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Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to [#permalink]

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30 Aug 2015, 23:29

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Question Stats:

65% (01:55) correct
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Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to one of two gear models: automatic or manual gear. Of the cars on sale, is the percent of hybrid vehicles at least 40%?

(1) Of the cars Nancy put on sale, 30 percent of the cars with automatic gear are hybrid vehicles.

(2) Of the cars Nancy put on sale, 80 percent of the cars with manual gear are hybrid vehicles.

Re: Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to [#permalink]

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31 Aug 2015, 05:08

420 cars total All cars on sale belong to one of two gear models: automatic or manual gear. Of the cars on sale, is the percent of hybrid vehicles at least 40%? are there at least 168 hybrid vehicles?

(1) Of the cars Nancy put on sale, 30 percent of the cars with automatic gear are hybrid vehicles. no actual numbers for the breakdown of cars insufficient

(2) Of the cars Nancy put on sale, 80 percent of the cars with manual gear are hybrid vehicles. no actual numbers for the breakdown of cars insufficient

Combined, there are still no numbers given for each type of car Answer:E

Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to [#permalink]

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28 Nov 2016, 17:58

Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to one of two gear models: automatic or manual gear. Of the cars on sale, is the percent of hybrid vehicles at least 40%?

(1) Of the cars Nancy put on sale, 30 percent of the cars with automatic gear are hybrid vehicles.

(2) Of the cars Nancy put on sale, 80 percent of the cars with manual gear are hybrid vehicles.

statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;

EACH statement ALONE is sufficient to answer the question asked;

statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Last edited by Vyshak on 29 Nov 2016, 00:21, edited 1 time in total.

Re: Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to [#permalink]

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24 Dec 2016, 02:29

swanidhi wrote:

Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to one of two gear models: automatic or manual gear. Of the cars on sale, is the percent of hybrid vehicles at least 40%?

(1) Of the cars Nancy put on sale, 30 percent of the cars with automatic gear are hybrid vehicles.

(2) Of the cars Nancy put on sale, 80 percent of the cars with manual gear are hybrid vehicles.

Hit +Kudos, if this was any learning!

clearly each alone is insuff

both

let auntomatic cars = A and Manual = M , thus M = 420-A

from 1

0.3A is automatic Hybrid and 0.7A is automatic not Hybrid

from 2

0.8(420-A) ARE Manual Hybrid and 0.2(420-A) ARE Manual not hybrid

total Hybrid Vehicles = 336-0.8A + 0.3A = 336-0.5A , Question becomes is 336-0.5A >= 168

Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to [#permalink]

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24 Dec 2016, 10:40

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Each answer by itself is insufficient - information only about one gear type.

1) & 2): The smallest number of hybrid vehicles will occur when the number of manual gear cars is lowest. 80% of manual cars are hybrid. 30% of automatics are hybrid. These percentages must be integers because you cannot have a fraction of a car. So, the lowest number of manual cars is 10, which makes the number of automatics 410.

80% of 10 = 8 30% of 410 = 123

123 is less than 40% of 420.

Now, maximising the number of manual cars gives the number of manuals as 410 and the number of automatics as 30.

80% of 410 is 328. 30% of 10 is 3.

331 is more than 40% of 420 and therefore we can conclude that 1) and 2) are not sufficient. E

Re: Nancy, a car dealer, put 420 cars on sale. All cars on sale belong to [#permalink]

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07 Sep 2017, 01:02

Let x be the number of Automatics cars, and y be the number of Manual cars.

total cars on sale = x+y= 420 (x, y ranges from 0 to 420 )

(1) Of the cars Nancy put on sale, 30 percent of the cars with automatic gear are hybrid vehicles.

=> we have 0.3x as hybrid but we got no clue about the cars with manual gear that are hybrid. Insuff.

(2) Of the cars Nancy put on sale, 80 percent of the cars with manual gear are hybrid vehicles. => we have 0.8y as hybrid but we got no clue about the cars with automatic gear that are hybrid. Insuff.

(1+2) => total hybrid cars = 0.3x + 0.8 y total cars on sale = x+y= 420 => x,y ranges from 0 to 420 Hybrid ratio = Z = (0.3x + 0.8 y) / 420 . Min(x) = 0 : y = 420 => Z = 0.8 or 80% . Min (y) = 0 : x =420 => Z = 0.3 or 30% So, Z ranges from 30% to 80%.