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22 Jan 2017, 01:09
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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
[spoiler]Thanks,
Saquib
Quant Expert
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[/spoiler]
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
[spoiler]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
[/spoiler]
22 Jan 2017, 11:27
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EgmatQuantExpert
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
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
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
27 Jan 2017, 23:30
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Hey,
PFB the official solution -
Given:
To find:
Approach:
Working Out:
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
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
