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09 Jan 2020, 01:40
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
53% (02:48) correct
47%
(02:34)
wrong
based on 329
sessions
History
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Dealership A and Dealership B both sell cars and trucks. If the ratio of cars to trucks each dealership sold in the last month is the same for both dealerships, did Dealership A sell the same number of cars and trucks last month?
(1) The number of trucks sold by Dealership B was three times the number of cars sold by Dealership A.
(2) The number of cars sold by Dealership B was equal to the number of trucks sold by Dealership A plus twice the number of cars sold by Dealership A.
Are You Up For the Challenge: 700 Level Questions
09 Jan 2020, 04:13
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Let the number of cars & trucks sold by Dealership A be \(c_A\) & \(t_A\) respectively and that of Dealership B be \(c_B\) & \(t_B\)
Given, \(\frac{c_A}{t_A} = \frac{c_B}{t_B}\)
Question: Is \(c_A\) = \(t_A\)?
(1) The number of trucks sold by Dealership B was three times the number of cars sold by Dealership A.
--> \(t_B\) = 3\(c_A\)
Does not talk anything about \(t_A\) --> Insufficient
(2) The number of cars sold by Dealership B was equal to the number of trucks sold by Dealership A plus twice the number of cars sold by Dealership A.
--> \(c_B\) = \(t_A\) + 2\(c_A\)
Does not talk anything about \(t_B\) --> Insufficient
Combining (1) & (2),
\(t_B\) = 3\(c_A\) & \(c_B\) = \(t_A\) + 2\(c_A\)
and we have \(\frac{c_A}{t_A} = \frac{c_B}{t_B}\)
--> \(\frac{c_A}{t_A} = \frac{t_A + 2c_A}{3c_A}\)
--> \(3c_A^2 = t_A^2 + 2c_At_A\)
--> \(3c_A^2 - 2c_At_A - t_A^2 = 0\)
--> \(3c_A^2 - 3c_At_A + c_At_A - t_A^2 = 0\)
--> \(3c_A(c_A - t_A) + t_A(c_A - t_A) = 0\)
--> \((3c_A + t_A)(c_A - t_A) = 0\)
--> c_A = t_A [Note that 3c_A + t_A = 0 is not possible] --> Sufficient
IMO Option C
Given, \(\frac{c_A}{t_A} = \frac{c_B}{t_B}\)
Question: Is \(c_A\) = \(t_A\)?
(1) The number of trucks sold by Dealership B was three times the number of cars sold by Dealership A.
--> \(t_B\) = 3\(c_A\)
Does not talk anything about \(t_A\) --> Insufficient
(2) The number of cars sold by Dealership B was equal to the number of trucks sold by Dealership A plus twice the number of cars sold by Dealership A.
--> \(c_B\) = \(t_A\) + 2\(c_A\)
Does not talk anything about \(t_B\) --> Insufficient
Combining (1) & (2),
\(t_B\) = 3\(c_A\) & \(c_B\) = \(t_A\) + 2\(c_A\)
and we have \(\frac{c_A}{t_A} = \frac{c_B}{t_B}\)
--> \(\frac{c_A}{t_A} = \frac{t_A + 2c_A}{3c_A}\)
--> \(3c_A^2 = t_A^2 + 2c_At_A\)
--> \(3c_A^2 - 2c_At_A - t_A^2 = 0\)
--> \(3c_A^2 - 3c_At_A + c_At_A - t_A^2 = 0\)
--> \(3c_A(c_A - t_A) + t_A(c_A - t_A) = 0\)
--> \((3c_A + t_A)(c_A - t_A) = 0\)
--> c_A = t_A [Note that 3c_A + t_A = 0 is not possible] --> Sufficient
IMO Option C
09 Jan 2020, 07:53
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Quote:
Dealership A and Dealership B both sell cars and trucks. If the ratio of cars to trucks each dealership sold in the last month is the same for both dealerships, did Dealership A sell the same number of cars and trucks last month?
(1) The number of trucks sold by Dealership B was three times the number of cars sold by Dealership A.
(2) The number of cars sold by Dealership B was equal to the number of trucks sold by Dealership A plus twice the number of cars sold by Dealership A.
(1) The number of trucks sold by Dealership B was three times the number of cars sold by Dealership A.
(2) The number of cars sold by Dealership B was equal to the number of trucks sold by Dealership A plus twice the number of cars sold by Dealership A.
Dealer A: car/trucks=x/y
Dealer B: car/trucks=z/w
ratio A=B: x/y=z/w
Is x=y?
(1): w=3x; x/y=z/w, x/y=z/3x, 3x^2=yz insufic
(2): z=y+2x; x/y=z/w, xw=zy, xw=(y+2x)y insufic
xw=zy, 3x^2=yz, 3x^2=y(y+2x), 3x^2-2xy-y^2=0
(3x+y)(x-y)=0, 3x+y=0, x=-y/3 (invalid), x=y (valid)
Ans (C)
