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

 It is currently 15 Jun 2019, 22:32 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.  If x is an integer, what is the value of x?

Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55609
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

1
1
NikhilDev wrote:
Hey bunuel,
I got x=-1,2 from the first statement.
But in the second statement, i took positive and negative possibilities and came up with 4 equations.
the 4 equations are
1.(x^2)-x=2
2.(x^2)+x=2
3. -(x^2)+x=2
4. -(x^2)-x=2
Out of these four equations, according to me, only the 1st and the second have real solutions.
So from the 1st equation above i got x=-1,2(Same as the result from our First Statement )
and from the second equation i got x=1,-2.
But everywhere people have written that they got x=-2,2 from the second statement. Can you please explain it to me as to what the issue is.

Does -1, or 1 satisfy the equation? No. So, x cannot be -1 or 1.

Next, you get x^2 - x = 2 for positive x, so when solving you should discard negative solutions. Similarly, you get x^2 + x = 2 for negative x, so when solving you should discard positive solutions.
_________________
Manager  Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 130
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23 GMAT 2: 560 Q42 V26 GPA: 3.5
WE: Consulting (Computer Hardware)
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

Bunuel wrote:
rohitgoel15 wrote:
If x is an integer, what is the value of x?
1) |x - |x2|| = 2
2) |x2 - |x|| = 2

I saw the solution and I think i cant even get close. On the test, I would prefer not to solve this question. But is there a short way to make an educated guess. Answer is not E as given in above posts, it's C. Also note that 1 and -1 does not satisfy statement (2).

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2. First of all: $$|x^2|=x^2$$ (as $$x^2$$ is a non-negative value). Square both sides: $$(x-x^2)^2=4$$ --> factor out $$x$$: $$x^2*(1-x)^2=4$$ --> as $$x$$ is an integer then $$x=2$$ or $$x=-1$$ (by trial and error: the product of two perfect square is 4: 1*4=4 or 4*1=4). Not sufficient.

(2) |x^2 - |x|| = 2 --> square both sides: $$(x^2-|x|)^2=4$$ --> factor out $$|x|$$: $$x^2*(|x|-1)^2=4$$ --> as $$x$$ is an integer then $$x=2$$ or $$x=-2$$. Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is $$x=2$$. Sufficient.

Hope it's clear.

if x^2 = 4 then isn't x= (2,-2) ?
Math Expert V
Joined: 02 Sep 2009
Posts: 55609
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

1
email2vm wrote:
Bunuel wrote:
rohitgoel15 wrote:
If x is an integer, what is the value of x?
1) |x - |x2|| = 2
2) |x2 - |x|| = 2

I saw the solution and I think i cant even get close. On the test, I would prefer not to solve this question. But is there a short way to make an educated guess. Answer is not E as given in above posts, it's C. Also note that 1 and -1 does not satisfy statement (2).

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2. First of all: $$|x^2|=x^2$$ (as $$x^2$$ is a non-negative value). Square both sides: $$(x-x^2)^2=4$$ --> factor out $$x$$: $$x^2*(1-x)^2=4$$ --> as $$x$$ is an integer then $$x=2$$ or $$x=-1$$ (by trial and error: the product of two perfect square is 4: 1*4=4 or 4*1=4). Not sufficient.

(2) |x^2 - |x|| = 2 --> square both sides: $$(x^2-|x|)^2=4$$ --> factor out $$|x|$$: $$x^2*(|x|-1)^2=4$$ --> as $$x$$ is an integer then $$x=2$$ or $$x=-2$$. Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is $$x=2$$. Sufficient.

Hope it's clear.

if x^2 = 4 then isn't x= (2,-2) ?

Yes, but if x=-2, then x^2*(1-x)^2 does not equal to 4.
_________________
CEO  S
Joined: 20 Mar 2014
Posts: 2622
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

NikhilDev wrote:
Hey bunuel,
I got x=-1,2 from the first statement.
But in the second statement, i took positive and negative possibilities and came up with 4 equations.
the 4 equations are
1.(x^2)-x=2
2.(x^2)+x=2
3. -(x^2)+x=2
4. -(x^2)-x=2
Out of these four equations, according to me, only the 1st and the second have real solutions.
So from the 1st equation above i got x=-1,2(Same as the result from our First Statement )
and from the second equation i got x=1,-2.
But everywhere people have written that they got x=-2,2 from the second statement. Can you please explain it to me as to what the issue is.

You are making a mistake while interpreting different scenarios after you open up the absolute sign.

Per statement 2, |x^2-|x||=2

Consider 2 cases,

Case 1: when $$x \geq 0$$, $$|x| =x$$ --->$$|x^2-|x||=2$$ becomes $$|x^2-x|=2$$ ---> $$x^2-x=\pm 2$$ , giving you 2 quadratic equations

$$x^2-x-2=0$$ and $$x^2-x+2=0$$ (no real solutions, eliminate). From $$x^2-x-2=0$$ , you get x=2 and x=-1 but x=-1 is NOT allowed as you are assuming that for this case, $$x \geq 0$$.

Thus x=2 is the only possible solution from this scenario.

Case 2: when $$x<0$$---> $$|x| = -x$$ ---> $$|x^2-|x||=2$$ becomes $$|x^2+x|=2$$---> $$x^2+x=\pm 2$$ , giving you 2 quadratic equations again,
$$x^2+x-2=0$$ and$$x^2+x+2=0$$ (no real solutions, eliminate). From $$x^2+x-2=0$$, you get x=-2 and x=1 but x=1 is NOT allowed as you are assuming that for this case, $$x < 0$$.

Thus x=-2 is the only possible solution from this scenario.

Finally, when you combine both the scenarios, you see that the allowed values are $$x=\pm 2$$. Thus this statement is NOT sufficient to answer the question asked.

Hope this help. You have to be very careful about your assumptions in absolute value questions.
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2940
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

1
rohitgoel15 wrote:
If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2
(2) |x^2 - |x|| = 2

Question : x=?

Statement 1: |x - |x^2|| = 2
The solutions of the given equation are
x=2 and -1
NOT SUFFICIENT

Statement 2: |x^2 - |x|| = 2
The solutions of the given equation are
x=2 and -2
NOT SUFFICIENT

Combining the two statements
x = 2
SUFFICIENT

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7456
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2
(2) |x^2 - |x|| = 2

In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), it becomes |x^2|=x^2 -> x-x^2=-2, +2. In x-x^2=-2, +2, x^2-x-2=0, (x-2)(x+1)=0 -> x=2, -1, which is not unique and not sufficient.
For 2), in x^2-|x|=-2, 2, x^2=|x|^2 is derived. |x|^2-|x|=2, |x|^2-|x|-2=0, (|x|-2)(|x|+1)=0 -> x|=2, -1. -1 is impossible. |x|=2 -> x=-2,2, which is not unique and not sufficient.
When 1) & 2), x=2 is unique, which is sufficient.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
Intern  Joined: 06 May 2016
Posts: 15
WE: Education (Education)
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

A slightly different approach:

Statement 1
X is -1 or 2
Insufficient

Statement 2
X is 2 or -2
Insufficient

Combined
2 is the only common root for both equations = hence X must be 2.
Manager  S
Joined: 17 Jul 2017
Posts: 106
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

Bunuel wrote:
rohitgoel15 wrote:
If x is an integer, what is the value of x?
1) |x - |x2|| = 2
2) |x2 - |x|| = 2

I saw the solution and I think i cant even get close. On the test, I would prefer not to solve this question. But is there a short way to make an educated guess. Answer is not E as given in above posts, it's C. Also note that 1 and -1 do not satisfy statement (2).

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2. First of all: $$|x^2|=x^2$$ (as $$x^2$$ is a non-negative value). Square both sides: $$(x-x^2)^2=4$$ --> factor out $$x$$: $$x^2*(1-x)^2=4$$ --> as $$x$$ is an integer then $$x=2$$ or $$x=-1$$ (by trial and error: the product of two perfect square is 4: 1*4=4 or 4*1=4). Not sufficient.

(2) |x^2 - |x|| = 2 --> square both sides: $$(x^2-|x|)^2=4$$ --> factor out $$|x|$$: $$x^2*(|x|-1)^2=4$$ --> as $$x$$ is an integer then $$x=2$$ or $$x=-2$$. Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is $$x=2$$. Sufficient.

Hope it's clear.

Do square and mod cancel each other?
Intern  B
Joined: 18 Mar 2018
Posts: 20
If x is an integer, what is the value of x?  [#permalink]

Show Tags

In this circumstance, especially in the test, doing pure algebra may not be your first instinct. By looking at the question, we know that x is an integer and from the statements, it is clear we are dealing with small numbers so draw a table.

Attachment: 4.PNG [ 5.42 KiB | Viewed 307 times ]

Statement 1 alone: both x = -1 and x = 2 gives 2 --> Not sufficient
Statement 2 alone: both x = -2 and x = 2 gives 2 --> Not sufficient

Together, when they overlap, only x = 2 gives 2 - Sufficient.

The table seems tedious but squaring 1's and 2's should come to you instantly and this table can be drawn in <1.5 mins and hence this question can be solved in <2 mins.
Attachments 4.PNG [ 6.93 KiB | Viewed 304 times ]

Manager  S
Joined: 31 Oct 2018
Posts: 79
Location: India
Re: If x is an integer, what is the value of x?  [#permalink]

Show Tags

This is the correct explanation. Correct answer is E.

Apex231 wrote:
If x is an integer, what is the value of x?
1) |x - |x^2|| = 2
x^2 is always positive. so |x^2| = x^2

x - x^2 is negative since X^2 > x for an integer

-(x - x^2) = 2
-x + x^2 = 2
x^2 -x - 2 = 0
x^2 -2x +x - 2 = 0
(x-2) (x+1)
x = 2 or x = -1 , two values , not sufficient.

2) |x2 - |x|| = 2
x^2 - |x| is positive since X^2 > x for an integer

|x| can be positive or negative. so two scenarios.

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

or

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

Multiple values so not sufficient.

(1) + (2) , still not sufficient.

_________________
Happy to receive feedback on my post. Please give kudos if you find my content interesting. Re: If x is an integer, what is the value of x?   [#permalink] 06 Feb 2019, 09:18

Go to page   Previous    1   2   [ 30 posts ]

Display posts from previous: Sort by

If x is an integer, what is the value of x?  