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

It is currently 17 Oct 2019, 14:18

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 24 Nov 2015
Posts: 2
What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post Updated on: 26 Jan 2016, 14:15
3
33
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

55% (01:40) correct 45% (01:50) wrong based on 647 sessions

HideShow timer Statistics

What is the value of x?

(1) \(x^2 + x + 10 = 16\)
(2) \(x = 4y^4+2y^2+2\)

Originally posted by GMAT4937 on 26 Jan 2016, 13:54.
Last edited by GMAT4937 on 26 Jan 2016, 14:15, edited 1 time in total.
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4007
Location: Canada
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 26 Jan 2016, 14:09
13
10
Quote:
What is the value of x ?

(1) x² + x + 10 = 16

(2) x = 4y⁴ + 2y² +2


Target question: What is the value of x?

Statement 1: x² + x + 10 = 16
Rewrite as: x² + x - 6 = 0
Factor: (x + 3)(x - 2) = 0
So, x = -3 OR x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 4y⁴ + 2y² + 2
As you can see, the value of x depends on the value of y.
Consider these two cases:
Case a: y = 0, in which case x = 4(0⁴) + 2(0²) + 2. Evaluate to see that x = 2
Case b: y = 1, in which case x = 4(1⁴) + 2(1²) + 2. Evaluate to see that x = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = -3 OR x = 2
Statement 2: Since y⁴ and 2y² are greater than or equal to zero FOR ANY value of y, we can see that 4y⁴ + 2y² + 2 MUST BE POSITIVE. In other words, x must be POSITIVE.

If x must be POSITIVE, then x MUST equal 2

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
General Discussion
Intern
Intern
avatar
Joined: 24 Nov 2015
Posts: 2
What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 26 Jan 2016, 14:31
Thanks for your explanation! I was thrown off by the extra variable "y" in the second statement, but when I got a positive and negative solution for x in statement one, that should've helped me figure out how to make use of the second.
Manager
Manager
avatar
B
Joined: 06 Aug 2015
Posts: 56
Concentration: General Management, Entrepreneurship
GMAT Date: 10-30-2016
GRE 1: Q160 V135
GPA: 3.34
WE: Programming (Consulting)
GMAT ToolKit User Reviews Badge
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 15 May 2016, 09:34
Hi,

Can anyone clarify my query here?

Nothing is stated about 'y' rite...??
So y can be irrational, rational, integer, etc.

If i assume an extreme case: y an irrational number, then the answer is E rite?

Please clarify? Should i not take this case into consideration?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58402
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 15 May 2016, 09:40
3
2
HARRY113 wrote:
Hi,

Can anyone clarify my query here?

Nothing is stated about 'y' rite...??
So y can be irrational, rational, integer, etc.

If i assume an extreme case: y an irrational number, then the answer is E rite?

Please clarify? Should i not take this case into consideration?


For (2): regardless what real number y is (rational, irrational, ...), y in even power would be nonnegative. Thus, \(x = 4y^4+2y^2+2=nonnegative+nonnegative+positive=positive\).

From (1) x = -3 OR x = 2 and from (2) that x is a positive number, therefore when we combine the statements, x can only be 2. Sufficient.

Answer: C.
_________________
Current Student
avatar
B
Joined: 20 Jan 2014
Posts: 39
Location: United States
GMAT 1: 720 Q47 V41
GPA: 3.71
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 21 May 2016, 14:03
1
1
This is good question to help you make start thinking on a higher level for the GMAT and start for DS questions start asking the question "Why are they giving me this information?"

The question is x = ?

Statement 1:

When factored works out to be x = 2 or x = -3. This is clearly insufficient as we have two answers for x, one positive and one negative. When I solve and quadratic and I get one positive and one negative answer its usually a good idea to double check the question to make it doesn't provide a small bit of info that could eliminate one of the answer choices. In this case, there's no additional info so we'll carry on.

Statement 2:

Just by looking at the question we can see it's insufficient. Plug in 1 for y and we get one answer and plug in 2 and we get a different answer.

Statements 1 & 2:

This is where it might look insufficient. But if we look back at statement 2 and ask ourselves why did the test makers give us this info? We have one negative answer for x and one positive answer. Is there any value for y we can plug in that will give us an negative answer for x? No, all of the powers of Y are even so the answer will always be positive. Therefore, X = 2 and we pick answer C.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4007
Location: Canada
Re: What is the value of x?  [#permalink]

Show Tags

New post 28 Feb 2017, 15:04
1
Top Contributor
souvonik2k wrote:
What is the value of x?

(1) x² + x + 10 = 16
(2) x = 4y⁴ + 2y² +2



Target question: What is the value of x?

Statement 1: x² + x + 10 = 16
Given: x² + x + 10 = 16
Subtract 16 from both sides: x² + x - 6 = 0
Factor: (x + 3)(x - 2) = 0
So, EITHER x = -3 OR x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 4y⁴ + 2y² +2
Since we don't know anything about the value of y, there are many possible values of x. Here are two:
Case a: if y = 0, then x = 4(0)⁴ + 2(0)² +2 = 2
Case b: if y = 1, then x = 4(1)⁴ + 2(1)² +2 = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = -3 OR x = 2
Statement 2 tells us that x is POSITIVE.
How do we know that x is POSITIVE?
Well, 4y⁴ ≥ 0 and 2y² ≥ 0 for all values of y. So, the SUM 4y⁴ + 2y² +2 MUST BE POSITIVE.
Since x = 4y⁴ + 2y² +2, we know that x is POSITIVE.
If x is positive, then x cannot equal -3, which means x must equal 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 743
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 27 Jul 2017, 18:50
GMAT4937 wrote:
What is the value of x?

(1) \(x^2 + x + 10 = 16\)
(2) \(x = 4y^4+2y^2+2\)


(1) \(x^2 + x + 10 = 16\)
\(x^2 + x + 10 - 16 = 0\)
\(x^2 + x + 6 = 0\)
\(x^2 + 3x - 2x + 6 = 0\)
\(x(x + 3) - 2 (x + 3) = 0\)
\((x-2)(x + 3) =0\)

Therefore \(x\) could be \((2)\) or \((-3)\)

I is Not sufficient.

(2) \(x = 4y^4+2y^2+2\)

Value of \(x\) depends on value of \(y\). We do not know value of \(y\), hence we cannot find value of \(x\) from the equation alone.

II is Not Sufficient.

Combining (1) and (2)

From (1) we get \(x\) could be \((2)\) or \((-3)\)

From (2) we get \(x\) should be positive.

Hence \(x\) should be \(2\)

Answer (C)...
Intern
Intern
avatar
B
Joined: 31 Jul 2017
Posts: 8
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 08 Oct 2017, 13:23
Solve that in a similar way. In condition 2 x must be even since all numbers on the right side are even. So, only possible answer is x = 2 considering condition 1.
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 832
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 08 Oct 2017, 13:51
GC2808 wrote:
Solve that in a similar way. In condition 2 x must be even since all numbers on the right side are even. So, only possible answer is x = 2 considering condition 1.


You can only make that assumption if you know the numbers are integers. For instance, here's a much simpler problem:

x = 2y + 4

If you know that x and y are both integers, x definitely has to be even.

But if they don't have to be integers, you could say that y = 0.5. In that case, x = 1 + 4 = 5, which is odd.
_________________
Image

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!
Intern
Intern
avatar
B
Joined: 29 Oct 2016
Posts: 24
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 10 Dec 2017, 10:43
Can someone please tell me if my approach is correct or incorrect:

If we plug in x as -3 into the second statement, we get 4y^4 + 2y^2 + 5 = 0 - but if we try to solve for a value of y, we are unable to because we cannot factor.

If we plug in x as 2 into the second statement, we get 4y^4 + 2y^2 = 0, we get either 2y^2 = 0, which means y must be 0, or we get 2y^2 = -1 which, when we simplify, get a negative root - y = root(-1/2). So only one case will work where y is equal to 0 -- so x must be 2? Is there anything wrong with this approach?

Thank you!
Intern
Intern
avatar
B
Joined: 16 Aug 2017
Posts: 8
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 11 Dec 2017, 03:00
Bunuel wrote:
HARRY113 wrote:
Hi,

Can anyone clarify my query here?

Nothing is stated about 'y' rite...??
So y can be irrational, rational, integer, etc.

If i assume an extreme case: y an irrational number, then the answer is E rite?

Please clarify? Should i not take this case into consideration?


For (2): regardless what real number y is (rational, irrational, ...), y in even power would be nonnegative. Thus, \(x = 4y^4+2y^2+2=nonnegative+nonnegative+positive=positive\).

From (1) x = -3 OR x = 2 and from (2) that x is a positive number, therefore when we combine the statements, x can only be 2. Sufficient.

Answer: C.




Hi Bunuel,

If you substitute X=-3 back into the equation, it does not satisfy L.H.S=R.H.S

Can you help me understand, when should we substitute back and when not? I am told that always to substitute back in such equations and in case of MODS.

?
Retired Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 11 Dec 2017, 05:54
GMP12 wrote:
Bunuel wrote:
HARRY113 wrote:
Hi,

Can anyone clarify my query here?

Nothing is stated about 'y' rite...??
So y can be irrational, rational, integer, etc.

If i assume an extreme case: y an irrational number, then the answer is E rite?

Please clarify? Should i not take this case into consideration?


For (2): regardless what real number y is (rational, irrational, ...), y in even power would be nonnegative. Thus, \(x = 4y^4+2y^2+2=nonnegative+nonnegative+positive=positive\).

From (1) x = -3 OR x = 2 and from (2) that x is a positive number, therefore when we combine the statements, x can only be 2. Sufficient.

Answer: C.




Hi Bunuel,

If you substitute X=-3 back into the equation, it does not satisfy L.H.S=R.H.S

Can you help me understand, when should we substitute back and when not? I am told that always to substitute back in such equations and in case of MODS.

?



I assume you are talking about the equation x^2 + x + 10 = 16 . If you substitute x=-3 in this, then LHS = (-3)^2 + (-3) + 10 = 9-3+10 = 16, which is same as RHS

But this same value of x=-3 cannot be substituted in second statement's equation (it wont make sense) x = 4y^4 + 2y^2 + 2 because RHS can never be negative, as other people (including Bunuel) have already explained in this thread.
Intern
Intern
avatar
B
Joined: 16 Aug 2017
Posts: 8
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 11 Dec 2017, 22:51
From (1) x = -3 OR x = 2 and from (2) that x is a positive number, therefore when we combine the statements, x can only be 2. Sufficient.

Answer: C.[/quote]



Hi Bunuel,

If you substitute X=-3 back into the equation, it does not satisfy L.H.S=R.H.S

Can you help me understand, when should we substitute back and when not? I am told that always to substitute back in such equations and in case of MODS.

?[/quote]


I assume you are talking about the equation x^2 + x + 10 = 16 . If you substitute x=-3 in this, then LHS = (-3)^2 + (-3) + 10 = 9-3+10 = 16, which is same as RHS

But this same value of x=-3 cannot be substituted in second statement's equation (it wont make sense) x = 4y^4 + 2y^2 + 2 because RHS can never be negative, as other people (including Bunuel) have already explained in this thread.[/quote]


Apologies.. I made a stupid calculation mistake!!
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13245
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2  [#permalink]

Show Tags

New post 18 Jan 2019, 16:33
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.
_________________
GMAT Club Bot
Re: What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2   [#permalink] 18 Jan 2019, 16:33
Display posts from previous: Sort by

What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2

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





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