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

 It is currently 22 Feb 2019, 17:34

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0

Author Message
TAGS:

### Hide Tags

Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1207
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

### Show Tags

20 Oct 2018, 08:59
5
00:00

Difficulty:

15% (low)

Question Stats:

85% (01:32) correct 15% (01:13) wrong based on 45 sessions

### HideShow timer Statistics

If x is a number such that $$x^2-3x+2 = 0$$ and $$x^3+2x^2-x-2 = 0$$, what is the value of $$x+3$$?

A) 1
B) 2
C) 3
D) 4
E) 5

GMATbuster's Weekly GMAT Quant Quiz #5 Ques No 1

_________________
Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1207
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

### Show Tags

20 Oct 2018, 09:00

Official Explanation:

$$x^2-3x+2 = (x-1)(x-2)$$

hence x = 1,2

No need to solve the cubic equation, $$x^3+2x^2-x-x=0$$, We can just substitute the value of x = 1, 2 in cubic equation to verify.

only x = 1 satisfy the equation, hence x =1

Question asks for value of x+3

hence Answer = x+3 = 4.
_________________
Intern
Joined: 05 Sep 2016
Posts: 20
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

### Show Tags

20 Oct 2018, 09:03
x^2−3x+2=0

i.e. (x+3) (x-1)
therefore x can be -3 or 1

x=1 satisfies the equation therefore x+3 = 4

_________________

[i]"Take up one idea. Make that one idea your life"

Intern
Joined: 08 Feb 2018
Posts: 20
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

### Show Tags

20 Oct 2018, 09:07
D.
Factorising the first quadratic gives x=2 and x=1, the second quadratic gives x=1,-2. For common value x=1, x+3 equals 4.
Manager
Joined: 16 Sep 2011
Posts: 97
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

### Show Tags

Updated on: 20 Oct 2018, 20:12
x^2-3x+2=0 and x^3+2x^2-x-2=0
A) 1
B) 2
C) 3
D) 4
E) 5

x^2-3x+2=0
which is x^2-2x-x+2=0
which is x(x-2)-1(x-2)=0
which means (x-1) (x-2)=0, which means 1 and 2 are roots of the equation

Now x^3+2x^2-x-2=0
which is x^2(x+2)-1(x+2)=0
which is (x^2-1)(x+2)=0
which is (x-1)(x+1)(x+2)=0. ..(as a^2-b^2 = (a-b)(a+b))
so x can be either 1, -1 or -2 i.e 1, -1 and -2 are roots of the cubic equation

Common root between the two equation(quadratic and cubic) is only 1 at which both equation becomes zero, hence x = 1
hence x+3= 4 is the answer

Originally posted by pk123 on 20 Oct 2018, 10:22.
Last edited by pk123 on 20 Oct 2018, 20:12, edited 2 times in total.
Intern
Joined: 17 Dec 2016
Posts: 19
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

### Show Tags

Updated on: 20 Oct 2018, 19:49
Below is my attempt

$$x^2$$ - 3x + 2 = 0 --> (x-2)(x-1) = 0 --> x =2 or x = 1
$$x^3$$ + 2$$x^2$$-x-2 = 0 --> (x+2)($$x^2$$-1) = 0 --> x = 1 or x = -1 or x = -2

Combine 2 solutions --> x = 1
--> x +3 = 4

Thank you!

Originally posted by yenbh on 20 Oct 2018, 10:23.
Last edited by yenbh on 20 Oct 2018, 19:49, edited 1 time in total.
Intern
Joined: 04 Apr 2018
Posts: 21
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

### Show Tags

20 Oct 2018, 10:30
This reply is hidden until the winner is announced.
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0   [#permalink] 20 Oct 2018, 10:30
Display posts from previous: Sort by