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In the XY-plane, a line l passes through the origin and has a slope 3.

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In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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New post 16 Oct 2018, 03:52
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In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 9/2

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Re: In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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New post 16 Oct 2018, 04:10
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Bunuel wrote:
In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 92


A line l passes through the origin and has a slope 3

Slope of Origin (0,0) and (1, a) = (a-0)/(1-0)=3

a=3

Slope of Origin (0,0) and (b,2) = (2-0)/(b-0) =3

b=2/3

a/b= 3/(2/3) = 9/2

Bunuel Seems like typo Option E must be 9/2
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Re: In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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New post 16 Oct 2018, 04:12
NandishSS wrote:
Bunuel wrote:
In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 92


A line l passes through the origin and has a slope 3

Slope of Origin (0,0) and (1, a) = (a-0)/(1-0)=3

a=3

Slope of Origin (0,0) and (b,2) = (2-0)/(b-0) =3

b=2/3

a/b= 3/(2/3) = 9/2

Bunuel Seems like typo Option E must be 9/2

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Fixed. Thank you.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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New post 16 Oct 2018, 04:18
Bunuel wrote:
In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 9/2


line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l,

i,e. Slope of line using points (0,0) and (1,a) = (a-0)/(1-0) = 3

i.e. a = 3

Now, Slope of line using points (0,0) and (b,2) = (2-0)/(b-0) = 3

i.e. b = 2/3

i.e. a/b = 3/(2/3) = 9/2

Answer: Option E
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Re: In the XY-plane, a line l passes through the origin and has a slope 3.  [#permalink]

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New post 16 Oct 2018, 10:51
Bunuel wrote:
In the XY-plane, a line l passes through the origin and has a slope 3. If points (1, a) and (b, 2) are on the line l, what is the value of a/b?

(A) 2
(B) 3
(C) 2/3
(D) 2/9
(E) 9/2


let (0,0) = \((x_1,y_1)\)

\(slope = \frac{y_2 - y_1}{x_2 - x_1}\)

\(3 = \frac{a - 0}{1 - 0}\)

a = 3

then \(3 = \frac{2 - 0}{b - 0}\)

3b = 2

\(b = \frac{2}{3}\)

\(\frac{a}{b}\) = \(3/\frac{2}{3}\)

\(\frac{a}{b}\) = \(3 * \frac{3}{2}\) = \(\frac{9}{2}\)

Answer choice E
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Re: In the XY-plane, a line l passes through the origin and has a slope 3.   [#permalink] 16 Oct 2018, 10:51
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