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

 It is currently 14 Oct 2019, 08:54 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 x?

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58316
What is the value of x?  [#permalink]

Show Tags

2
1 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:19) correct 33% (02:08) wrong based on 287 sessions

HideShow timer Statistics

What is the value of x?

(1) $$(x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0$$

(2) $$x^2 + x -2 = 0$$

Kudos for a correct solution.

_________________
Manager  Joined: 13 Dec 2013
Posts: 59
Location: Iran (Islamic Republic of)
Re: What is the value of x?  [#permalink]

Show Tags

1
Answer is A ....

DATA # 1) : ( x^2 + 3 ) ^2 - 11 ( x^2 +3 ) ^2 + 28=0

For making the equation simple, lets consider the whole term ( x^2 +3 ) ^2 to be T .

So plug -in this letter in the equation and we will have : T -11 T +28=0 Or 10 T =28 and then T = 28/10 = 14/5

so we have ( x ^2 + 3 ) ^2 = T = 14/5 and we have : x^2 + 3 = (14/5 ) ^(1/2) then : x^2 = (14/5) ^ (1/2 ) -3 and then : x = ( (14/5)^(1/2) - 3 ) ^ (1/2 ) !!!!! so this info

Gives us Only one valid value for x and is Sufficient .... NOTICE : IN GMAT ONLY positive ROOT of EVEN ROOT is accepted and negative root is not. so, this info is sufficient ...

DATA #2 ) : x ^2 + x -2 =0 or : ( x+2 ) (x-1 ) =0 OR X =-2 Or X=1 this data Gives us TWO possible value for X and is not Sufficient

1 sufficient , 2 NOT sufficient , so answer is A....
Intern  Joined: 12 Oct 2014
Posts: 45
Location: India
Concentration: Finance, General Management
GMAT 1: 550 Q44 V21 WE: Analyst (Investment Banking)
Re: What is the value of x?  [#permalink]

Show Tags

Have a doubt, in GMAT can we consider imaginary values for X ?

After solving like we did above we will have, x^2 + 3 = (14/5 ) ^(1/2). This will give you x^2 <0

14/5=2.8 and if we take root of this then it should give us value <1.7

so, x^2 +3 = 1.7 (taking approx. value)

This implies ,x^2 less than zero ?

Anyone, any thoughts over this ?

Thanks,
Gaurav
CEO  S
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: What is the value of x?  [#permalink]

Show Tags

GauravSolanky wrote:
Have a doubt, in GMAT can we consider imaginary values for X ?

After solving like we did above we will have, x^2 + 3 = (14/5 ) ^(1/2). This will give you x^2 <0

14/5=2.8 and if we take root of this then it should give us value <1.7

so, x^2 +3 = 1.7 (taking approx. value)

This implies ,x^2 less than zero ?

Anyone, any thoughts over this ?

Thanks,
Gaurav

GMAT always deals with Real numbers as written on the first page of the PS section in the official guide.
Intern  Joined: 12 Oct 2014
Posts: 45
Location: India
Concentration: Finance, General Management
GMAT 1: 550 Q44 V21 WE: Analyst (Investment Banking)
Re: What is the value of x?  [#permalink]

Show Tags

Engr2012 wrote:
GauravSolanky wrote:
Have a doubt, in GMAT can we consider imaginary values for X ?

After solving like we did above we will have, x^2 + 3 = (14/5 ) ^(1/2). This will give you x^2 <0

14/5=2.8 and if we take root of this then it should give us value <1.7

so, x^2 +3 = 1.7 (taking approx. value)

This implies ,x^2 less than zero ?

Anyone, any thoughts over this ?

Thanks,
Gaurav

GMAT always deals with Real numbers as written on the first page of the PS section in the official guide.

Thanks. Then, if we solve above we will get imaginary values for x. How come we can go for answer as A.

Can you please explain that as well ?

Thanks,
Gaurav CEO  S
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: What is the value of x?  [#permalink]

Show Tags

GauravSolanky wrote:
Engr2012 wrote:
GauravSolanky wrote:
Have a doubt, in GMAT can we consider imaginary values for X ?

After solving like we did above we will have, x^2 + 3 = (14/5 ) ^(1/2). This will give you x^2 <0

14/5=2.8 and if we take root of this then it should give us value <1.7

so, x^2 +3 = 1.7 (taking approx. value)

This implies ,x^2 less than zero ?

Anyone, any thoughts over this ?

Thanks,
Gaurav

GMAT always deals with Real numbers as written on the first page of the PS section in the official guide.

Thanks. Then, if we solve above we will get imaginary values for x. How come we can go for answer as A.

Can you please explain that as well ?

Thanks,
Gaurav The OA is E as statement 1 DOES NOT give you any real values and statement 1 gives you x=1 and x=-2. Thus even after combining you will get 2 values of x and hence E is the correct answer.

Here is the excerpt from Official Guide 2013 page 272 (this is the same note for both PS and DS) : "Numbers: All numbers used are real numbers."
Intern  Joined: 12 Oct 2014
Posts: 45
Location: India
Concentration: Finance, General Management
GMAT 1: 550 Q44 V21 WE: Analyst (Investment Banking)
Re: What is the value of x?  [#permalink]

Show Tags

Oops..sorry, I overlooked it. Somehow, I had in mind that A is official answer.

I was also expecting E as an answer. Thanks. Cheers,
Gaurav
Intern  Joined: 21 Jun 2015
Posts: 11
Schools: Kellogg '18
Re: What is the value of x?  [#permalink]

Show Tags

GauravSolanky wrote:
Oops..sorry, I overlooked it. Somehow, I had in mind that A is official answer.

I was also expecting E as an answer. Thanks. Cheers,
Gaurav

Just wanted to check..
statement 1 gives x=+-2,+-1. right?
CEO  S
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: What is the value of x?  [#permalink]

Show Tags

snowygari wrote:

Just wanted to check..
statement 1 gives x=+-2,+-1. right?

No, statement 1 gives you no real solutions while statement 2 gives you x = 1 or -2.

Originally posted by ENGRTOMBA2018 on 15 Aug 2015, 09:57.
Last edited by ENGRTOMBA2018 on 16 Aug 2015, 06:55, edited 1 time in total.
Edited the solution
Senior Manager  B
Joined: 01 Nov 2013
Posts: 283
GMAT 1: 690 Q45 V39 WE: General Management (Energy and Utilities)
Re: What is the value of x?  [#permalink]

Show Tags

On the GMAT all numbers are real numbers.

A gives us unreal solutions and B gives us two real solutions.

So, E .

However, I mistakenly chose A even though I noticed the tricky presentation in statement 1. _________________
Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.

I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.-Mohammad Ali
Intern  Joined: 21 Jun 2015
Posts: 11
Schools: Kellogg '18
Re: What is the value of x?  [#permalink]

Show Tags

Engr2012 wrote:
snowygari wrote:

Just wanted to check..
statement 1 gives x=+-2,+-1. right?

No, statement 1 gives you no real solutions while statement 2 gives you x = 1 or -2.

oops.. got it.. calucation mistake VP  P
Joined: 12 Dec 2016
Posts: 1493
Location: United States
GMAT 1: 700 Q49 V33 GPA: 3.64
Re: What is the value of x?  [#permalink]

Show Tags

after realizing that each st1 cannot conclude the value of x, take values of x from st2 and put in equations in st1 => E
Intern  B
Joined: 24 Jul 2017
Posts: 43
Location: India
WE: Information Technology (Computer Software)
Re: What is the value of x?  [#permalink]

Show Tags

1 ---> Taking (x^2+3)^2 common, we get the equation as : (x^2+3)^2 = 28/10. We cannot get value of x. Hence not sufficient.
2 ---> Solving, we get x=1 or x=-2. Hence, not sufficient.

(1) + (2) ---> Values from statement 2 does not satisfy 1. Hence, we cannot find value of x. Hence E.
Intern  B
Joined: 18 Sep 2009
Posts: 13
Location: India
WE: Business Development (Internet and New Media)
Re: What is the value of x?  [#permalink]

Show Tags

Answer is A ....

DATA # 1) : ( x^2 + 3 ) ^2 - 11 ( x^2 +3 ) ^2 + 28=0

For making the equation simple, lets consider the whole term ( x^2 +3 ) ^2 to be T .

So plug -in this letter in the equation and we will have : T -11 T +28=0 Or 10 T =28 and then T = 28/10 = 14/5

so we have ( x ^2 + 3 ) ^2 = T = 14/5 and we have : x^2 + 3 = (14/5 ) ^(1/2) then : x^2 = (14/5) ^ (1/2 ) -3 and then : x = ( (14/5)^(1/2) - 3 ) ^ (1/2 ) !!!!! so this info

Gives us Only one valid value for x and is Sufficient .... NOTICE : IN GMAT ONLY positive ROOT of EVEN ROOT is accepted and negative root is not. so, this info is sufficient ...

DATA #2 ) : x ^2 + x -2 =0 or : ( x+2 ) (x-1 ) =0 OR X =-2 Or X=1 this data Gives us TWO possible value for X and is not Sufficient

1 sufficient , 2 NOT sufficient , so answer is A....

Hi, Can you please clarify why you mention root cannot be negative - x^2 = (14/5) ^ (1/2 ) -3
root of 14/5 - this itself can be -ve or +ve right? I mean if 14/5 would have been 9 instead, when we take root of 9, we do consider +/- 3 as options
then we have to take the second root and again the same thing follows
Math Expert V
Joined: 02 Sep 2009
Posts: 58316
Re: What is the value of x?  [#permalink]

Show Tags

1
shettytarun wrote:
Answer is A ....

DATA # 1) : ( x^2 + 3 ) ^2 - 11 ( x^2 +3 ) ^2 + 28=0

For making the equation simple, lets consider the whole term ( x^2 +3 ) ^2 to be T .

So plug -in this letter in the equation and we will have : T -11 T +28=0 Or 10 T =28 and then T = 28/10 = 14/5

so we have ( x ^2 + 3 ) ^2 = T = 14/5 and we have : x^2 + 3 = (14/5 ) ^(1/2) then : x^2 = (14/5) ^ (1/2 ) -3 and then : x = ( (14/5)^(1/2) - 3 ) ^ (1/2 ) !!!!! so this info

Gives us Only one valid value for x and is Sufficient .... NOTICE : IN GMAT ONLY positive ROOT of EVEN ROOT is accepted and negative root is not. so, this info is sufficient ...

DATA #2 ) : x ^2 + x -2 =0 or : ( x+2 ) (x-1 ) =0 OR X =-2 Or X=1 this data Gives us TWO possible value for X and is not Sufficient

1 sufficient , 2 NOT sufficient , so answer is A....

Hi, Can you please clarify why you mention root cannot be negative - x^2 = (14/5) ^ (1/2 ) -3
root of 14/5 - this itself can be -ve or +ve right? I mean if 14/5 would have been 9 instead, when we take root of 9, we do consider +/- 3 as options
then we have to take the second root and again the same thing follows

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt{x}$$, then the only accepted answer is the positive root. Even roots have only a positive value on the GMAT. That is, $$\sqrt{25}=5$$, NOT +5 or -5.

In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5.

$$\sqrt{n}$$ denotes the positive number whose square is n.
_________________
Manager  S
Status: GMAT Coach
Joined: 05 Nov 2012
Posts: 141
Location: Peru
GPA: 3.98
What is the value of x?  [#permalink]

Show Tags

1
Bunuel wrote:
What is the value of x?

(1) (x^2 + 3)^2 - 11(x^2 + 3)^2 + 28 = 0
(2) x^2 + x -2 = 0

This is not a valid GMAT DS question.

Statements 1 and 2 must be true, not contradictory.

It is clear that statement 2 gives us x = 1 or x = -2, so it is not sufficient.
But the answer in 1 is neither of these answers, so the problem is wrong as it is.

Choice E will tell us that using both statements together is insufficient; however, in this instance, using both statements together is not that is insufficient, it is impossible.

Definitely, not a valid GMAT question.

However, This might be a misprint. I suppose that (x^2 + 3)^2 - 11(x^2 + 3)^2 + 28 = 0 is wrong
- 11(x^2 + 3)^2 should be 11(x^2 + 3)without squaring it.

In that case statement 1 would give us x = 1, x = -1, x = 2, and x = -2

Then the answer would be E
_________________
Clipper Ledgard
GMAT Coach

Originally posted by cledgard on 31 Aug 2017, 09:00.
Last edited by cledgard on 31 Aug 2017, 09:11, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58316
Re: What is the value of x?  [#permalink]

Show Tags

cledgard wrote:
Bunuel wrote:
What is the value of x?

(1) (x^2 + 3)^2 - 11(x^2 + 3)^2 + 28 = 0
(2) x^2 + x -2 = 0

This is not a valid GMAT DS question.

Statements 1 and 2 must be true, not contradictory.

It is clear that statement 2 gives us x = 1 or x = -2, so it is not sufficient.
But the answer in 1 is neither of these answers, so the problem is wrong as it is.

Choice E will tell us that using both statements together is insufficient; however, in this instance, using both statements together is not that is insufficient, it is impossible.

Definitely, not a valid GMAT question.

Yes, you are right. Edited the typo. (1) reads: $$(x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0$$

thank you for noticing it.
_________________
Intern  B
Joined: 18 Dec 2018
Posts: 1
Re: What is the value of x?  [#permalink]

Show Tags

Post the edit in the question,

Statement i suggests x = 2 or 1
Statement ii suggests x = -2 or 1

Shouldn't the answer be C? with x=1 being confirmed by both statements.
Math Expert V
Joined: 02 Sep 2009
Posts: 58316
Re: What is the value of x?  [#permalink]

Show Tags

1
Pi8 wrote:
Post the edit in the question,

Statement i suggests x = 2 or 1
Statement ii suggests x = -2 or 1

Shouldn't the answer be C? with x=1 being confirmed by both statements.

(x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0 --> x = -2, -1, 1, or 2.
x^2 + x -2 = 0 --> x = -2, or 1.

So, when taken together x can be -2 or 1.
_________________
Senior Manager  P
Joined: 13 Jan 2018
Posts: 342
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23 GMAT 2: 640 Q49 V27 GPA: 4
WE: Consulting (Consulting)
Re: What is the value of x?  [#permalink]

Show Tags

(1) $$(x^2+3)^2 − 11(x^2+3) + 28=0$$

Let $$(x^2+3) = a$$

Now statement 1 can be written as $$a^2 - 11a + 28 = 0$$

$$a^2 - 4a - 7a + 28 = 0$$
$$a(a-4) - 7(a-4) = 0$$
$$(a-7)(a-4) = 0$$
a = 7 or 4

$$x^2+3$$ = 7 or 4
$$x^2$$ = 4 or 1
x = 2, -2 or 1, -1

Clearly INSUFFICIENT

(2) $$x^2 + x − 2 = 0$$

$$x^2 + 2x - x - 2 = 0$$
$$x(x+2) -1(x+2) = 0$$
$$(x-1)(x+2) = 0$$
x = 1 or -2

Clearly INSUFFICIENT

Combining 1) + 2) Still x can be either of 1 and -2. So combining didn't work.

OPTION: E
_________________
____________________________
Regards,

Chaitanya

+1 Kudos

if you like my explanation!!! Re: What is the value of x?   [#permalink] 01 Jan 2019, 04:37
Display posts from previous: Sort by

What is the value of x?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  