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14 Mar 2020, 19:22
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Difficulty:
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Question Stats:
55% (02:38) correct
45%
(02:48)
wrong
based on 133
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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 $18 per Laptop for every Laptop sold after first 12. This week, he earned more than twice as much as he did last week. If he sold a Laptops last week and b Laptops this week, which of the following statements must be true?
I. b>2a
II. b>a
III. b>3
A. I only
B. II only
C. I and II
D. II and III
E. I, II, III
14 Mar 2020, 20:52
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Fixed Salary = 20$ / 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
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
14 Mar 2020, 21:38
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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
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
