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# Dealership A and Dealership B both sell cars and trucks

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Intern
Joined: 04 Apr 2018
Posts: 21
Dealership A and Dealership B both sell cars and trucks  [#permalink]

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26 Nov 2018, 16:12
1
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:37) correct 42% (02:21) wrong based on 77 sessions

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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.
Intern
Joined: 09 Nov 2018
Posts: 11
Re: Dealership A and Dealership B both sell cars and trucks  [#permalink]

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27 Nov 2018, 09:12
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.

How does one solve this?
I'm not getting C... lost in the equations...
Intern
Joined: 19 Jan 2017
Posts: 14
Re: Dealership A and Dealership B both sell cars and trucks  [#permalink]

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27 Nov 2018, 09:53
1
RK007 wrote:
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.

How does one solve this?
I'm not getting C... lost in the equations...

From statement 1:
Assume dealership A sold c cars, then dealership B sold 3*c trucks. This information will not tell us whether dealership A sold the same amount of cars and trucks. Insufficient

From statement 2;
Assume dealership A sold t trucks. Then dealership B sold (t + 2*c) cars. This information will not tell us whether dealership A sold the same amount of cars and trucks. Insufficient

Combined:
Since we are told ratios of cars to trucks is the same for both dealerships:

(t+ 2*c)/3*c = c/t

Cross multiply:
t^2 + 2ct = 3c^2
t^2 + 2ct - 3c^2 = 0

Factor:
(t + 3c)(t - c) = 0
t + 3c = 0 (not possible since there cannot be a negative number of trucks)

So we are left with t - c = 0, which is sufficient to say that dealership A sold the same number of cars and trucks since t = c.

Posted from my mobile device
Intern
Joined: 09 Nov 2018
Posts: 11
Re: Dealership A and Dealership B both sell cars and trucks  [#permalink]

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27 Nov 2018, 10:00
truplayer257 wrote:
RK007 wrote:
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.

How does one solve this?
I'm not getting C... lost in the equations...

From statement 1:
Assume dealership A sold c cars, then dealership B sold 3*c trucks. This information will not tell us whether dealership A sold the same amount of cars and trucks. Insufficient

From statement 2;
Assume dealership A sold t trucks. Then dealership B sold (t + 2*c) cars. This information will not tell us whether dealership A sold the same amount of cars and trucks. Insufficient

Combined:
Since we are told ratios of cars to trucks is the same for both dealerships:

(t+ 2*c)/3*c = c/t

Cross multiply:
t^2 + 2ct = 3c^2
t^2 + 2ct - 3c^2 = 0

Factor:
(t + 3c)(t - c) = 0
t + 3c = 0 (not possible since there cannot be a negative number of trucks)

So we are left with t - c = 0, which is sufficient to say that dealership A sold the same number of cars and trucks since t = c.

Posted from my mobile device

Do you know any short cut to factorize these kind of weird equations?
Intern
Joined: 19 Jan 2017
Posts: 14
Re: Dealership A and Dealership B both sell cars and trucks  [#permalink]

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28 Nov 2018, 20:14
Hi,

You may have a point on being intuitive about factoring these types of equations. I guess it's best to realize that you can factor these based on the rule of factoring (What two numbers multiply to the coefficient of the middle term and add up to the number in the last term) . In this case our two variables are "c" and "t". Note that in t^2 + 2ct - 3c^2 = 0, we must try to think of two numbers that multiply to 2c and add up to -3c^2, 3c and -c work well. Therefore, factor it into (t + 3c)(t - c).

I hope this helps.
Intern
Joined: 05 Nov 2018
Posts: 7
Dealership A and Dealership B both sell cars and trucks  [#permalink]

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29 Nov 2018, 05:15
Easier Way. Make a 2x2 Matrix

Statement 1
........ A| B
Car | x |
Truck| | 3x

Insufficient.

Statement 2
........ A | B
Car | x |
Truck| y | 2x+y

Insufficient.

Combining both.

We see that 3x=2x+y
x=y

Statement 1+2
........ A | B
Car | x |
Truck| y | 2x+y

........ A | B
Car | x | 3x
Truck| x | 3x
Intern
Joined: 05 Oct 2018
Posts: 43
Location: United States
GMAT 1: 770 Q49 V47
GPA: 3.95
WE: General Management (Other)
Re: Dealership A and Dealership B both sell cars and trucks  [#permalink]

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29 Nov 2018, 08:57
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.

S1 Clearly insufficient
S2 Any combination of cars and trucks for dealership A can be used to solve for cars for dealership B, so any combination is possible. Not sufficient.

Combined
Call the ratio of cars to trucks at A c:t
Then the ratio of cars to trucks at B is t+2c:3c (the left side from statement 2 and the right side from statement 1)
Setting these equal to each other and cross-multiplying yields 3c^2 = t^2 + 2ct OR 3c^2 - 2ct - t^2 = 0
Factor to get (3c+t)(c-t) = 0
Since 3c+t = 0 is illogicial, we know c-t = 0 or c = t

SUFFICIENT
Intern
Joined: 05 Oct 2018
Posts: 43
Location: United States
GMAT 1: 770 Q49 V47
GPA: 3.95
WE: General Management (Other)
Re: Dealership A and Dealership B both sell cars and trucks  [#permalink]

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29 Nov 2018, 09:00
st1gg3r wrote:
Easier Way. Make a 2x2 Matrix

Statement 1
........ A| B
Car | x |
Truck| | 3x

Insufficient.

Statement 2
........ A | B
Car | x |
Truck| y | 2x+y

Insufficient.

Combining both.

We see that 3x=2x+y
x=y

Statement 1+2
........ A | B
Car | x |
Truck| y | 2x+y

........ A | B
Car | x | 3x
Truck| x | 3x

I think you misread statement 2 although you have arrived at the correct answer. 2x+y represents the number of cars sold at B not the number of trucks sold at B.
Intern
Joined: 05 Nov 2018
Posts: 7
Re: Dealership A and Dealership B both sell cars and trucks  [#permalink]

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29 Nov 2018, 09:22
kylebecker9 wrote:
st1gg3r wrote:
Easier Way. Make a 2x2 Matrix

Statement 1
........ A| B
Car | x |
Truck| | 3x

Insufficient.

Statement 2
........ A | B
Car | x | 2x+y
Truck| y |

Insufficient.

Combining both.

We see that 3x=2x+y
x=y

Statement 1+2
........ A | B
Car | x | 2x+y
Truck| y | 3x

........ A | B
Car | x | 3x
Truck| x | 3x

I think you misread statement 2 although you have arrived at the correct answer. 2x+y represents the number of cars sold at B not the number of trucks sold at B.

Good catch. I mixed up the rows. I could not upload a picture and tried making it here.

Anyways Fixed it.
Re: Dealership A and Dealership B both sell cars and trucks   [#permalink] 29 Nov 2018, 09:22
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