Julie bought 2 adult tickets, 1 child ticket

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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Thu Sep 05, 2013 3:59 am

Julie bought 2 adult tickets, 1 child ticket, and 1 senior ticket to an amusement park. She received 30% off the adult tickets and 15% off the child and senior tickets. Was the total amount of the 4 discounts greater than 20% of the sum of the regular prices of the 4 tickets?

1. The original price of an adult ticket was $48, the original price of the senior ticket was $24, and the original price of the child ticket was less than the senior ticket.

2. The original price of the child ticket was $12.

I have got the answer to this question but as I was reading the explanation as to what approach has been explained I noticed a small confusion in a concept

Statement 1

30% off adult tickets and 15% off senior and child ticket

The explanation gives an equation
0.30(2)(48) + 0.15(24) + 0.15(c) > 0.20(2(48) + 24 + c)

I am confused with a small thing here. If we say 30% discount then we should multiply by .70 instead of .30? Same with the other one - we should multiply by .85 instead of .15.

For example - 30% discount on $100 is $70 (100*.70) not $30. What am I missing? Please help. Thanks

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Source: Beat The GMAT — Data Sufficiency | Thu Sep 05, 2013 3:59 am

vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Thu Sep 05, 2013 4:16 am

Hmm it's something like this:

If we say "20% discount on $ 50, then we mean (20/100) * 50 = $10, so new price will be 50-10= 40.This can be arrived at, instead by "considering that 20% discount on $ 50 is effectively 80 % of the price i.e (80/100) * 50 = 40

Thus in your case "If we say 30% discount then we should multiply by .70(to get the answer directly) instead of .30(to first find the discounted amount, then deducting this from the original price, cumbersome!)

30% discount on $100 is $70 (100*.70) not $30. What am I missing?

You are considering the discount rate of 30%, then you calculate it in your head that 30% off 100 is effectively 70% of 100 (this is what you are arriving at, then you say 0.70*100=70, which is 100-30(100*0.30).

Hope I am clear

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Thu Sep 05, 2013 7:35 pm

melguy wrote:Julie bought 2 adult tickets, 1 child ticket, and 1 senior ticket to an amusement park. She received 30% off the adult tickets and 15% off the child and senior tickets. Was the total amount of the 4 discounts greater than 20% of the sum of the regular prices of the 4 tickets?

1. The original price of an adult ticket was $48, the original price of the senior ticket was $24, and the original price of the child ticket was less than the senior ticket.

2. The original price of the child ticket was $12.

I have got the answer to this question but as I was reading the explanation as to what approach has been explained I noticed a small confusion in a concept

Statement 1

30% off adult tickets and 15% off senior and child ticket

The explanation gives an equation
0.30(2)(48) + 0.15(24) + 0.15(c) > 0.20(2(48) + 24 + c)

I am confused with a small thing here. If we say 30% discount then we should multiply by .70 instead of .30? Same with the other one - we should multiply by .85 instead of .15.

For example - 30% discount on $100 is $70 (100*.70) not $30. What am I missing? Please help. Thanks

Question:
0.3*2A + 0.15*(C+S) > 0.2*(2A+C+S) ?
0.6A + 0.15C + 0.15S > 0.4A + 0.2C + 0.2S ?
0.2A > 0.05(C+S) ?
4A > (C+S) ?

Statement 1: A = 48, S = 24, C < S
C + S < 24 + 24
C + S < 48
Sufficient.

Statement 2: C = 12
Not sufficient.

Choose A

The explanation compares the discounts in the two cases, not the price.

Cheers

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Sep 08, 2013 8:59 am

Julie bought 2 adult tickets, 1 child ticket, and 1 senior ticket to an amusement park. She received 30% off the adult tickets and 15% off the child and senior tickets. Was the total amount of the 4 discounts greater than 20% of the sum of the regular prices of the 4 tickets?

1. The original price of an adult ticket was $48, the original price of the senior ticket was $24, and the original price of the child ticket was less than the senior ticket.

2. The original price of the child ticket was $12.

Statement 1: The original price of an adult ticket was $48, the original price of the senior ticket was $24, and the original price of the child ticket was less than the senior ticket.
Try EXTREMES.

Case 1: Plug in the THRESHOLD price for the original price of the child ticket.
Since the original price of the child ticket must be less than the original price of the senior ticket, the threshold price for the child ticket = 24.
In this case:
(sum of the discounts)/(sum of the original prices) = (.3*2*48 + .15*24 + .15*24)/(2*48 + 24 + 24) = (28.8 + 3.6 + 3.6)/144 = 36/144 = 25%.

Case 2: Plug in a very small value for the original price of the child ticket.
Let the original price of a child ticket = 1 cent.
Here, the original price and the discounted price of the child ticket will both be so small that they can be disregarded in our calculations.
In this case:
(sum of the other discounts)/(sum of the other original prices) = (.3*2*48 + .15*24)/(2*48 + 24) = (28.8 + 3.6)/120 â‰ˆ 32/120 = 26.66%.

Since the discount is greater than 20% in each case, SUFFICIENT.

Statement 2: The original price of the child ticket was $12.
No way to determine whether the sum of the discounts was greater than 20%.
INSUFFICIENT.

The correct answer is A.

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