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E
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Difficulty:
(N/A)
Question Stats:
38% (02:50) correct
63%
(02:22)
wrong
based on 8
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A wedding planner charges $120 per guest for the first 50 guests. If there are more than 50 but fewer than 200 guests, she charges $110 per guest, and if there are at least 200 guests, she charges $100 per guest. For her wedding, Paula has a list of n confirmed guests and a second list of potential guests. For how many values of n can Paula reduce the wedding planner’s charge by inviting at least one potential guest?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
29 Apr 2026, 03:09
Kudos
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Potential guest >=1
120*50 and 110* 50. Difference is 500. Different values of n would be 500/120 = 4.
110*200 and 100* 200. Difference is 2000. Different values of n would be 2000/110 = 18.
Ans E
120*50 and 110* 50. Difference is 500. Different values of n would be 500/120 = 4.
110*200 and 100* 200. Difference is 2000. Different values of n would be 2000/110 = 18.
Ans E
kevincan
29 Apr 2026, 03:44
Kudos
Bookmarks
Th gap will exist in two situations:
1) Transition from less than 50 to more than 50.
2) Transition from less than 200 but more than 50 to more than 200.
Taking case 1:
51*110 = 5610
Taking an easier value to calculate:
45*120 = 5400>5610.
46 also yields the same.
47 is where the value is higher here and as we move to 51 value becomes lower.
So 47 to 50 = 4 values.
Taking case 2:
We have 200*100 = 20000.
Now from 182*110 to 199*110 we see the values being higher than 20000 satisdfying our condition.
182 to 199, 18 values here.
Total = 4+18 = 22.
Answer: Option E
1) Transition from less than 50 to more than 50.
2) Transition from less than 200 but more than 50 to more than 200.
Taking case 1:
51*110 = 5610
Taking an easier value to calculate:
45*120 = 5400>5610.
46 also yields the same.
47 is where the value is higher here and as we move to 51 value becomes lower.
So 47 to 50 = 4 values.
Taking case 2:
We have 200*100 = 20000.
Now from 182*110 to 199*110 we see the values being higher than 20000 satisdfying our condition.
182 to 199, 18 values here.
Total = 4+18 = 22.
Answer: Option E
kevincan
