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Working in Laptop company, Robin earns a fixed

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Working in Laptop company, Robin earns a fixed  [#permalink]

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New post 14 Mar 2020, 18:22
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GMATBusters’ Quant Quiz Question -5



Working in Laptop company, Robin earns a fixed salary of $20 per week plus $6 per Laptop for the first 6 laptops he sells, $12 per Laptop for the next 6 Laptops he sells, and $18 per Laptop for every Laptop sold after first 12. This week, he earned more than twice as much as he did last week. If he sold a Laptops last week and b Laptops this week, which of the following statements must be true?

I. b>2a
II. b>a
III. b>3

A. I only
B. II only
C. I and II
D. II and III
E. I, II, III

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Re: Working in Laptop company, Robin earns a fixed  [#permalink]

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New post 14 Mar 2020, 19:52
Fixed Salary = 20$ / Week
First 6 laptops = $6 / laptop
7-12 laptops = $12 / laptop
After 12 laptops = $ 18 / laptop

Given: This week, he earned more than twice as much as he did last week

Laptops sold last week = a
Laptops sold this week = b

Note: This is a Must be True question

Lets substitute numbers for quick calculation

a) b > 2a.
Set 2=1: a=1, b=6
a = last week salary = 20 + 1(6) = 20+06 = $26 , when b = 3 which more than 2a , we get this week earnings as = 20 +6(3) = $38

In above set this week's salary is less than twice last week's salary but b > 2a. So this option is not a must true option.

b) b > a
We know that b>a always to get this week earnings more than lalst week's also if a=b , when a=b, then earnings would
be same. This statement must be true.

c) b > 3
We know a is not equal to b and when a=1 , b=2 or 3 does not work. Since the fixed salary is $20 , we need atleast 20$ difference to achieve twice the earnings. So one quick way to measure is a=1 and b=3. if a=1, the earnings is $26 whwn b=3, salary is $38, which is less than twice the last week's salary, we know b > 3.

Ans: D
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Re: Working in Laptop company, Robin earns a fixed  [#permalink]

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New post 14 Mar 2020, 20:38
Working in Laptop company, Robin earns a fixed salary of $20 per week plus $6 per Laptop for the first 6 laptops he sells, $12 per Laptop for the next 6 Laptops he sells, and $18 per Laptop for every Laptop sold after first 12. This week, he earned more than twice as much as he did last week. If he sold a Laptops last week and b Laptops this week, which of the following statements must be true?

Let's assume, no. of laptops sold last week = 1, Total salary = 20+6=26
Total salary this week > 52, let's say 52,Total salary = Basic, 20+ extra 32 means min. 5 laptops sold this week. a = 1, b = 5
Let's take another case, no. of laptops sold last week = 4, Total salary = 20+24=44
Total salary this week > 88, let's say 88,Total salary = Basic, 20+ extra 68 (20+36+32) means min. 6+2 =8 laptops sold this week. a = 4, b = 8

I. b>2a, 5>2*1, sufficient as we took 52, but if we take 88, then it's insufficient, 8>2*4. So insufficient.
II. b>a, Sufficient, as mentioned in both cases.
III. b>3 Sufficient, as mentioned in both cases (as we took the lower extreme case, even if 0 laptops sold in last week).

D. II and III, is the correct answer.

Imo. D
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Re: Working in Laptop company, Robin earns a fixed  [#permalink]

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New post 14 Mar 2020, 20:57
OA is A
As per the constraints given in the question. Robin earned more than twice this week than that of last week.
So if he earned X last week so this week earning is 2X+K
Now assuming he sold 12 laptops already. And is selling after 12 laptops in later weeks. For which he is getting 18$ each. His 20$ income is fixed for both.
So if he sold 15 laptops in last week.
He must have sell more than 30 laptops this week to earn such profit. And statement one is proving that.
So OA is A

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Re: Working in Laptop company, Robin earns a fixed  [#permalink]

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New post 15 Mar 2020, 01:41
Given:
1. Working in Laptop company, Robin earns a fixed salary of $20 per week plus $6 per Laptop for the first 6 laptops he sells, $12 per Laptop for the next 6 Laptops he sells, and $18 per Laptop for every Laptop sold after first 12.
2. This week, he earned more than twice as much as he did last week.

Asked: If he sold a Laptops last week and b Laptops this week, which of the following statements must be true?

Robins's earning last week = $20 + $6a if a<=6; $56 + $12(a-6) if 6<a<=12; $128 +$18 (a-12) if 12<a
Robins's earning this week = $20 + $6b if b<=6; $56 + $12(b-6) if 6<b<=12; $128 +$18 (b-12) if 12<b

I. b>2a
Case I:
If a = 6
Robin's earning last week = $20 + $6*6 = $56
If b = 11
Robin's earning this week = $20 + $6*6 + $12 *5 = $116 > 2*$56 = $112
But b<2a
Case 2:
If a = 6
Robin's earning last week = $20 + $6*6 = $56
If b = 13
Robin's earning this week = $20 + $6*6 + $12 *6 + $18 = $146 > 2*$56 = $112
But b>2a
b> 2a is NOT NECESSARILY TRUE

II. b>a
This week, he earned more than twice as much as he did last week.
II. b>a MUST BE TRUE

III. b>3
For earning this week > 2*20 = 40
$20 + 6b > $40
6b > $20
b > 20/6 = 3 1/3 > 3
III. b>3 MUST BE TRUE

A. I only
B. II only
C. I and II
D. II and III
E. I, II, III

IMO D
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Re: Working in Laptop company, Robin earns a fixed  [#permalink]

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New post 15 Mar 2020, 05:26
Answer:A

consider 3 cases:
CaseI:in which ,less than equal to 6 laptop
Earned this week >2 X earned last week
20+6b>2X(6a+20)
b>2a+3
Case II:Laptop selling between 6-12
20+36+b-6X12>2x(20+36+(a-6)X12)
b>2a-1.3(apprx)
Case III:Laptop selling >12
20+6*6+6*12+(b-12)*18>2*(20+6*6+6*12+(a-12)*18)
b>2a-apprx4.8
Combining all 3 cases ,b>2a
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Re: Working in Laptop company, Robin earns a fixed  [#permalink]

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New post 15 Mar 2020, 06:58
Quote:
Working in Laptop company, Robin earns a fixed salary of $20 per week plus $6 per Laptop for the first 6 laptops he sells, $12 per Laptop for the next 6 Laptops he sells, and $18 per Laptop for every Laptop sold after first 12. This week, he earned more than twice as much as he did last week. If he sold a Laptops last week and b Laptops this week, which of the following statements must be true?

I. b>2a
II. b>a
III. b>3

A. I only
B. II only
C. I and II
D. II and III
E. I, II, III


Understand the difference here

Last week = 20+6+6+... so on.

This week=20+6+6+6+6+6+6+12+12.. so on.

The only way this week can be more than double the last week is if we have every 12 for every 6 in last week and at least one 18.. which is exactly as statement 1 b>2a.. Hence that is the only one true.

Statement 2 is clearly not must be true because we have 1 as must true.

Statement 3 is true but not always. It is true when a=0 but not otherwise. For example b=4 gives us 20+24=44 and if a=0 then it works but if a=1 the we have 26 and 44 is not more than double of 26.. Hence not always true.

Answer A
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Re: Working in Laptop company, Robin earns a fixed   [#permalink] 15 Mar 2020, 06:58

Working in Laptop company, Robin earns a fixed

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