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

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

Answer:

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hi..
if you do not know how to start, 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

so ans is 30

B
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Solution:

The ticket bought by Helen can be exactly 5, 30, or 60 days in advance since, if she had bought the ticket 1 day later, she would surely have had to pay a higher price. The question becomes which of these days in advance did she buy the ticket. To find out, we can let the original price of the ticket (i.e., no discount) be x dollars.

If she bought it 5 days in advance, then she paid 0.85x, and had she bought it 4 days in advance, she would have paid x. That is, if x = 306, is 0.85x = 252? Since 0.85 * 306 = $206.10 and this is not $252, she couldn’t have bought the ticket 5 days in advance.

If she bought it 30 days in advance, then she paid 0.7x, and had she bought it 29 days in advance, she would have paid 0.85x. That is, if 0.85x = 306, is 0.7x = 252? Since x = 306/0.85 = 360 and 0.7 * 360 = $252, she must have bought the ticket 30 days in advance.

Answer: B
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Given: Helen bought a ticket for $252. If she had bought it 1 day later, she would have paid $306.
So, if Helen had waited 1 extra day, she would have paid MORE.
30 days before the conference, she pays $252
The next day (which is 29 days before the conference), she pays $306
This works nicely.

Now let's examine what happens if she pays 59 days before the conference.
The next day (which is 58 days before the conference), still falls within the 30-59 day time frame.
So, the ticket price 59 days before the conference is exactly the same as the ticket price 58 days before the conference.

For this reason, the answer can't be 59 days

Cheers,
Brent

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

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

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

Yes, let's first understand the options provided and negate the impossible choices.

Since options A, C and E do not change the ranges of discount if the person bought the tickets a day later, doesn't make sense testing these options. This leaves option B and D. Clearly option B states 30% discount which means x*(70%) = 252, where this is completely divisible and we get x = 360$. Now simply check for the 5 to 29 days range i.e. 15% discount and you'll get 306$ as your answer. Hence, option B is correct.

Here's how I solved this problem. Please note that as a reply to this question, this explanation may seem long but most of this can be done mentally.

We're given three discount brackets. We are also told that Helen bought the ticket for $252 but if she'd been a day late, then she'd have bought it for $306. So we immediately know that the answer within the options will end with a '0' and not a '9'. This eliminates options (C) and (E).

Now, considering the original price of the ticket to be 'X', there are three possibilities:

1. Helen bought the tickets at a 40% discount, which means that 0.6X = $252, which means X=$420
2. Helen bought the tickets at a 30% discount, which means that 0.7X = $252, which means X=$360
3. Helen bought the tickets at a 15% discount, which means that 0.85X = $252, which means X=$306

Option 3 be eliminated immediately since LHS is not equal to RHS. This means she did not buy the tickets at a 15% discount, so we can now eliminate (A).

So if she bought these tickets at a 40% discount, that'd mean that 0.7 * 420 = $306 but this is not true. So, clearly, she bought the tickets at a 30% discount, which'd mean that she bought it 30 days in advance.

Hence, the answer is (B). This process should take you not more than 30-60 seconds, and is a logic based approach instead of an algebraic approach.

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 ....

BrentGMATPrepNow
Since 14/17 falls in the range of 30-59 days in advance. The answer is 30 days in advance. Why not the answer is 59 days? Is it due to Halen will prefer to pay 30 day advance to 59 days advance?

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A "test all scenarios" method with only very simple/fast manual calculations, if you can't intuitively find the answer by the other suggested, smarter, solutions...

Given: 306 - 252 = 54

Scenario 1:
Full price = 306
85% = 252

Calculate 15% of full price to see if it matches the difference
306*0,15 = 45,9

Can't be scenario one since 45,9 != 54

Scenario 2
Full price = x
70% = 306
60% = 252

Define ten percent of x as the given difference
54 = 0,1x

Calculate x from the 70% alternative, by multiplying 54 by 3
x -54*3 = x - 162 = 306
x = 468
Test if ten percent of x is the given difference
468 * 0,1 = 46,8

Can't be this scenario since 46,8 != 54

Scenario 3
Full price = x
85% = 306
70% = 252

Set 15% of x as the difference
x*0,15 = 54

Calculate x
x - 54 = 306
x = 360

Calculate 15% of x
360 * 0,15 = 54

Since 54 = 54, we've found our answer
Scenario 3, which means that the cheaper ticket was purchased on day 30.

#Approach 1:
Let's assume that actual price of the ticket = T

Conference Ticket Advance Discounts:

5-29 days in advance -> 15% Discount
Ticket price in this time window = 85 % of T


30-59 days in advance -> 30% Discount
Ticket price in this time window = 70 % of T

60-89 days in advance -> 40% Discount
Ticket price in this time window = 60% of T

Helen bought a ticket for $252. Let's say after discount she paid X % of T = 252 ----(1)
If she had bought it 1 day later, she would have paid $306.
That means, one day after, the discount slab will change and she needs pay 306 $ after discount. we can assume that Y % of T = 306----(2)

On dividing eq 1/ eq 2,

Y % of T/X % of T = 306/252
Y/X = 34/28 = 17/14

On multiplying the ratio 17/14 by a 5, it becomes Y/X = 85/70

i.e Y is 85 % and X is 70%

X % of T = 252 => 70 % of T = 252

Y % of T = 306 => 80 % of T = 306
So we can conclude that she bought the ticket 30 days in advance. That's why she got 30 % discount and she paid 70 % of ticket price.
One day after, it would be 29 days in advance and the discount will change to 15 % and she need to pay 85 % of the ticket price.


#Approach 2:

Since the price change from $ 252 to $ 306 after 1 day, we can conclude the discount slab should change after 1 day.

From this conclusion, we can eliminate the options C and E as the discount % will not change even after 1 day.
Example: Option C : 59
If she bought the ticket 59 days in advance , she gets 30 % discount.
One day after that it would be 58 days in advance but discount % is same for 30-59 days in advance. So the buying price will not change even after 1 day. Hence it could be eliminated. Similarly Option E also can be eliminated.

Lets try back solving method to eliminate the other options .

If option A is the right answer, she bought the ticket 5 days in advance and paid $ 252
i.e 85 % ticket price = 252

One day after, there is no discount and she need to pay full amount of 306 $. So we need to cross check whether ticket price is 306 $ or not
85 % ticket price = 252
Ticket price = (252/85) * 100 . we can easily figure out that Ticket price is less than 300 $ ≠ 306 $ . Hence Option A is eliminated.

If option B is the right answer, she bought the ticket 30 days in advance and paid $ 252
i.e 70 % of ticket price = 252
One day after, the discount % is 15 % and she need to pay 85 % of ticket price. So we need to cross check whether 85 % of ticket price is 306 $ or not.
70 % of ticket price = 252
85 % of ticket price = (252/70)*85 = (36/10)*85 = 18 * 17 = 306

Ureeekaa!!

Since the values match, Option B would be the correct answer.

Thanks,
Clifin J Francis,
GMAT SME
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