AnkitK wrote:
As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true?
I. y>2x
II. y>x
III. y>3
A. I only
B. II only
C. I and II
D. II and III
E. I, II, III
Given:
1. The number of bicycles sold last week = x
2. The number of bicycles sold this week = y
3. Let earnings of last week and this week be s1 and s2 resp.
s2> 2s1Question:
1. Is y > 2x
2. Is y > x
3. Is y > 3
Basically the question asks us to relate number of bicycles sold in each of 2 weeks based on the relation between the earnings in those 2 weeks.
1. Earnings in the current week can be higher than that of the last week only when the number of bicycles sold
is higher in the current week. i.e., only when y>x
2. If the number of bicycles sold during the current week <4, then the earnings in the current week cannot be more than double that of the previous week.
3. Now let us assume y=2x. Since we are assuming twice the bicycles are sold this week over that of the previous week , if we take x=18, then y=36.
4. Let us calculate s1 and s2.
s1= earnings from the first 12 bicycles + earnings from the next 6 bicycles = 128+ 108= 236
s2= earnings from the 12 bicycles+ earnings from the next 24 bicycles= 128+ 432= 560
5. s2>2s1 even when y=2x
We see from (1) above statement II is true, from (2) above statement III is true, from (5) above statement I need not be true.
The answer is choice D.
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