By what percent was the price of a certain television set discounted

In percentage questions, you can assume some price to be 100 and then do your calculations and get your answer in percentage terms. The reason for this is that it doesn't matter what the price actually is. The percentage will remain the same.
e.g.
Discounted price is 100. When we increase it by 25%, we get 125 as the original price. Discount given = (125 - 100)/125 * 100 = 20%

Let us say discounted price is 200. When we increase it by 25%, we get 250 as the original price. Discount given = (250 - 200)/250 * 100 = 20%
No matter what you assume your discounted price to be, you will always get a discount of 20%.
You can use any one of these values to get your answer. It holds for all values of discount price, hence you are not assuming anything here. Or you can use 'x' and then do your calculations as done above. For our calculations, we generally use 100 as the price since it is easiest to work with.

You don't have to assume...but can define a variable..

e.g. lets take X as the discounted price
so the price before discount = 1.25X
so the discount was 0.25X

Now all you have to do is to calculate the % of 0.25X in 1.25X which is 20%.

Hope its clear

PS: Consider a kudos if you like my post

Lets consider cost price is c
selling price after discount is s

Statement1: cost price is 25% greater than selling price
\(c = s + (25/100) s\)
\(c = (100s+25s)/100\)
\(c = 125s/100\)
\(s = 100c/125 = 4c/5\)
multiply by 20 to get 100 in denominator
\(s = 80c/100\)
That means 80% of cost price is selling price ==> 20% is the discount applied.

Sufficient

Statement2: s = c-60
from this statement we can not find the percentage. Not sufficient.

Ans A

t is the discounted price.
p is the price before discounted

=> we need to know: (p-t)/p or t/p
(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.
=> p=1.25t
=> know t/p
=> sufficient
(2) The price of the television set was discounted by $60 for the sale
We know t but do not know p

=> insufficient

Ans: A

Will go with A

Let original price = x
Let the discount percentage = k
lets discounted price = d
The equation: x - (k/100)x = d --------- (1)
To Find: k

Statement 1:
d + (25/100)d = x ===>> (5/4)d = x ===>> if we put the value of x in equation (1) we will get the value of 'k' as all the value of d will be cancelled out.
We will get k = 20. Hence sufficient.

Statement 2:
given that kx/100 = 60. One equation and 2 unknown variables. Hence will not be able to find the value of K. Thus, insufficient.

By what percent was the price of a certain television set discounted for a sale?

(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.
(2) The price of the television set was discounted by $60 for the sale.

Sol.
we need to find
Let price of television is x
Price after Discount is d

1) x = 1.25 d so x/d =1.25 or d/x = 100/125 i.e 0.80 i.e 20 % discount
2) x - 60 = d Not sufficient

so first is sufficient Hence A

Hi Guys,
I am a newcomer here and i am not sure if this is the right place to ask, I have a GMAT problem here, and its not that hard apparently but maybe I am stupid .
By what percent was the price of a certain television set discounted for a sale?


(1) The price of the television set before it was discounted for the sale was 25 percent
greater than the discounted price.
(2) The price of the television set was discounted by $60 for the sale.


ok so I keep getting E, now can someone just call me stupid and explain to me, and make me understand what this 25% greater is. I just dont get this concept. We are saying the D(1.25) = O , with O being original price and D being discount price. If Original price is 25% greater than the Discounted price, then how is it possbile that the discount is 20%?? thats what is driving me crazy. How is orginal price greater by 25%, if discount is 20% off, should the original price be 20% more than the discounted price???
sorry if i sound stupid but this got me very frustrated

Hi jakejake
I can feel you! but hope this could help
there are certain concepts in increase/decrease percent questions which I think you may have misunderstood

1. if a is x percent greater than b
it means: (a-b)/b = x %

2. if b is y percent less than a
it means: (a-b)/a = y %

For example:
8 is (8-5)/5 = 60% greater than 5
but 5 is (8-5)/8 = 37.5% less than 8

you can see the difference, right? In short, a is x percent greater than b, but b is not x percent less than a

For discounted problem, it's more straightforward and, well, common sense:
original price: a
discounted: x percent
discounted price: a(1-x)/100

I hope you could re-solve the problem based on this

Hi VeritasPrepKarishma ,
Quick and maybe stupid question. How do you decide what will go in the denominator, as in it could be (100-125)/125 or (125-100)/100 ?
or in terms of variables would it be (B-D)/B or (D-B)/D where B= Price before sale and D=Discounted price

your reply is much appreciated. Thank you

Jakejake, let me try.
First, in DS we do not need to calculate till the end. We need to know whether the information provided is SUFFICIENT to perform the calculation.
Second, we have only one variable and asked not for the exact value, but for the % change, so we need the relationship between old and new price.

Statement 1 gives us the relationship, hence sufficient.
Statement 2 gives only value change, without any relationship- insufficient.

If you want to check yourself plug in the values. When you see percents go for 100:
Let the discount price = 100, then base price = 100*1,25=125.
Percentage change= (new-old)/old=(100-125)/125=-25/125=-1/5=-20%
The price was discounted by 20%.

Posted from my mobile device

1) % D = (D/CP ) * 100
= (D/ 1.25D)*100
= 80
The price of a certain television set discounted for a sale by 20%
sufficient

2)%D = 60/CP *100
No info about CP
insufficient
_________________

We need to determine the percent discount of the television.

Statement One Alone:

The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.

We can let n = the regular price and d = the discounted price:

1.25d = n

d = n/1.25

d = 100n/125 = n(100/125) = n(4/5)

So the television was discounted 20%.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

The price of the television set was discounted by $60 for the sale.

Since we do not know the regular price of the television, statement two alone is not sufficient to answer the question.

Answer: A
_________________

your approach is flawed

the after price is 100,
the before price is 125
it is after - before / before

therefore -20% = a discount of 20%

please don't promote a flawed approach - this is extremely harmful for learning.
I trust this is an oversight on your part.

Thanks - great approach to this question.
The veritas rep didn't know what she was doing.

1) Let the discounted Price is $100
so, the price was $125 (100 + 100*25%)
Then the discount was 25
(25/125)*100 = 20%
Option 1 is sufficient.

2) No information about original price. ; Insufficient.

Ans. A

Answer: Option A

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