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

 It is currently 15 Nov 2019, 13:48 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straig

Author Message
TAGS:

### Hide Tags

Senior Manager  V
Joined: 25 Dec 2018
Posts: 496
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straig  [#permalink]

### Show Tags

2 00:00

Difficulty:   65% (hard)

Question Stats: 41% (02:10) correct 59% (01:39) wrong based on 17 sessions

### HideShow timer Statistics

The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straight line if

A) a= -1 or 2
B) a = 2 or 1
C) a=2or−12
D) a=2or12
E) None of these.
Director  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 995
WE: Supply Chain Management (Energy and Utilities)
Re: The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straig  [#permalink]

### Show Tags

1
mangamma wrote:
The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straight line if

A) a= -1 or 2
B) a = 2 or 1
C) a=2or−12
D) a=2or12
E) None of these.

Three points are collinear if the value of area of triangle formed by the three points is zero.

So, $$(a+1)(3-2a)–1(2a+1–2a–2) +2a(2a+1)–3(2a+2)=0$$
Or, $$2a^2-3a-2=0$$
Or, $$2a^2-4a+a-2=0$$
Or, 2a(a-2)+1(a-2)=0
Or, (a-2)(2a+1)=0
Or a=2, -1/2

Ans. (C)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Director  V
Joined: 27 May 2012
Posts: 936
Re: The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straig  [#permalink]

### Show Tags

1
1
mangamma wrote:
The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straight line if

A) a= -1 or 2
B) a = 2 or 1
C) a=2or−12
D) a=2or12
E) None of these.

If the points lie in a straight line then their slope will be equal.
Taking slopes of point 2 and 3 and equating with the slope of point 1 and 2
$$\frac{2a-3}{1} =\frac{2}{a}$$
solving this gives a= 2 or a= $$-\frac{1}{2}$$

P.S. option C should be corrected it's not -12 but -$$\frac{1}{2}$$ Re: The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straig   [#permalink] 12 Mar 2019, 04:37
Display posts from previous: Sort by

# The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straig  