GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 05:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The price of a dress was first discounted by a certain percent and lat

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58464
The price of a dress was first discounted by a certain percent and lat  [#permalink]

### Show Tags

13 Jun 2017, 05:55
3
1
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:51) correct 16% (02:27) wrong based on 83 sessions

### HideShow timer Statistics

The price of a dress was first discounted by a certain percent and later by 25 percent of the discounted price. If these
two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

A. 10%
B. 15%
C. 20%
D. 30%
E. 65%

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: The price of a dress was first discounted by a certain percent and lat  [#permalink]

### Show Tags

13 Jun 2017, 06:30
2
Bunuel wrote:
The price of a shirt was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

A. 10%
B. 15%
C. 20%
D. 30%
E. 65%

(1-x/100)*0.75 = 0.6

x = 20

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Director
Joined: 04 Dec 2015
Posts: 742
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: The price of a dress was first discounted by a certain percent and lat  [#permalink]

### Show Tags

13 Jun 2017, 06:38
1
Bunuel wrote:
The price of a shirt was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

A. 10%
B. 15%
C. 20%
D. 30%
E. 65%

Let the price of article be = \$100
Given Final selling price is 40% discount on the original price; ie; 60% of 100 $$= \frac{60}{100} * 100 = 60$$
Let the first discount be x%. Second discount is 25% on first discounted price. ie; 75% on first discount price.

If successive discounts of x% and y% are given on article P; Selling price of article after successive discounts = (100 - y) % of (100 - x)% of P
$$60 = (\frac{100 - 25}{100}) * (\frac{100 - x}{100}) * 100$$
$$60 = \frac{75}{100} * (100 - x)$$
$$60 = \frac{3}{4}(100 - x)$$
$$100 - x = 80$$
$$x = 100 - 80 = 20%.$$ Answer C...
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8137
Location: United States (CA)
Re: The price of a dress was first discounted by a certain percent and lat  [#permalink]

### Show Tags

15 Jun 2017, 16:15
1
Bunuel wrote:
The price of a shirt was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

A. 10%
B. 15%
C. 20%
D. 30%
E. 65%

Let n denote the original price of the shirt and let the first discount be x percent. Then, after the first discount, the price is reduced to n(1 - x/100). After the second discount, the price is reduced to n(1 - x/100)(1 - 25/100) = n(1 - x/100)(75/100) = n(1 - x/100)(3/4).

Since the two discounts are equivalent to a single discount of 40 percent of the original price, we have:

n(1 - x/100)(3/4) = (60/100)n

(1 - x/100)(3/4) = 3/5

1 - x/100 = 4/5

x/100 = 1/5

x = 100/5 = 20

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 29 Jan 2017
Posts: 42
Re: The price of a dress was first discounted by a certain percent and lat  [#permalink]

### Show Tags

29 Dec 2017, 19:25
1
Bunuel wrote:
The price of a shirt was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

A. 10%
B. 15%
C. 20%
D. 30%
E. 65%

Working backwards/picking numbers was the easiest for me.

100 - 40% = 60

We need an answer choice that matches 60

D) 100 - 30% = 70
This part is the second discount (25%): 70 x (3/4) does not = 60

C) 100 - 20% = 80
80 x (3/4) = 60

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3092
Re: The price of a dress was first discounted by a certain percent and lat  [#permalink]

### Show Tags

30 Dec 2017, 00:36
Bunuel wrote:
The price of a shirt was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

A. 10%
B. 15%
C. 20%
D. 30%
E. 65%

There are a number of ways to solve this question. Let me start with the smallest one.

Method 1:

We can use the percentage formula to get the first discount.

$$A + B + \frac{(A * B)}{100}$$ = Overall Percentage.

A is unknown, B = -25 and Overall Percentage Discount = -40 [Note : We are using a negative sign, since these percentages are discounts]

Plugging in the numbers in the above formula we get :

$$A - 25 + A * \frac{(-25)}{100} = -40$$

$$A - \frac{A}{4} = - 15$$

$$A = - 15 * \frac{4}{3}$$

$$A = - 20$$

Thus the first discount = 20%

Regards,
Saquib
e-GMAT
Quant Expert
_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3092
Re: The price of a dress was first discounted by a certain percent and lat  [#permalink]

### Show Tags

30 Dec 2017, 00:44
Bunuel wrote:
The price of a shirt was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

A. 10%
B. 15%
C. 20%
D. 30%
E. 65%

Method 2:

The second method is similar to the first one, but instead of using a formula, we will solve it by assuming the original price to P and applying the discounts on it.

Original Price : P

Price after first discount $$= P ( 1 - \frac{F}{100})$$ , where F is the first discount.

Price after the second discount $$= P ( 1 - \frac{F}{100}) ( 1 - \frac{25}{100}) = \frac{3P}{4} * ( 1 - \frac{F}{100})$$ ......(i)

According to the question stem, the two successive discount is equivalent to one discount of 40%.

Thus, price after overall discount can be written as $$P ( 1 - \frac{40}{100}) = \frac{3P}{5}$$ ........(ii)

Equating equation (i) and (ii), we will get

$$\frac{3P}{4} * (1 - \frac{F}{100}) = \frac{3P}{5}$$

$$5 - \frac{5F}{100} = 4$$

$$\frac{F}{20} = 1$$

$$F = 20$$%

Thus, the correct answer is Option C.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13417
Re: The price of a dress was first discounted by a certain percent and lat  [#permalink]

### Show Tags

13 Oct 2019, 08:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The price of a dress was first discounted by a certain percent and lat   [#permalink] 13 Oct 2019, 08:25
Display posts from previous: Sort by