes zero, making y=2.
if you put x as any other value, it will make 3*|x^2 - 4| positive, and add 2 to that, making y > 2.
so, y is either 2 or greater.

Hope this helps.
_________________
Manager  Joined: 09 Feb 2011
Posts: 202
Concentration: General Management, Social Entrepreneurship
Schools: HBS '14 (A)
GMAT 1: 770 Q50 V47 Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

1
1st equation:
x^2 - 4 can be positive, or negative ( say x = 1, then x^2 - 4 is -3, and say x = 3, then x^2-4 is 5. However since its absolute value is taken, it will always be a positive number, which when multiplied by 3 will give either zero (if x=2) or a positive number. This added to 2 brought pver fom RHS of the equation will have to be a positive number still. So while Statement 1 is insufficient in telling us the value of y, it does tell us that y is positive.
Equation 2:
by telling us that absolute value of 3-y is 11 implies that the vlue inside the absolute value lines is either 11 or -11, which means that y is either 14 or -8. since it gives two values of y it is insufficient by itself.
However since statement tells us for certain that y i s positive and statement two give sus two values of y one positive and one negative, both combined we can pick the positive value and be sure that that is the correct value of y
hence both together ae sufficient
Retired Moderator B
Joined: 16 Nov 2010
Posts: 1254
Location: United States (IN)
Concentration: Strategy, Technology
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

The answer is C. (1) says y is +ve, and (2) gives 2 values of y, one +ve and one -ve. So combining both we get y = 14.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Director  Joined: 01 Feb 2011
Posts: 550
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

1. Insufficient

because all we know here is y>2

2. Insufficient.

because y can be -8 or 14

together . Sufficient.

Intern  Joined: 22 Mar 2013
Posts: 18
Concentration: Operations, Entrepreneurship
GMAT 1: 620 Q47 V28 GMAT 2: 680 Q45 V38 WE: Engineering (Manufacturing)
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

What is the value of y?
(1) 3|x^2 – 4| = y – 2
(2) |3 – y| = 11

Stmt 1: Y=3|x^2-4|+2. The value of y will change with the value of x. insufficient.
Stmt2: 3-y=11 OR 3-y=-11. We get y=-8 in first case and y=14 in second. Insufficient.
Together: Anything inside a Modulus is ALWAYS positive. Therefore, |x^2-4| will always positive. And when we add 2 to it, the result still remains positive. That means, y cannot be -8 from stmt2. Sufficient. Answer C.
Manager  Joined: 07 Apr 2012
Posts: 87
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23 GPA: 3.9
WE: Operations (Manufacturing)
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

[quote="Bunuel"]What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) As 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."

Bunuel,

In this case we said since the LHS has a mod so its value is positive always. But we also know mod function is negative for values of x < 0 , or we dont always assume for a given equation say |x-2| =2 , that LHS is positive always ? we say x-2 = x-2 , when x> 2 and 2-x when x < 2.
So this looks a contradiction, can you please explain ?
Manager  Status: Persevering
Joined: 15 May 2013
Posts: 146
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

ygdrasil24 wrote:
Bunuel wrote:
What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) As 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."

Bunuel,

In this case we said since the LHS has a mod so its value is positive always. But we also know mod function is negative for values of x < 0 , or we dont always assume for a given equation say |x-2| =2 , that LHS is positive always ? we say x-2 = x-2 , when x> 2 and 2-x when x < 2.
So this looks a contradiction, can you please explain ?

In this case for statement 1,

as it is in modulus so LHS will always be positive, its x whose value can be -ve or +ve, but LHS will always be +ve.
Therefore we conclude that y-2>=0 or y>=2

From statement 2 we get y=-8,14

Combining 1 and 2, we get y=14

Hope it is clear.
_________________
--It's one thing to get defeated, but another to accept it.
Manager  Joined: 07 Apr 2012
Posts: 87
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23 GPA: 3.9
WE: Operations (Manufacturing)
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

In this case for statement 1,

as it is in modulus so LHS will always be positive, its x whose value can be -ve or +ve, but LHS will always be +ve.
Therefore we conclude that y-2>=0 or y>=2

From statement 2 we get y=-8,14

Combining 1 and 2, we get y=14

Hope it is clear.[/quote]

Let us take an example. y =|X-2|
So y = x-2 , when x-2>0 or x-2=0
and y = 2-x, when x-2<0 ro x <2

If we take x = 3, then y = -1, how ? I am doing something silly here for sure!
If you see graph of mod function Y is always positive, so how is Y = -1 above at x =3 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

ygdrasil24 wrote:
Bunuel wrote:
What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) As 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."

Bunuel,

In this case we said since the LHS has a mod so its value is positive always. But we also know mod function is negative for values of x < 0 , or we dont always assume for a given equation say |x-2| =2 , that LHS is positive always ? we say x-2 = x-2 , when x> 2 and 2-x when x < 2.
So this looks a contradiction, can you please explain ?

It seems that you should brush up your fundamentals.

First of all: absolute value is always greater than or equal to zero ($$\geq{0}$$), not $$>0$$.

Next, |x|=-x, when x<0 --> $$|x|=-x=-negative=positive$$.

Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

_________________
Manager  Joined: 07 Apr 2012
Posts: 87
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23 GPA: 3.9
WE: Operations (Manufacturing)
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

Ok Thanks. I was missing this - of -x = +x, So basically in mod function x can range from - to +, but y will always be >0 or = 0. Correct me if I understood it wrongly.
Math Expert V
Joined: 02 Sep 2009
Posts: 58381
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

ygdrasil24 wrote:
Ok Thanks. I was missing this - of -x = +x, So basically in mod function x can range from - to +, but y will always be >0 or = 0. Correct me if I understood it wrongly.

Apart from the red part all is correct. The red part does not make sense.
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13209
Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11   [#permalink] 22 Oct 2018, 08:25
Display posts from previous: Sort by

What is the value of y? (1) 3|x^2 - 4| = y - 2 (2) |3 - y| = 11

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  