Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. : Problem Solving (PS)

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Abby, Brandon, Cedric, and Deirdre are planning to attend a concert.

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Math Expert

Joined: 02 Sep 2009

Posts: 50058

Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. [#permalink]

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15 Aug 2016, 03:59

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Difficulty:

25% (medium)

Question Stats:

74% (01:32) correct

26% (01:30) wrong

based on 168 sessions

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Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. If their friend Kim also goes with them, they will get a group discount on their tickets. If the total price of the tickets with the group discount is the same as the total price of the tickets without the group discount, how much is the discount?

A. 5%
B. 10%
C. 20%
D. 25%
E. 33%

Spoiler: OA

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Re: Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. [#permalink]

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15 Aug 2016, 04:24

Bunuel wrote:

Let A,B,C and D individual tickets be X and total tickets is 4X..

Now with Kelly they get a discount , total tickets here is 5x.

We are told that group discount is same as total price without discount..

When we need to solve 5X till we get 4X..

Take options..5X - 5%(5X) = 5x - (0.05)(5X) = 5x - 0.25X = 4.75X...not same as 4X..
(B) 5X - 10% of 5x => 5x - (0.1)(5x) = 4.5X, which is again not equal to 4x. So, this is not the correct option.
(C) 5X - 20% of 5x => 5x - (0.2)(5x) = 4X, this is same as 4X...no need to do other options..

IMO option C is correct answer...

OA please...will correct if I missed anything..

CEO

Joined: 12 Sep 2015

Posts: 3037

Location: Canada

Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. [#permalink]

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15 Aug 2016, 08:11

Top Contributor

Bunuel wrote:

One approach is to ASSIGN SOME "NICE" VALUES

Let's say the price per ticket = $1
So, the TOTAL cost (i.e., without a discount) for Abby, Brandon, Cedric, and Deirdre will be $4

The total price of the tickets with the group discount is the same as the total price of the tickets without the group discount
When Kim comes too, the TOTAL discounted price will be $4

Of course, if tickets are $1 each, then the TOTAL cost (without discount) for the five people SHOULD be $5

So, what's the discount (expressed as a percent)?
The discount = (100)(5 - 4)/5
= 100/5
= 20%

Answer:

Spoiler: ::

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12 Jun 2018, 11:11

Bunuel wrote:

We can create the equation in which p = the regular price and n = the percent of the discount:

5p(1 - n/100) = 4p

(100 - n)/100 = 4/5

5(100 - n) = 400

500 - 5n = 400

100 = 5n

n = 20 percent

Answer: C
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