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

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

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New post 22 Jan 2017, 01:09
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Difficulty:

  75% (hard)

Question Stats:

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

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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


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Saquib
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Word Problem - A furniture retailer bought 100 identical chairs at a c  [#permalink]

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New post Updated on: 27 Jan 2017, 23:43

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.
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Re: Word Problem - A furniture retailer bought 100 identical chairs at a c  [#permalink]

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New post 22 Jan 2017, 11:27
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

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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
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Re: Word Problem - A furniture retailer bought 100 identical chairs at a c  [#permalink]

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New post 27 Jan 2017, 23:30
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
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Re: Word Problem - A furniture retailer bought 100 identical chairs at a c   [#permalink] 27 Jan 2017, 23:30
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