GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 09 Apr 2020, 20:16

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

The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2

  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: 62676
The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post 14 Feb 2020, 00:55
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:34) correct 14% (01:37) wrong based on 49 sessions

HideShow timer Statistics

Director
Director
avatar
V
Joined: 30 Sep 2017
Posts: 785
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
Re: The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post 14 Feb 2020, 01:16
1
(1) x = 1/4*y + a
(2) y = 1/4*x + b

(1)+(2)
(x+y) = (x+y)/4 + (a+b)
3.(x+y)/4 = (a+b)

(x,y) =(1,2) then
3.(1+2)/4=(a+b)
(a+b)=9/4

FINAL ANSWER IS (D)

Posted from my mobile device
CEO
CEO
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3480
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post 14 Feb 2020, 01:17
1
Quote:
The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2). What is the value of a + b?

A. 0
B. 3/4
C. 1
D. 9/4
E. 3


For intersection of x = 1/4*y + a i.e. y = 4*(x-a) and y = 1/4*x + b

4*(x-a) = 1/4*x + b

i.e. 16(x-a) = x+4b
i.e. 16x - 16a = x + 4b
i.e. 15x = 4b + 16a
i.e. x = (1/15)*(4b + 16a) = 1 [i.e. x coordinate of point (1,2)]
i.e. 4b + 16a = 15

and y = 4*(x-a) = 4*(x-a) = 2 [i.e. y coordinate of point (1,2)]

i.e. x - a = 1/2
i.e. (1/15)*(4b + 16a) - a = 1/2
i.w. 4b + 16a - 15a = 15/2
i.e. 4b + a = 15/2

Taking the difference of the two equations in bold letters

(4b + 16a) - (4b + a) = 15 - (15/2)

i.e. 15 a = 15/2
i.e. a = 1/2

Since, 4b + a = 15/2
i.e. 4b = (15/2) - (1/2) = 7
i.e. b = 7/4

i.e. a+b = (1/2)+(7/4) = 9/4

Answer: Option D
_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
Click Here for Uneditable GOOGLE reviews

Click here for Our VERBAL & QUANT private tutoring package details
My Recent Posts Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Standard Deviation l Q-4-Functions
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Intern
Intern
avatar
B
Joined: 30 Nov 2019
Posts: 21
Re: The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post 14 Feb 2020, 01:20
1
as both the lines pass through point (1,2)
substitute 1,2 in each of the given equation we get values of a and b as 1/2 and 7/4 which adds to 9/4

IMO ans is D
VP
VP
avatar
D
Joined: 24 Nov 2016
Posts: 1369
Location: United States
Re: The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post 14 Feb 2020, 03:37
1
Quote:
The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2). What is the value of a + b?

A. 0
B. 3/4
C. 1
D. 9/4
E. 3


x = 1/4*y + a… 1=1/4(2)+a…a=1-1/2=1/2=2/4
y = 1/4*x + b…2=1/4+b…b=2-1/4=8-1/4=7/4
a+b=(2+7)/4=9/4

Ans (D)
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6036
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post 14 Feb 2020, 08:34
for given two eqn of line substitute value of x & y
we get
a= 1/2 and b = 7/4
a+b ; 9/4
IMO D


The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2). What is the value of a + b?

A. 0
B. 3/4
C. 1
D. 9/4
E. 3
Director
Director
User avatar
V
Joined: 28 Jul 2016
Posts: 921
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE: Project Management (Investment Banking)
Reviews Badge
Re: The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post 14 Feb 2020, 12:05
1
The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2). What is the value of a + b?

point (1,2) would satisfy both equations then
or
\( x = \frac{1}{4}*y + a\)
\(1 =\frac{2}{4}+a\) or a =\(\frac{1}{2}\)
\(y = \frac{1}{4}*x + b \)
\(2= \frac{1}{4}+b \)or b = \(\frac{7}{4}\)
\(a+b = \frac{1}{2}+\frac{7}{4} = \frac{9}{4} \)
D
_________________

Keep it simple. Keep it blank
Director
Director
avatar
P
Joined: 01 Mar 2019
Posts: 502
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GMAT 1: 580 Q48 V21
GPA: 4
Reviews Badge
The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post Updated on: 19 Feb 2020, 09:57
.

Originally posted by madgmat2019 on 15 Feb 2020, 01:16.
Last edited by madgmat2019 on 19 Feb 2020, 09:57, edited 1 time in total.
Director
Director
avatar
P
Joined: 25 Jul 2018
Posts: 614
Re: The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2  [#permalink]

Show Tags

New post 16 Feb 2020, 13:33
1
The lines \(x = \frac{1}{4}*y + a\) and \(y = \frac{1}{4}*x + b\) intersect at the point (1, 2). What is the value of a + b?

--> \(1= (\frac{1}{4})*2+a\) --> \(a=\frac{1}{2}\)

--> \(2=(\frac{1}{4})*1+ b\) --> \(b= \frac{7}{4 }\)

\(a+b = \frac{1}{2}+ \frac{7}{4} = \frac{(2+7)}{4}= \frac{9}{4}
\)

The answer is D.
GMAT Club Bot
Re: The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2   [#permalink] 16 Feb 2020, 13:33
Display posts from previous: Sort by

The lines x = 1/4*y + a and y = 1/4*x + b intersect at the point (1, 2

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





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