At a certain car dealership, the 40 vehicles equipped with

Question

At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

A. 41/50
B. 9/50
C. 6/50
D. 21/25
E. 8/25

A. 41/50 
B. 9/50
C. 6/50
D. 21/25
E. 8/25

fluke · Accepted Answer

Convertible  Non-Convertible  Total  
  AC  14  26  40  
  Non-AC  1  9  10  
  Total  15  35  50

Fill it in this order:

AC cars=40
Total Cars=40/0.8=50
Non-AC Cars=50-40=10
Total Convertibles=15
Convertible AC=14
Convertible Non-AC=15-14=1
Non-Convertible/Non-AC=10-1=9
Non-Convertible/AC=40-14=26

Total Convertible+All AC= 15+26=41
Total cars=50

P=41/50.

Ans: 41/50

ScottTargetTestPrep · Answer

We are given that the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. We can let n = the total number of cars and create the following equation:

40 = 0.8n

n = 40/0.8 = 50

Thus, there are a total of 50 cars at the dealership. Furthermore, we are given that there are 15 convertibles, and 14 of them are equipped with air conditioning.

So, the the probability that a randomly selected vehicle will be a convertible or a car with air conditioning is:

/50 = 41/50

Note that we double-counted the 14 cars that are both convertibles and are cars with air conditioning, and so we had to subtract the 14 from the total.

DeeptiM · Answer

Fluke, we din't count 14 while calculating all AC..is it because it was already counted while calculating Convertible?? hence, re-count would contribute to a double figure??

Pls correct me, if I am wrong..

sandeeptela · Answer

Till the table finding, it seems all correct as per my findings. But, since the question is asking either A.C or Convertible ...not both. 
so, my answer is coming as below.
1 (Non A.C and Convertible) + 26 (A.C and non-convertible) = 27.
Therefore, require probability = 27/50. Please correct me if seems wrong.

gmatprav · Answer

total cars is 50. since 40 is 80% of 50.

40 cars are AC---given.
15 cars are convertible of which 14 are AC. means 
14 are AC+convertible.
1 is Non-AC convertible. 
AC+non-convertible is 40 -14 = 26. 
9 are neither.

So either AC or convertible = 26+14+1 = 41.

Probability is 41/50.

christianbze · Answer

Is this really a "700+ difficulty" question?
It was easy to solve (or to write down all that stuff) though it took me 2min 27sec.
Should be a Verbal question with all that writing :D :D

rohanatt · Answer

other way to see it is:

9 cars are neither AC nor Convertibles:

So 50-9=41 (either AC or Convertibles)

Hence prob: 41/50

testcracker · Answer

hi 80% = 40 so, 100% = 50 = total now, 50 = 40 + 15 - 14 + none so, niether A/C nor convertible = 9 probability: (either convertible or equipped with A/C) / total = (50 - 9) / 50 = 41/50 thanks

Rahulihavenoclue · Answer

P(A or B) = P(A) + P(B) - P (A and B) . 80% of total is 40 , so total = 50
P(convertible or AC ) = 40/50 + 15/50 - 14/50 = 41/50 
40 is the number of cars with AC , 15 the number of convertibles of which 14 are with AC

750Barrier · Answer

The answer can be 41/50, if the premise says - either Conv or AC or both.
the answer should be 27/50 as per the premise.

What is the source of this prob?

Hi  Bunuel  - is my understanding correct?

Kinshook · Answer

Given: At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system.

Asked: If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

Air conditioning  No air conditioning  Total  
  Convertible  14  15-14=1  15  
  Non convertible      50-15=35  
  Total  40  10  50

Total cars = 50
Number of Convertible Cars or cars with air-conditioning = 40 + 1 = 41
The probability that a randomly selected vehicle will fit customer specifications = 41/50

IMO A

thakurarun85 · Answer

40 vehicles equipped with air conditioning represent 80% of all cars.

How do we know all 40 are cars?

IanStewart · Answer

We have 50 cars in total. We have 40 cars with AC, and we have one convertible (15 - 14 = 1) that does not have AC, so there are 41 cars with either AC or that are convertibles, or both, and the answer is 41/50.

nm202367 · Answer

Thanks , it helped me to get the fact.

LittleKidLover96 · Answer

If 27/50 was an option I would have marked that, because the question says either a convertible or an AC, not both. Please let me know if my reasoning for this is incorrect.

Bunuel · Answer

In mathematics OR is always, unless explicitly stated, an inclusive OR, which means anything that satisfies either one or both conditions is included. So “either a convertible or a car with AC” includes cars that have both, and you cannot exclude the overlap.

At a certain car dealership, the 40 vehicles equipped with

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	Convertible	Non-Convertible	Total
AC	14	26	40
Non-AC	1	9	10
Total	15	35	50

	Air conditioning	No air conditioning	Total
Convertible	14	15-14=1	15
Non convertible			50-15=35
Total	40	10	50

GMAT Problem Solving (PS) Questions

At a certain car dealership, the 40 vehicles equipped with

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