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twobagels
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Let 'n' be the number of pairs of values of 'b' and 'c' 22 Feb 2022, 23:01
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C
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95% (hard)

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40% (01:54) correct 60% (02:10) wrong based on 136 sessions

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Let 'n' be the number of pairs of values of 'b' and 'c' such that 3*x + b*y + c = 0 and c*x - 2*y + 12 = 0 have the same graph. Then n is:

A. 0
B. 1
C. 2
D. Finite but more than 2
E. greater than any finite number
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C
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gkumar08
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Let 'n' be the number of pairs of values of 'b' and 'c' 02 Apr 2022, 10:32
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Ans is C
Since they have same graph so
3/c = b/(-2)=c/12
So we get c=6,-6 b=1
So two set of values

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Let 'n' be the number of pairs of values of 'b' and 'c' 06 Jun 2022, 09:13
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gkumar08
Ans is C
Since they have same graph so
3/c = b/(-2)=c/12
So we get c=6,-6 b=1
So two set of values

Posted from my mobile device


Why cant B be -1
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Let 'n' be the number of pairs of values of 'b' and 'c' 06 Jun 2022, 09:43
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gkumar08
Ans is C
Since they have same graph so
3/c = b/(-2)=c/12
So we get c=6,-6 b=1
So two set of values

Posted from my mobile device


Why cant B be -1

It can:

There are two solution pairs for the answer:

1st solution pair for (b , c) = (-1 , 6)

2nd solution pair for (b , c) =. (+1 , -6)

Only these two solution pairs will make the lines represented by the linear equations coincident lines (I.e., the same line with infinite number of solutions)
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Let 'n' be the number of pairs of values of 'b' and 'c' 07 Feb 2024, 22:46
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twobagels
Let 'n' be the number of pairs of values of 'b' and 'c' such that 3*x + b*y + c = 0 and c*x - 2*y + 12 = 0 have the same graph. Then n is:

A. 0
B. 1
C. 2
D. Finite but more than 2
E. greater than any finite number

 
Though GMAT Focus does not have geometry, this part of co-ordinate geometry is included under graphing. 

For the lines

3*x + b*y + c = 0 and
c*x - 2*y + 12 = 0

to be the same, \(\frac{3}{c} = \frac{b}{-2} = \frac{c}{12}\)
\(c^2 = 36\)
c = 6, -6
When c = 6, b = -1 and when c = -6, b = 1

Answer (C)

­
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Let 'n' be the number of pairs of values of 'b' and 'c' 08 Feb 2024, 00:56
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@twobagelsGiven: Let 'n' be the number of pairs of values of 'b' and 'c' such that 3*x + b*y + c = 0 and c*x - 2*y + 12 = 0 have the same graph.
Asked: Then n is:

3x + by + c = 0
cx - 2y + 12 = 0
have the same graph.

3/c = -b/2 = c/12
cˆ2 = 36; c = 6 or -6

Case 1: c=6
b = -c/6 = -1

Case 2: c=-6
b = -c/6 = 1

(b,c) = {(1,-6),(-1,6)} : 2 pair of values 

IMO C­
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Let 'n' be the number of pairs of values of 'b' and 'c' 22 Jan 2025, 23:57
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KarishmaB can you explain this graph equation pls ? Why should they be equal
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Let 'n' be the number of pairs of values of 'b' and 'c' Updated on: 23 Jan 2025, 22:06
Originally posted by KarishmaB on 23 Jan 2025, 06:26.
Last edited by KarishmaB on 23 Jan 2025, 22:06, edited 2 times in total.
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Elite097
KarishmaB can you explain this graph equation pls ? Why should they be equal


This is related to the basics of linear simultaneous equations.

If two equations represent the same line, then

ax + by + c = 0
dx + ey + f = 0

a/d = b/e = c/f

If the lines are parallel, then

a/d = b/e but not equal to c/f


If the lines are intersecting,

a/d is not equal to b/e

Here is a video explaining this and other relations:
Linear Equations: https://youtu.be/Nh77CobN9mQ
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Let 'n' be the number of pairs of values of 'b' and 'c' 23 Jan 2025, 06:40
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3*x + b*y + c = 0 and
c*x - 2*y + 12 = 0



c = 6, -6
c = 6, b = -1
c = -6, b = 1
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