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

 It is currently 17 Nov 2019, 01:02 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Word Problem - A furniture retailer bought 100 identical chairs at a c

Author Message
TAGS:

### Hide Tags

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3142
Word Problem - A furniture retailer bought 100 identical chairs at a c  [#permalink]

### Show Tags 00:00

Difficulty:   75% (hard)

Question Stats: 57% (02:23) correct 43% (02:23) wrong based on 105 sessions

Q.)
A furniture retailer bought 100 identical chairs at a cost of $20 each. He sold some of the chairs within the first week for$35 each. In the second week, he sold all the remaining chairs for $30 each. If his total profit on the sale of the chairs was greater in the second week than in the first week, which of the following can be the number of chairs sold by the retailer in the second week? I. 30 II. 60 III. 80 A. I only B. II only C. III only D. I and II only E. II and III only Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts  _________________ e-GMAT Representative V Joined: 04 Jan 2015 Posts: 3142 Word Problem - A furniture retailer bought 100 identical chairs at a c [#permalink] ### Show Tags The official solution has been posted. Looking forward to a healthy discussion.. _________________ Originally posted by EgmatQuantExpert on 22 Jan 2017, 01:11. Last edited by EgmatQuantExpert on 27 Jan 2017, 23:43, edited 1 time in total. Director  D Joined: 05 Mar 2015 Posts: 986 Re: Word Problem - A furniture retailer bought 100 identical chairs at a c [#permalink] ### Show Tags 1 EgmatQuantExpert wrote: Q.) A furniture retailer bought 100 identical chairs at a cost of$20 each. He sold some of the chairs within the first week for $35 each. In the second week, he sold all the remaining chairs for$30 each. If his total profit on the sale of the chairs was greater in the second week than in the first week, which of the following can be the number of chairs sold by the retailer in the second week?
I. 30
II. 60
III. 80

A. I only

B. II only

C. III only

D. I and II only

E. II and III only

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts  1) second week 30
means first week=70 chairs sol
CP of 70 chairs = 20*70= 1400
SP of 70 chairs = 35*70=2450
Profit of 1st week = 2450-1400=$1050 2nd week CP of chairs =20*30 =600 SP of 30 chairs = 30*30 =900 Profit of 2nd week = 900-600=$300

clearly profit 1> profit 2
thus this option is incorrect.

2) for 1st week 40 chairs profit = $600 for 2nd week 60 chair profit=$600
Profit1 = Profit2...incorrect

3) for 1st week 20 chairs profit = $300 for 2nd week 60 chair profit=$800
Profit1 < Profit2...correct

only option 3 is correct

Ans C
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3142
Re: Word Problem - A furniture retailer bought 100 identical chairs at a c  [#permalink]

### Show Tags

2
Hey,

PFB the official solution -

Given:

• Number of chairs bought by retailer = $$100$$
• Cost price of 1 chair = $$$20$$ • First Week o Let the number of chairs sold in the first week be$$z$$. o Selling price per chair =$$$35$$
o So, profit per chair = $$$35$$ -$$$20$$ = $$$15$$ o So, total profit on selling z chairs =$$$15z$$

• Second Week
o The number of chairs sold $$=100 – z$$
o Selling price per chair = $$$30$$ o So, profit per chair =$$$30$$ - $$$20$$ =$$$10$$
o So, total profit on selling $$100 - z$$ chairs = $$$10(100 – z)$$ =$$$(1000-10z)$$

• Profit in 2nd week > Profit in 1st week

To find:

• Which of the 3 values is/are possible for$$(100 – z)$$?

Approach:

1. To answer the question, we need to find the possible values of z
2. We’ve already inferred above the profit of 1st and 2nd weeks in terms of z. We’re also given a relation between the profit of 1st and 2nd weeks. We’ll use this relation to find the possible values of z.

Working Out:

• Finding possible values of z
o Profit in 2nd week > Profit in 1st week
o $$1000 - 10z > 15z$$
o So, $$1000 > 25z$$
o Or $$z < \frac{1000}{25}$$
o That is, $$z < 40$$

• Finding possible values of $$100 – z$$
o Since $$z < 40$$, $$-z > -40$$
o So, $$100-z > 100 – 40$$
o That is, number of chairs sold in the 2nd week$$> 60$$

• Evaluating the 3 given values
o Of the 3 given values, the only value that is greater than 60 is the 3rd value (80)

Looking at the answer choices, we see that the correct answer is Option C

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts  _________________ Re: Word Problem - A furniture retailer bought 100 identical chairs at a c   [#permalink] 27 Jan 2017, 23:30
Display posts from previous: Sort by

# Word Problem - A furniture retailer bought 100 identical chairs at a c  