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At a car dealership that sells only cars, trucks, and SUVs, the dealer

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At a car dealership that sells only cars, trucks, and SUVs, the dealer  [#permalink]

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New post 08 Jul 2017, 05:48
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Question Stats:

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At a car dealership that sells only cars, trucks, and SUVs, the dealership's inventory has a ratio of 6 cars for every 7 trucks for every 9 SUVs. Which of the following CANNOT represent the number of vehicles in the dealership's inventory?

A. 198
B. 242
C. 282
D. 308
E. 418

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Re: At a car dealership that sells only cars, trucks, and SUVs, the dealer  [#permalink]

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New post 08 Jul 2017, 06:22
Bunuel wrote:
At a car dealership that sells only cars, trucks, and SUVs, the dealership's inventory has a ratio of 6 cars for every 7 trucks for every 9 SUVs. Which of the following CANNOT represent the number of vehicles in the dealership's inventory?

A. 198
B. 242
C. 282
D. 308
E. 418


Since Car : Truck : SUV is 6: 7: 9 any option which is not a multiple of 22 will be the winner

Option C here
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At a car dealership that sells only cars, trucks, and SUVs, the dealer  [#permalink]

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New post 08 Jul 2017, 18:22
Bunuel wrote:
At a car dealership that sells only cars, trucks, and SUVs, the dealership's inventory has a ratio of 6 cars for every 7 trucks for every 9 SUVs. Which of the following CANNOT represent the number of vehicles in the dealership's inventory?

A. 198
B. 242
C. 282
D. 308
E. 418

The ratio of cars to trucks to SUVs is 6x:7x:9x. Assume x = 1, total is at least 6 + 7 + 9 = 22 vehicles. To keep the ratio, the number of vehicles in the dealer's inventory must be divisible by 22. AND,

22 = 11*2, so the answer also has to be divisible by 11.

Divisibility rule for 11: sum every second digit, then subtract the sum of the other digits. If result is 0 or a multiple of 11, the number is divisible by 11.

A. 198: 9 - (8+1) = 0. Keep

B. 242: 4 - (2+2) = 0. Keep

C. 282: 8 - (2+2) = 4. Reject. 4 is not divisible by 11.

D. 308: 0 - (3+8) = -11. Keep

E. 418: 1 - (4+8) = -11. Keep

Answer C
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Re: At a car dealership that sells only cars, trucks, and SUVs, the dealer  [#permalink]

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New post 08 Jul 2017, 19:15
C:T:S = 6:7:9

6+7+9 = 22. The total number of vehicles must be divisible by 22.

Only option C is divisible by 22. So, Ans-C.
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Re: At a car dealership that sells only cars, trucks, and SUVs, the dealer  [#permalink]

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New post 08 Jul 2017, 19:17
Answer should be C as 282/22 does not yield an integer

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Re: At a car dealership that sells only cars, trucks, and SUVs, the dealer  [#permalink]

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New post 09 Jul 2017, 07:27
the ratio is 6:7:9...adds up to 22

ans C not divsible by 22
hence ans C
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Re: At a car dealership that sells only cars, trucks, and SUVs, the dealer  [#permalink]

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New post 13 Jul 2017, 05:33
The answer is C as the answer should be a multiple of 2 and 11. As all are even nos., they are divisible by 2 so check for only 11.
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At a car dealership that sells only cars, trucks, and SUVs, the dealer  [#permalink]

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New post 16 Jul 2017, 17:29
Bunuel wrote:
At a car dealership that sells only cars, trucks, and SUVs, the dealership's inventory has a ratio of 6 cars for every 7 trucks for every 9 SUVs. Which of the following CANNOT represent the number of vehicles in the dealership's inventory?

A. 198
B. 242
C. 282
D. 308
E. 418


We are given that the ratio of cars to trucks to SUVs = 6x : 7x : 9x.

The sum of the vehicles in the car dealership is 6x + 7x + 9x = 22x. Thus, the number of vehicles must be a multiple of 22.

Of our answer choices, the only number that is not a multiple of 22 is 282.

Answer: C
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At a car dealership that sells only cars, trucks, and SUVs, the dealer   [#permalink] 16 Jul 2017, 17:29
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