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

 It is currently 10 Dec 2018, 21:48

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

# If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al

Author Message
TAGS:

### Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4489
If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al  [#permalink]

### Show Tags

26 Nov 2016, 12:20
13
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:37) correct 29% (02:50) wrong based on 324 sessions

### HideShow timer Statistics

If $$|(x – 3)^2 + 2| < |x – 7|$$ , which of the following expresses the allowable range for x?

(A) 1 < x < 4

(B) 1 < x < 7

(C) – 1 < x < 4 and 7 < x

(D) x < – 1 and 4 < x < 7

(E) – 7 < x < 4 and 7 < x

Absolute value inequalities are a rare and tricky topic on the GMAT. For a detailed discussion of this question type, as well as the OE for this particular question, see:
Absolute Value Inequalities

Mike

_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Current Student
Joined: 06 Jul 2016
Posts: 39
Location: India
Concentration: Operations, General Management
GMAT 1: 610 Q49 V25
WE: General Management (Energy and Utilities)
If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al  [#permalink]

### Show Tags

27 Nov 2016, 00:03
6
Hi,

I always go for plugging in for these kind of questions. Its fast and quite reliable.

Lets look at one option at at time:-

A. 1<x<4: Lets take X= 2 and 3, the equation is satisfied. Hold on to it.

B. 1<x<7: We have already tested the equation for x=2 and 3. Now, we can check it with X=5, which gives the result as false. So, discard this option.

C. -1<x<4 and x<7: In the above statement, we have already tested for X=5 or we can say that for the second part of this statement x<7. So, this statement is false. However, just to be sure, putting x=0 will give false. So, discard.

D. X<-1 and 4<x<7: As done earlier, the statement has proven to be false for X=5. So, this statement can also be discarded.

E. -7<x<4 and x<7: Already tested for X=0, 2 and 5. So discard.

Thus the correct answer is A.
##### General Discussion
Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1376
Location: Viet Nam
If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al  [#permalink]

### Show Tags

26 Nov 2016, 19:41
3
2
mikemcgarry wrote:
If $$|(x – 3)^2 + 2| < |x – 7|$$ , which of the following expresses the allowable range for x?

(A) 1 < x < 4

(B) 1 < x < 7

(C) – 1 < x < 4 and 7 < x

(D) x < – 1 and 4 < x < 7

(E) – 7 < x < 4 and 7 < x

Note that $$(x-3)^2+2 \geq 2 >0 \quad\forall x \implies |(x – 3)^2 + 2| = (x – 3)^2 + 2$$

If $$x \geq 7 \implies (x – 3)^2 + 2 < x – 7 \implies x^2 -6x +9+2<x-7 \implies x^2 -7x +18 <0$$
We have $$x^2 -7x+18 = x^2 -2 \times x \times \frac{7}{2} +(\frac{7}{2})^2 +\frac{23}{4} = (x-\frac{7}{2})^2 +\frac{23}{4} >0$$
So in this case, there is no $$x$$ satisfied the equation.

If $$x <7 \implies (x – 3)^2 + 2 < 7-x \implies x^2 -6x +9+2<7-x \implies x^2 -5x +4 <0$$
$$\implies (x-1)(x-4)<0 \implies 1<x<4$$

_________________
Manager
Joined: 09 Jun 2018
Posts: 184
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
Re: If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al  [#permalink]

### Show Tags

17 Jun 2018, 19:50
I looked at the options and substituted 6 and saw anything greater than 6 was also not going to work and was able to eliminate B,C,D,E in one shot.
_________________

If you found this relevant and useful, please Smash that Kudos button!

Manager
Joined: 18 Apr 2018
Posts: 73
Re: If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al  [#permalink]

### Show Tags

09 Jul 2018, 05:04
broall wrote:
mikemcgarry wrote:
If $$|(x – 3)^2 + 2| < |x – 7|$$ , which of the following expresses the allowable range for x?

(A) 1 < x < 4

(B) 1 < x < 7

(C) – 1 < x < 4 and 7 < x

(D) x < – 1 and 4 < x < 7

(E) – 7 < x < 4 and 7 < x

Note that $$(x-3)^2+2 \geq 2 >0 \quad\forall x \implies |(x – 3)^2 + 2| = (x – 3)^2 + 2$$

If $$x \geq 7 \implies (x – 3)^2 + 2 < x – 7 \implies x^2 -6x +9+2<x-7 \implies x^2 -7x +18 <0$$
We have $$x^2 -7x+18 = x^2 -2 \times x \times \frac{7}{2} +(\frac{7}{2})^2 +\frac{23}{4} = (x-\frac{7}{2})^2 +\frac{23}{4} >0$$
So in this case, there is no $$x$$ satisfied the equation.

If $$x <7 \implies (x – 3)^2 + 2 < 7-x \implies x^2 -6x +9+2<7-x \implies x^2 -5x +4 <0$$
$$\implies (x-1)(x-4)<0 \implies 1<x<4$$

Yes the answer may seem correct but I don't understand how (x−1)(x−4)<0⟹1<x<4⟹(x−1)(x−4)<0⟹1<x<4
Shouldn't it be x< 1 and x<4 and the correct answer just x<4 It looks like a subset.

Posted from my mobile device
Manager
Joined: 07 Feb 2017
Posts: 188
Re: If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al  [#permalink]

### Show Tags

09 Jul 2018, 05:41
Based on Answer Choices, try x=5
Inequality not true
Eliminate B, C, D, E
Re: If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al &nbs [#permalink] 09 Jul 2018, 05:41
Display posts from previous: Sort by

# If |(x – 3)^2 + 2| < |x – 7| , which of the following expresses the al

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.