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

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Director
Joined: 25 Dec 2018
Posts: 607
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]

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05 Mar 2019, 22:19
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Difficulty:

65% (hard)

Question Stats:

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

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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
Status: Learning stage
Joined: 01 Oct 2017
Posts: 980
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]

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05 Mar 2019, 22:48
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)
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Director
Joined: 27 May 2012
Posts: 952
Re: The points (a+1, 1), (2a+1, 3) and (2a + 2, 2a) lie on the same straig  [#permalink]

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12 Mar 2019, 03:37
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, 03:37
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