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Re: Conference Ticket Advance Discounts 5-29 days in advance -> 15% 30-59
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09 Jun 2017, 07:08

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hazelnut wrote:

Conference Ticket Advance Discounts 5-29 days in advance -> 15% 30-59 days in advance -> 30% 60-89 days in advance -> 40%

Helen bought a ticket for $252. If she had bought it 1 day later, she would have paid $306. How many days in advance did she buy her ticket?

(A) 5 (B) 30 (C) 59 (D) 60 (E) 89

Let's say the regular ticket price is $100 and see what kinds of prices we pay. 5-29 days in advance: we pay $85 30-59 days in advance: we pay $70 60-89 days in advance: we pay $60

Now let's examine the following ratios:

(Price paid 30-59 days in advance)/(Price paid 5-29 days in advance) = 70/85 = 14/17 (Price paid 60-89 days in advance)/(Price paid 30-59 days in advance) = 60/70 = 6/7

Now compare the given information. (price paid)/(price WOULD HAVE paid a day later) = 252/306 = 126/153 = 42/51 = 14/17

The ratio of 14/17 matches the first scenario. So, it must be the case that Helen paid the $252 amount 30 days in advance. A day later would have been 29 days in advance, in which case she would have paid $306

Re: Conference Ticket Advance Discounts 5-29 days in advance -> 15% 30-59
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20 Aug 2017, 02:03

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1

hazelnut wrote:

Conference Ticket Advance Discounts 5-29 days in advance -> 15% 30-59 days in advance -> 30% 60-89 days in advance -> 40%

Helen bought a ticket for $252. If she hadd bought it 1 day later, she would have paid $306. How many days in advance did she buy her ticket?

(A) 5 (B) 30 (C) 59 (D) 60 (E) 89

hi.. if you do not know anything about, a small logic can get you close to answer.. it should be a day, where the next day decreases the discount so it has to be 5, 30 or 60..

the prices are - <5 days - 100% 5-29 days in advance -> 85% 30-59 days in advance -> 70% 60-89 days in advance -> 60%

now the discounted price are 252 and 306..

CASE I - if the day was 60 to 59 60% of Total = 252....\(0.6T=252...T = 252*\frac{100}{60}=420\) 70% of T = 306.....\(0.7T=306...... T = 306*\frac{100}{70}\).. 306 is not div by 7, so ans will be a FRACTION different values of T..... NOT possible CASE II - if the day was 30 to 29 70% of T = 252....\(0.7T=252...T = 252*\frac{100}{70}=360\) 85% of T = 306.....\(0.85T=306...... T = 306*\frac{100}{85}=360\).. SAME values of T..... ANSWER

Re: Conference Ticket Advance Discounts 5-29 days in advance -> 15% 30-59
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20 Aug 2017, 02:19

santro789 wrote:

is there any other way to solve this problem? can we find out the change in percentage and then check with given three options?

i did it kind of a hit and trial :

let he got 40% discount .. x-40/100*x = 252 x = 420 ..--actual cost now if would have brought 1 day later ...more amount he would have paid .. next level discount is 30 % 30/100 * 420 = 126 .....420 - 126 = 294 <> 306 --- 1st possibility is out ...

let he got 30% discount .. x-30/100*x = 252 x= 360 ....actual cost now next level discount is 15 % 15% * 360 = 54 360 - 54 = 306 ..bingo ...

Conference Ticket Advance Discounts 5-29 days in advance -> 15% 30-59
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24 Nov 2017, 00:19

We can do it with the below process:

let x be the price without any discount. First calculate the difference in percentage that is present for different date rage: 10% = 40% to 30% 15% = 30% to 15%

Now we know that the difference in the percentage should be equal to 306-252=54, and difference is given in in the question and it either is equal to 10% or 15%

Finally we have two conditions: 1. 10% of x =54 , therefore either x=540 2. 15% of x =54 , or x=360

Take any one of above and take (if you take 10% of x), then 70% of x=253 and 85% of x= 306, (since 70% of 360=253, hence the change was from 30% to 15%) Thus , for 1 day difference to be cause the change in discount, the ticket was bought 30 days advance.

(If you remove the language then its pretty quick) :p