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By what percent was the price of a certain television set discounted  [#permalink]

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Question Stats: 77% (01:07) correct 23% (01:23) wrong based on 1294 sessions

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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. _________________ Most Helpful Expert Reply Veritas Prep GMAT Instructor V Joined: 16 Oct 2010 Posts: 9704 Location: Pune, India Re: By what percent was the price of a certain television set discounted [#permalink] Show Tags 11 5 rite2deepti wrote: 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.

If we suppose that the initial price was 100 then the Answer is A , but can we assume in DS questions ?

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.
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Re: By what percent was the price of a certain television set discounted  [#permalink]

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11
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

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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
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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. Kudos for a correct solution. _________________ Manager  Joined: 11 Sep 2013 Posts: 105 Re: By what percent was the price of a certain television set discounted [#permalink] Show Tags 1 Bunuel wrote: 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.

Kudos for a correct solution.

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 Intern  Joined: 22 Sep 2014 Posts: 31 Re: By what percent was the price of a certain television set discounted [#permalink] Show Tags Bunuel wrote: 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.

Kudos for a correct solution.

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.
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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 _________________ Click +1 KUDOS , You can make me happy with just one click! Thanks Intern  Joined: 20 Aug 2014 Posts: 2 Re: By what percent was the price of a certain television set discounted [#permalink] Show Tags 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
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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 Intern  Joined: 26 Jan 2016
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Re: By what percent was the price of a certain television set discounted  [#permalink]

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VeritasPrepKarishma wrote:
rite2deepti wrote:
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. If we suppose that the initial price was 100 then the Answer is A , but can we assume in DS questions ? Please clarify 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. 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 Current Student G Status: No matter how bad it is or how bad it gets: I am going to make it. Joined: 06 Apr 2016 Posts: 48 Location: Ukraine Concentration: Finance, Entrepreneurship GMAT 1: 670 Q49 V32 GMAT 2: 730 Q50 V38 GPA: 3.8 WE: Sales (Other) Re: By what percent was the price of a certain television set discounted [#permalink] Show Tags 1 jakejake wrote: 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

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%.

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Re: By what percent was the price of a certain television set discounted  [#permalink]

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Bunuel wrote:
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. 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 _________________ ------------------------------ "Trust the timing of your life" Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq Target Test Prep Representative G Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2815 Re: By what percent was the price of a certain television set discounted [#permalink] Show Tags Bunuel wrote: 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.

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.

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