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22 Jul 2022, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
7% (01:03) correct
93%
(02:10)
wrong
based on 28
sessions
History
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Time
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Not Attempted Yet
\((K/3)x + Ty = C\)
\(Kx + 12y = 21\)
\(Px + 15y = R\)
\((x, y) = (1, 1)\) is a solution of the system shown above. Is there any other solution?
(1) \(C = 7\)
(2) \(R = 24\)
Are You Up For the Challenge: 700 Level Questions
\(Kx + 12y = 21\)
\(Px + 15y = R\)
\((x, y) = (1, 1)\) is a solution of the system shown above. Is there any other solution?
(1) \(C = 7\)
(2) \(R = 24\)
Are You Up For the Challenge: 700 Level Questions
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
25 Jul 2022, 09:25
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(K/3)x+Ty=C
Kx+12y=21
Px+15y=R
(x,y)=(1,1) is a solution
Putting these values of x and y in the equations, we get
K/3 + T = C
K+12=21 => K=9
P+15=R
K=9 so 9/3 +T= C => 3+ T= C
Any two of the equations are needed to solve for x and y.
Knowing either the value of C or the value of R will give us two equations to work with (since the middle equation already has a known constant i.e. K=9)
Therefore both options are individually sufficient.
Ans is D
Kx+12y=21
Px+15y=R
(x,y)=(1,1) is a solution
Putting these values of x and y in the equations, we get
K/3 + T = C
K+12=21 => K=9
P+15=R
K=9 so 9/3 +T= C => 3+ T= C
Any two of the equations are needed to solve for x and y.
Knowing either the value of C or the value of R will give us two equations to work with (since the middle equation already has a known constant i.e. K=9)
Therefore both options are individually sufficient.
Ans is D
27 Jul 2022, 06:41
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Replace (x,y)=(1,1) into 3 equations, we have K = 9 & the relationship between C & T, P & P. In other words, the 3 equations equal:
(1) 3x + (C-3)y = C
(2) 9x + 12y = 21
(3) (R-15)x + 15y = R
These are all linear equations of 2 variables, so we can present them as lines on the coordinate plane.
These 3 lines already 1 shared point (1,1), so the question 'Is there any other solution?' = "Are these 3 actually just 1 same line?"
Statement 1: Replace C=7 into line (1) to find (1) & (2) is 1 line (let's call it l). Depend on R, (3) can be either l or another separate line crossing l at (1,1).
=> Insufficient
Statement 2: Replace R = 24 into line (3) to find (3) & (2) are 2 separate line regardless of (1). We can confidently answer No.
=> Sufficient
IMO B
(1) 3x + (C-3)y = C
(2) 9x + 12y = 21
(3) (R-15)x + 15y = R
These are all linear equations of 2 variables, so we can present them as lines on the coordinate plane.
These 3 lines already 1 shared point (1,1), so the question 'Is there any other solution?' = "Are these 3 actually just 1 same line?"
Statement 1: Replace C=7 into line (1) to find (1) & (2) is 1 line (let's call it l). Depend on R, (3) can be either l or another separate line crossing l at (1,1).
=> Insufficient
Statement 2: Replace R = 24 into line (3) to find (3) & (2) are 2 separate line regardless of (1). We can confidently answer No.
=> Sufficient
IMO B
Bunuel
