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# Conference Ticket Advance Discounts 5-29 days in advance -> 15% 30-59

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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1283
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09 Jun 2017, 07:22
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Difficulty:

95% (hard)

Question Stats:

48% (02:00) correct 52% (02:01) wrong based on 134 sessions

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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
[Reveal] Spoiler: OA

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09 Jun 2017, 08:08
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hazelnut wrote:
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

[Reveal] Spoiler:
B

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20 Aug 2017, 02:35
is there any other way to solve this problem? can we find out the change in percentage and then check with given three options?
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Joined: 02 Aug 2009
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20 Aug 2017, 03:03
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hazelnut wrote:
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.....$$0.85T=306...... T = 306*\frac{100}{85}=360$$..

so ans is 30

B
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Joined: 14 Nov 2014
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20 Aug 2017, 03:19
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 ...

so ans is B ....
Intern
Joined: 24 Nov 2017
Posts: 1

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24 Nov 2017, 01:19
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
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Joined: 02 Apr 2014
Posts: 451

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05 Feb 2018, 12:28
Ratio of 306/252 should help find the bucket it falls into, simplifying = 102/84 = 34/28 = 8.5/7
so she must have booked ticket 30 days in advance
Re: Conference Ticket Advance Discounts 5-29 days in advance -> 15% 30-59   [#permalink] 05 Feb 2018, 12:28
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