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

 It is currently 16 Dec 2018, 07:22

### 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 GMAT Prep Hour

December 16, 2018

December 16, 2018

03:00 PM EST

04:00 PM EST

Strategies and techniques for approaching featured GMAT topics
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

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

# If x is an integer, what is the value of x such that |-5x + 7| is mini

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51227
If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

10 Aug 2018, 02:32
00:00

Difficulty:

5% (low)

Question Stats:

81% (00:38) correct 19% (00:37) wrong based on 197 sessions

### HideShow timer Statistics

If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4

_________________
Director
Joined: 31 Oct 2013
Posts: 883
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

10 Aug 2018, 02:36
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4

Back solve the question. Scan each answer choice. Only option B works here.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

10 Aug 2018, 02:46
1
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4

Minimum value of |-5x + 7| is zero
Or, |-5x + 7|=0
Or, -5x+7=0
Or, -5x=-7
Or, x=7/5=1.4

So, integer value less than 1.4 is 1.
So, when x=1, |-5x + 7|=|-5+7|=2

Ans. (B)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2313
If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

13 Aug 2018, 06:53

Solution

Given:
• We are given an expression, |-5x + 7|
• x is an integer

To find:
• Value of x, such that |-5x + 7| is minimum

Approach and Working:
• The minimum value of a modulus function is 0.
• So, |-5x + 7| will be equal to 0, when x = 7/5 = 1.4
• But, we need to find an integer value of x, for which |-5x + 7| is minimum
• Since, the value of |-5x + 7|increases for both x > 1.4 and x < 1.4, so we need to check its value for the integers close to 1.4, which are 1 and 2.
o For x = 1, the value of |-5x + 7| is 2
o For x = 2, the value of |-5x + 7| is 3

Therefore, the value of |-5x + 7| is minimum when x = 1

Hence, the correct answer is option B

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

18 Aug 2018, 18:29
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4

Recall that the smallest possible value of an absolute value expression is zero. Thus, to minimize |-5x + 7|, we need to get |-5x + 7| as close to zero as possible.

When x is 1, we have:

|-5(1) + 7| = |2| = 2, which is the smallest we can make the given expression when x is an integer.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 01 Jan 2018
Posts: 69
Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

18 Aug 2018, 18:42
We can substitute for x and check. When x= 0 ,we get 7,
When x=1,we get 2
When x=2,we get 3
We can stop here and conclude that B is the correct choice.

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
_________________

+1 Kudos if you find this post helpful

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

18 Aug 2018, 19:15
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4

What is the minimum value of any absolute value? 0.
|-5x + 7| = 0
x = 7/5
But we need x to be an integer. 7/5 lies between 1 and 2, closer to 1. So when x = 1, |-5x + 7| will take the minimum value.

If you are not sure why, think of what the graph of y = |-5x + 7| would look like. It will be a symmetrical V resting on x = 7/5. The value of y will continuously increase on both sides of x = 7/5. When you move to the left on the x axis, at x = 1, y will be 2. When you move to the right on the x axis, at x = 2, y will be 3.
The minimum value for an integer value of x will be y = 2 for x = 1.
_________________

Karishma
Veritas Prep GMAT Instructor

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

18 Aug 2018, 19:24
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4

Responding to a pm:

Quote:
I am stuck b/w A and B. If they are looking for minimum value when you plug in A you get + / - 7 and with B you get +-2. So shouldn't the answer be A given that -7 is less than -2. (or minimum value.)??

We are looking for the minimum value of |-5x + 7|.
If we put x = 0, |-5x + 7| = |-5*0 + 7| = 7
Note that |7| is NOT 7 or -7.
|7| and |-7| both are equal to 7 ONLY

If we put x = 1, |-5x + 7| = |-5*1 + 7| = 2 ONLY

You are getting confused with the definition of absolute values:

|x| = x if x >= 0
|x| = -x if x < 0

So if x = 5, |x| = x = 5 (because x > 0)
If x = -5, |x| = -x = - (-5) = 5 (because x < 0)

That is the whole point of absolute value: It is never negative. It is the distance in physical terms so it cannot be negative.
_________________

Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: If x is an integer, what is the value of x such that |-5x + 7| is mini  [#permalink]

### Show Tags

17 Nov 2018, 01:50
Bunuel wrote:
If x is an integer, what is the value of x such that |-5x + 7| is minimized?

A. 0
B. 1
C. 2
D. 3
E. 4

What is the minimum value of any absolute value? 0.
|-5x + 7| = 0
x = 7/5
But we need x to be an integer. 7/5 lies between 1 and 2, closer to 1. So when x = 1, |-5x + 7| will take the minimum value.

If you are not sure why, think of what the graph of y = |-5x + 7| would look like. It will be a symmetrical V resting on x = 7/5. The value of y will continuously increase on both sides of x = 7/5. When you move to the left on the x axis, at x = 1, y will be 2. When you move to the right on the x axis, at x = 2, y will be 3.
The minimum value for an integer value of x will be y = 2 for x = 1.

math to english:

|x - 5| = 10 means "the distance of x is 10 centered around 5"

what does |-5x + 7| mean?
is this correct: distance of -5x centered around 7

regards
Re: If x is an integer, what is the value of x such that |-5x + 7| is mini &nbs [#permalink] 17 Nov 2018, 01:50
Display posts from previous: Sort by