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# In a group of 100 cars, 47 cars do not have air conditioning. If at

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Math Expert
Joined: 02 Sep 2009
Posts: 52297
In a group of 100 cars, 47 cars do not have air conditioning. If at  [#permalink]

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09 Sep 2015, 23:22
1
5
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:56) correct 22% (01:46) wrong based on 130 sessions

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In a group of 100 cars, 47 cars do not have air conditioning. If at least 51 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?

A) 45
B) 47
C) 49
D) 51
E) 53

Kudos for a correct solution.

Source: GMATPrepNow

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Senior Manager
Joined: 05 Apr 2015
Posts: 374
Re: In a group of 100 cars, 47 cars do not have air conditioning. If at  [#permalink]

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10 Sep 2015, 00:59
Hi,

Lets assume AC=53(includes only AC cars and cars with AC and racing stripes)

lets assume RS(racing stripes)>=51(includes cars with AC and racing stripes and only racing stripes).

Now since we want to maximize(only AC) we have to see to it that cars with AC and racing stripes is minimal(assume 0) But since RS>=51.. we have to assign atleast 4 to cars with AC and racing stripes .

Hence AC=53-4=49.

Regards,
Dom.
Manager
Joined: 10 Aug 2015
Posts: 103
Re: In a group of 100 cars, 47 cars do not have air conditioning. If at  [#permalink]

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10 Sep 2015, 02:59
1
Solution: 47 cars cannot have AC. So, 53 is maximum no. of cars that can have AC.
Minimum 51 cars have racing strips. 49 is the maximum no. of cars without racing strips.
Maximum no. of cars that can have AC without racing strips = minimum(53,49) = 49.

Option, C
Manager
Joined: 29 Jul 2015
Posts: 158
Re: In a group of 100 cars, 47 cars do not have air conditioning. If at  [#permalink]

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10 Sep 2015, 06:31
Bunuel wrote:
In a group of 100 cars, 47 cars do not have air conditioning. If at least 51 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?

A) 45
B) 47
C) 49
D) 51
E) 53

Kudos for a correct solution.

Source: GMATPrepNow

51 cars have racing stripes. These cars may also include the cars which have both AC and stripes.
Total number of cars is 100.
To maximize the number of cars which only have AC, we must consider the number of cars which have neither AC nor racing stripes to be 0.
Thus the number of cars with only AC will be
100-51 =49

Manager
Joined: 13 Mar 2013
Posts: 163
Location: United States
GPA: 3.5
WE: Engineering (Telecommunications)
Re: In a group of 100 cars, 47 cars do not have air conditioning. If at  [#permalink]

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11 Sep 2015, 21:11
As per the question we fill the set with the following details ...
group of 100 cars = total
47 cars do not have air conditioning.

If at least 51 cars have racing stripes = We give stripes car number 51 (because our aim to find Max AC car and not stripes .)
similarly we give not ac/not stripes = 0 ( because our aim to find Max AC car and not stripes .)

hence ans is 49 C
Attachments

ACStripes.PNG [ 4.21 KiB | Viewed 1436 times ]

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Regards ,

Intern
Joined: 02 Jan 2015
Posts: 22
Re: In a group of 100 cars, 47 cars do not have air conditioning. If at  [#permalink]

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11 Sep 2015, 22:59
4
And s (C) 49
See attachment. since non rs max can be only 49 we can say that 49 s the max AC cars with non rs tires

P.S SORRY FOR THE SHABBY WORK i am ANSWERING FROM MOBILE

give kudos to appreciate
Attachments

Screenshot_2015-09-12-12-24-55.jpg [ 72.35 KiB | Viewed 1358 times ]

Non-Human User
Joined: 09 Sep 2013
Posts: 9456
Re: In a group of 100 cars, 47 cars do not have air conditioning. If at  [#permalink]

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12 May 2018, 01:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a group of 100 cars, 47 cars do not have air conditioning. If at &nbs [#permalink] 12 May 2018, 01:49
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