As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2x
II. y > x
III. y > 3
A. I only
B. II only
C. I and II
D. II and III
E. I, II, and III
OA coming after few folks reply
MGMAT - bicycle sales
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- jayhawk2001
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Since a Fixed cost of 20$ dollars plus twice the cost af a x cycle in first week will always be involved the product of y cycle in second week and cost of each should always be greater.
also y>x always.
answer is E.
please tell what i left out if am wrong
also y>x always.
answer is E.
please tell what i left out if am wrong
I am ..therefore I am..
- jayhawk2001
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OA is D.
The key here is to consider the conditions at the boundary of the
price range(s)
Take y = 7 for example which just crosses the border of 6$ per bicycle
to 12$ per bicycle. Total price = 20 + 6*6 + 1*12 = 68
Now, take x=4 to disprove (y > 2x). Price = 20 + 6*4 = 44. Clearly
y not > 2x.
The key here is to consider the conditions at the boundary of the
price range(s)
Take y = 7 for example which just crosses the border of 6$ per bicycle
to 12$ per bicycle. Total price = 20 + 6*6 + 1*12 = 68
Now, take x=4 to disprove (y > 2x). Price = 20 + 6*4 = 44. Clearly
y not > 2x.
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As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman 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, and III
Statement II: Obviously true since the more bicycles Norman sells, the more commission (variable component) he earns. So y>x
Statement III: y>3. If y <= 3; then total amount earned by Norman would be $20 (fixed component) + Maximum 3*6 = $18 (variable component). So total amount earned by Norman would be 38. However, Norman is guaranteed a fixed return of $20 (even if he sells 0 bicycles) and $38 is not greater than twice of $20. Hence Statement III must be true
Statement I: y>2x; If y = 6 then amount earned = (6*6) +20 = 36+20 = 56
If x = 2 amount earned = 2*6 + 20 = 32; Here y>2x but earning of Norman in the second week is not more than twice the amount earned in the first week. Hence I may or may not be true
Answer should be D
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, and III
Statement II: Obviously true since the more bicycles Norman sells, the more commission (variable component) he earns. So y>x
Statement III: y>3. If y <= 3; then total amount earned by Norman would be $20 (fixed component) + Maximum 3*6 = $18 (variable component). So total amount earned by Norman would be 38. However, Norman is guaranteed a fixed return of $20 (even if he sells 0 bicycles) and $38 is not greater than twice of $20. Hence Statement III must be true
Statement I: y>2x; If y = 6 then amount earned = (6*6) +20 = 36+20 = 56
If x = 2 amount earned = 2*6 + 20 = 32; Here y>2x but earning of Norman in the second week is not more than twice the amount earned in the first week. Hence I may or may not be true
Answer should be D