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

It is currently 13 Dec 2019, 15:13

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

If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59721
If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 29 Nov 2019, 03:26
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

58% (02:23) correct 42% (02:33) wrong based on 53 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 29 Nov 2019, 03:50
1
value of y=|6x−18|+|−7x+7|+|3x+2| is minimised at x= 1 ; y = 17
IMO B

If y=|6x−18|+|−7x+7|+|3x+2|, for what x-value is the value of y minimized?

A. −23−23
B. 1
C. 2
D. 3
E. 7272
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 971
Location: United States
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 29 Nov 2019, 05:00
1
Quote:
If y=|6x−18|+|−7x+7|+|3x+2|, for what x-value is the value of y minimized?

A. −2/3
B. 1
C. 2
D. 3
E. 7/2


Replace each answer choice into y=|6x−18|+|−7x+7|+|3x+2| and the least value of y is when x=1.

Ans (B)
Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 337
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Reviews Badge
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 29 Nov 2019, 09:09
1
From options

A. -2/3.....33+
B. 1........17........ correct
C. 2........21
D. 3........25
E. 7/2......28+



OA:B

Posted from my mobile device
Senior Manager
Senior Manager
avatar
P
Joined: 25 Jul 2018
Posts: 401
CAT Tests
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 29 Nov 2019, 15:51
1
|6x —18|+ |—7x+7|+ |3x+2| Is always greater than zero(inclusive)

—> the minimum value of y could be 0, if 6x—18=0, —7x+7=0, and 3x+2=0 at the same time.
—> we have to check the values of y ( if x=3, x= 1, and x= —2/3)
y(3)= 0+ 14+ 11= 25
y(1)= 12+ 0+ 5= 17
y(—2/3)= 22+ 35/3+ 0= 101/3

Minimum value of y should be 17, if x is equal to 1.
The answer is B

Posted from my mobile device
VP
VP
avatar
D
Joined: 20 Jul 2017
Posts: 1147
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 29 Nov 2019, 18:24
1
If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value of y minimized?

We can substitute and check for which value of x from the option is the value of y least.

—> y = 6|x - 3| + 7|-x + 1| + |3x + 2|

A. -2/3 ; y = 6|-2/3 - 3| + 7|-(-2/3) + 1| + |3(-2/3) + 2| = 22 + 35/3 = 101/3

B. 1 ; y = 6|1 - 3| + 7|-1 + 1| + |3(1) + 2| = 12 + 0 + 5 = 17

C. 2 ; y = 6|2 - 3| + 7|-2 + 1| + |3(2) + 2| = 6 + 7 + 8 = 21

D. 3 ; y = 6|3 - 3| + 7|-3 + 1| + |3(3) + 2| = 0 + 14 + 11 = 25

E. 7/2 ; y = 6|7/2 - 3| + 7|-7/2 + 1| + |3(7/2) + 2| = 3 + 35/2 + 25/2 = 33

Least value of y is 17, when x = 1

IMO Option B

Posted from my mobile device
Director
Director
avatar
P
Joined: 18 May 2019
Posts: 554
GMAT ToolKit User Premium Member CAT Tests
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 29 Nov 2019, 20:28
2
y=|6x-18|+|7-7x|+|3x+2|
when x=-2/3
y=22+35/3+0=33+2/3
when x=1
y=12+5=17
when x=2
y=6+7+8=21
when x=3
y=14+11=25
Obviously, we can see that x=3.5 will yield a much larger value that x=3 since we can see a trend whereby when x increases, y also increases.
when x=3.5
y=3+17.5+12.5=31
The least value out of the options is when x=1

The answer is B.
Senior Manager
Senior Manager
avatar
D
Joined: 30 Sep 2017
Posts: 468
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 29 Nov 2019, 21:10
1
Fastest and surest way to do this is to plug-in numbers (from choices) to the equation and see any inflection point among x values.

y = |6x - 18| + |-7x + 7| + |3x + 2|

A. x=-2/3 --> y= 22 + 2.3 + 0 = 24.3

B. x=1 --> y= 12 + 0 + 5 = 17

C. x=2 --> y= 6 + 7 + 8 = 21

D. x=3 --> y= 0 + 14 + 11

E. x=3.5 --> y= 3 + 17.5 + 12.5

For this question, we just need to calculate choices (A),(B),(C). We see clear inflection point at choice (B).. Calculation on choices (D) and (E) is shown for clarity purpose only.

Final answer is (B)

Posted from my mobile device
Senior Manager
Senior Manager
avatar
P
Joined: 07 Mar 2019
Posts: 460
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
CAT Tests
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 30 Nov 2019, 01:41
1
If y=|6x−18|+|−7x+7|+|3x+2|, for what x-value is the value of y minimized?

A. -\(\frac{2}{3}\)
B. 1
C. 2
D. 3
E. \(\frac{7}{2}\)

Here x > 3 or x < 3 OR x > 1 or x < 1 OR x > -\(\frac{2}{3}\) or x < -\(\frac{2}{3}\)
Since y is sum of absolute values we have to find its least possible positive value which would be possible for only one value of x.

Checking for each value -
x = -\(\frac{2}{3}\), y = 24
x = 1, y = 17
x = 2, y = 21
x = 3, y = 25
x = \(\frac{7}{2}\), y = 33

Answer B.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Intern
Intern
avatar
B
Joined: 21 Apr 2019
Posts: 33
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value  [#permalink]

Show Tags

New post 09 Dec 2019, 05:21
Greatest coefficient of X is 7. So how can we minimize that term. We'd easily land up with 1 which makes that 0.
GMAT Club Bot
Re: If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value   [#permalink] 09 Dec 2019, 05:21
Display posts from previous: Sort by

If y = |6x - 18| + |-7x + 7| + |3x + 2|, for what x-value is the value

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





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