I30-66

Question

The list below outlines the annual membership plans available at a fitness center, along with any included benefits and discounts on personal training.
 
•  Basic Plan : $100 per year with access to all standard equipment and group classes.
 
•  Silver Plan : $200 per year with access to all standard equipment, group classes, and a 10% discount on personal training sessions.
 
•  Gold Plan : $300 per year with access to all standard equipment, group classes, a 20% discount on personal training sessions, and two free personal training sessions.
 
•  Platinum Plan : $450 per year with access to all standard equipment, group classes, a 30% discount on personal training sessions, and five free personal training sessions.
 
Personal training sessions cost $80 per session.The table below shows the personal training usage and group class interest for three new gym members.
    Member   Group Classes    Personal Training Sessions       Sally   Yes   5      Ray    No   20      Mindy    Yes   10The table below shows the number of members in each membership tier during the past year, along with the total revenue generated from personal training sessions over that same period. The fitness center’s only sources of revenue are membership fees and personal training sessions.
     Tier    Members   Total Revenue from Personal Training      Basic    1,500    $40,000       Silver    200    $72,000       Gold    100    $80,000       Platinum    60    $140,000

Bunuel · Answer

Official Solution:

Sally — 5 personal training sessions 
 
• Basic: $100 + 5 * $80 = $500
 
• Silver: $200 + 5 * $80 * 0.9 = $560
 
• Gold: $300 + 3 * $80 * 0.8 = $492
 
• Platinum: $450 + 0 = $450
 
 Answer: Yes  — Platinum has the lowest total cost.
 
 Ray — 20 personal training sessions 
 
• Basic: $100 + 20 * $80 = $1,700
 
• Silver: $200 + 20 * $80 * 0.9 = $1,640
 
• Gold: $300 + 18 * $80 * 0.8 = $1,452
 
• Platinum: $450 + 15 * $80 * 0.7 = $1,290
 
 Answer: Yes  — Platinum has the lowest total cost.
 
 Mindy — 10 personal training sessions 
 
• Basic: $100 + 10 * $80 = $900
 
• Silver: $200 + 10 * $80 * 0.9 = $920
 
• Gold: $300 + 8 * $80 * 0.8 = $812
 
• Platinum: $450 + 5 * $80 * 0.7 = $730
 
 Answer: Yes  — Platinum has the lowest total cost.

Correct answer:

Sally  "Yes"

Ray  "Yes"

Mindy  "Yes"

ApplyFall2928 · Answer

I think the question should state that the personal training sessions are PER MONTH because it is very vague.

Bunuel · Answer

Tab 1 clearly states that personal training sessions cost $80 per session, so they are calculated per session, not per month or any other time period. Nothing vague about that.

ApplyFall2928 · Answer

Yes, but it is asking for the lowest yearly total cost. If one were to do 12*450 = 5400, that would be more than 12*300 + 80 (.8) (3) = 3792. So then, would it be better if the question said lowest monthly instead of yearly?

Bunuel · Answer

Maybe I'm misunderstanding you, but the membership plan prices are clearly stated as per year in Tab 1, and the question asks for the lowest yearly total cost. There's no reason to multiply anything by 12. The $450 for the Platinum Plan covers the entire year, not per month. Personal training sessions are also priced per session, not monthly.

MarcoPag · Answer

I like the solution - it’s helpful. Hey, the question is really straightfoward, but its such a time soak anyways. Are exceptional arithmetics required to get this in 2 mins ?

Bunuel · Answer

The calculations in this question are fairly straightforward, so with some practice it can be done quite quickly. Also, two minutes per question is just the average time, for slightly harder ones, it’s fine to spend a bit more.

Confusion · Answer

my thinking of doing this a bit quicker:
✅ Platinum vs Basic

Extra Cost: $450 − $100 = $350
Value of Free Sessions: 5 × $80 = $400
Net Benefit: $400 − $350 = $50
Conclusion: Platinum is $50 cheaper if T ≥ 5, even before considering the $24/session discount.

✅ Platinum vs Silver

Extra Cost: $450 − $200 = $250
Value of Free Sessions: 5 × $80 = $400
Net Benefit: $400 − $250 = $150
Conclusion: Platinum is $150 cheaper if T ≥ 5, before considering the $16/session discount.

✅ Platinum vs Gold

Extra Cost: $450 − $300 = $150
Value of Extra Free Sessions: (5 − 2) × $80 = $240
Net Benefit: $240 − $150 = $90
Conclusion: Platinum is $90 cheaper if T ≥ 5, before considering the $8/session discount.

Bottom Line:
For T ≥ 5 sessions, Platinum beats all other plans even before per-session discounts. If usage goes beyond 5 sessions, Platinum becomes even more attractive because of the additional per-session discount.

repellatquas · Answer

One other way could be this and you can share if this makes sense - 
For Ray (for example), we need to calculate amount for 20 fitness sessions, we should note that with every upgrade in plan, the annual fees increases by $100. Even if we ignore the free sessions with each upgrade and just calculate for the entirety, we can get the answer if with each successive upgrade the discount we are getting is more $100 (increment in memebership fee).

Let's understand with example here -
20 sessions = 20*80 = $1600
1. From Basic to Silver - silver will charge 10% less = -160 on total sessions (which can cover the $100 increment in membership fees). So, Silver is better than Basic. 
2. Similarly, from Silver to Gold - Gold will charge 20% less = -320 (can cover the $100 increment in membership fees). So, Gold is better than Silver.
3. From Gold to Platinum - Platinum charges 30% off = -480. Again, Platinum is better than Silver.

Every subsequent upgrade plan will be better than earlier plan until the additional cost can be covered by the discount received on sessions. With the number of sessions increasing, the discount will increase.

bb · Answer

Yes, average time for this question is 3:39 ... so definitely a time suck.

counterclash1 · Answer

how about i just calculate the values for 5 sessions and after that for 10 and 20 the answer will come out to be similar since the initial membership cost is recovered by 5 sessions at most and then there is only discounted per session cost?

Bunuel · Answer

Yes, your shortcut works. Once Platinum is cheapest at 5 sessions, it remains cheapest for 10 and 20 because each additional session also costs less.

I30-66

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My Rewards

Tier	Members	Total Revenue from Personal Training
Basic	1,500	$40,000
Silver	200	$72,000
Gold	100	$80,000
Platinum	60	$140,000