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Updated on: 01 May 2026, 10:07
MetroLingua offers annual study plans for students preparing for language-proficiency exams. Each plan includes access to the academy’s online lesson library and weekly practice groups. The plans differ in annual fee, private-coaching discount, and the number of free private-coaching sessions included.
A private-coaching session costs $80 before any plan discount. Free sessions are used first. The discount applies only to paid sessions beyond the free sessions included in the plan.
A private-coaching session costs $80 before any plan discount. Free sessions are used first. The discount applies only to paid sessions beyond the free sessions included in the plan.
| Plan Name | Annual fee | Private-coaching benefit |
| Library | $120 | No discount and no free sessions |
| Plus | $230 | 10% discount and no free sessions |
| Coach | $340 | 20% discount and 2 free sessions |
| Pro | $480 | 30% discount and 5 free sessions |
| Immersion | $650 | 40% discount and 8 free sessions |
Elsa and Marco would each have the lowest yearly cost with the Library Plan.: No
Lena would spend less with the Coach Plan than Marco would spend with the Plus Plan.: No
Viktor and Sofia would each have the lowest yearly cost with the Immersion Plan.: Yes
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct
0%
(00:00)
wrong
based on 0
sessions
History
Date
Time
Result
Not Attempted Yet
Based on the Plan Rules and Student Forecasts tabs, select Yes if the statement is true. Otherwise, select No.
| Yes | No | |
| Elsa and Marco would each have the lowest yearly cost with the Library Plan. | ||
| Lena would spend less with the Coach Plan than Marco would spend with the Plus Plan. | ||
| Viktor and Sofia would each have the lowest yearly cost with the Immersion Plan. |
ShowHide Answer
Official Answer
Elsa and Marco would each have the lowest yearly cost with the Library Plan.: No
Lena would spend less with the Coach Plan than Marco would spend with the Plus Plan.: No
Viktor and Sofia would each have the lowest yearly cost with the Immersion Plan.: Yes
$16,000
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct
0%
(00:00)
wrong
based on 0
sessions
History
Date
Time
Result
Not Attempted Yet
Based on the Prior-Year Plan Data, by how much did the plan with the highest total revenue exceed the plan with the second-highest total revenue?
| $12,400 | |
| $16,000 | |
| $23,600 | |
| $40,600 | |
| $43,600 |
ShowHide Answer
Official Answer
$16,000
Paid private-coaching revenue exceeded annual plan-fee revenue in exactly 4 of the 5 plans.: Yes
The plan with the highest annual fee also generated the highest total revenue.: No
The median number of students per plan was greater than the mean number of students per plan.: No
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct
0%
(00:00)
wrong
based on 0
sessions
History
Date
Time
Result
Not Attempted Yet
Based on the Prior-Year Plan Data, select Yes if the statement is supported by the information provided. Otherwise, select No.
| Yes | No | |
| Paid private-coaching revenue exceeded annual plan-fee revenue in exactly 4 of the 5 plans. | ||
| The plan with the highest annual fee also generated the highest total revenue. | ||
| The median number of students per plan was greater than the mean number of students per plan. |
ShowHide Answer
Official Answer
Paid private-coaching revenue exceeded annual plan-fee revenue in exactly 4 of the 5 plans.: Yes
The plan with the highest annual fee also generated the highest total revenue.: No
The median number of students per plan was greater than the mean number of students per plan.: No
Multi-Source Reasoning (MSR) - Math/Hard
1. Based on the Plan Rules and Student Forecasts tabs, select Yes if the statement is true. Otherwise, select No.
A private-coaching session costs $80 before discounts. Free sessions are used first, and the discount applies only to paid sessions beyond the free sessions.
• Elsa and Marco would each have the lowest yearly cost with the Library Plan.
Elsa expects 1 session.
Library cost = 120 + 1 * 80 = 200
The annual fees for Plus, Coach, Pro, and Immersion are 230, 340, 480, and 650, respectively. Each of these is already greater than 200 before adding any paid coaching cost. So Elsa’s lowest cost is with the Library Plan.
Marco expects 4 sessions.
Library cost = 120 + 4 * 80 = 440.
Check only the plans that could still be below 440. Pro and Immersion can be ignored because their annual fees alone, 480 and 650, are already greater than 440.
Plus:
230 + 4 * 80 * 0.90 = 230 + 288 = 518
Coach:
340 + 2 * 80 * 0.80 = 340 + 128 = 468
So Marco’s lowest cost is also with the Library Plan.
Answer: Yes
• Lena would spend less with the Coach Plan than Marco would spend with the Plus Plan.
Lena expects 6 sessions.
Coach ($340, 20% discount and 2 free sessions): 340 + 4 * 80 * 0.80 = 340 + 256 = 596
Marco expects 4 sessions.
Plus ($230, 10% discount and no free sessions): 230 + 4 * 80 * 0.90 = 230 + 288 = 518
Lena’s cost with the Coach Plan is 596, which is greater than Marco’s cost with the Plus Plan.
Answer: No
• Viktor and Sofia would each have the lowest yearly cost with the Immersion Plan.
Viktor expects 10 sessions.
Library: 120 + 10 * 80 = 920
Plus: 230 + 10 * 80 * 0.90 = 950
Coach: 340 + 8 * 80 * 0.80 = 852
Pro: 480 + 5 * 80 * 0.70 = 760
Immersion: 650 + 2 * 80 * 0.60 = 746
Viktor’s lowest cost is with the Immersion Plan.
Sofia expects 14 sessions. Since Immersion is already the lowest-cost plan at 10 sessions and has the lowest cost for each additional paid session, increasing the number of sessions from 10 to 14 cannot make another plan become cheaper than Immersion. Therefore, Sofia’s lowest cost is also with the Immersion Plan.
Answer: Yes
Correct answer:
Elsa and Marco would each have the lowest yearly cost with the Library Plan. Yes
Lena would spend less with the Coach Plan than Marco would spend with the Plus Plan. No
Viktor and Sofia would each have the lowest yearly cost with the Immersion Plan. Yes
====================
2. Based on the Prior-Year Plan Data, by how much did the plan with the highest total revenue exceed the plan with the second-highest total revenue?
Total revenue is found by adding annual plan-fee revenue and revenue from paid private coaching.
• Library:
Annual plan-fee revenue = 800 * 120 = 96,000
Total revenue = 96,000 + 48,000 = 144,000
• Plus:
Annual plan-fee revenue = 300 * 230 = 69,000
Total revenue = 69,000 + 78,000 = 147,000
• Coach:
Annual plan-fee revenue = 220 * 340 = 74,800
Total revenue = 74,800 + 96,800 = 171,600
• Pro:
Annual plan-fee revenue = 140 * 480 = 67,200
Total revenue = 67,200 + 120,400 = 187,600
• Immersion:
Annual plan-fee revenue = 70 * 650 = 45,500
Total revenue = 45,500 + 100,800 = 146,300
The highest total revenue is from the Pro Plan: 187,600.
The second-highest total revenue is from the Coach Plan: 171,600.
Difference:
187,600 - 171,600 = 16,000
Correct answer: $16,000
====================
3. Based on the Prior-Year Plan Data, select Yes if the statement is supported by the information provided. Otherwise, select No.
• Paid private-coaching revenue exceeded annual plan-fee revenue in exactly 4 of the 5 plans.
Compare paid private-coaching revenue with annual plan-fee revenue for each plan.
Library:
Annual plan-fee revenue = 800 * 120 = 96,000
Paid private-coaching revenue = 48,000
Paid private-coaching revenue did not exceed annual plan-fee revenue.
Plus:
Annual plan-fee revenue = 300 * 230 = 69,000
Paid private-coaching revenue = 78,000
Paid private-coaching revenue exceeded annual plan-fee revenue.
Coach:
Annual plan-fee revenue = 220 * 340 = 74,800
Paid private-coaching revenue = 96,800
Paid private-coaching revenue exceeded annual plan-fee revenue.
Pro:
Annual plan-fee revenue = 140 * 480 = 67,200
Paid private-coaching revenue = 120,400
Paid private-coaching revenue exceeded annual plan-fee revenue.
Immersion:
Annual plan-fee revenue = 70 * 650 = 45,500
Paid private-coaching revenue = 100,800
Paid private-coaching revenue exceeded annual plan-fee revenue.
So the statement is true for exactly 4 of the 5 plans.
Answer: Yes
• The plan with the highest annual fee also generated the highest total revenue.
The highest annual fee is for the Immersion Plan: 650.
But from Q2, the highest total revenue is from the Pro Plan: 187,600.
So the plan with the highest annual fee did not generate the highest total revenue.
Answer: No
• The median number of students per plan was greater than the mean number of students per plan.
The numbers of students in ascending order are:
70, 140, 220, 300, 800
Median = 220
Mean = (800 + 300 + 220 + 140 + 70)/5 = 306
The median, 220, is not greater than the mean, 306.
Answer: No
Correct answer:
Paid private-coaching revenue exceeded annual plan-fee revenue in exactly 4 of the 5 plans. Yes
The plan with the highest annual fee also generated the highest total revenue. No
The median number of students per plan was greater than the mean number of students per plan. No
====================
Takeaway
In GMAT math-related MSR questions, do not default to full exact calculation. Exact calculation is needed only when estimation or logical comparison cannot decide the answer safely. Often, you can estimate, approximate, or skip calculation entirely when the structure of the numbers already shows which result must be larger, smaller, or sufficient. The goal is to use the least amount of calculation needed to reach a reliable answer.
What This Question Tests
This question tests math-related GMAT MSR skills, including interpreting information from multiple tabs, applying stated rules correctly, combining numerical information from different sources, and making efficient calculation decisions. It also tests comparison of quantities, evaluation of Yes/No statements, and basic statistical reasoning such as mean and median.
A private-coaching session costs $80 before discounts. Free sessions are used first, and the discount applies only to paid sessions beyond the free sessions.
• Elsa and Marco would each have the lowest yearly cost with the Library Plan.
Elsa expects 1 session.
Library cost = 120 + 1 * 80 = 200
The annual fees for Plus, Coach, Pro, and Immersion are 230, 340, 480, and 650, respectively. Each of these is already greater than 200 before adding any paid coaching cost. So Elsa’s lowest cost is with the Library Plan.
Marco expects 4 sessions.
Library cost = 120 + 4 * 80 = 440.
Check only the plans that could still be below 440. Pro and Immersion can be ignored because their annual fees alone, 480 and 650, are already greater than 440.
Plus:
230 + 4 * 80 * 0.90 = 230 + 288 = 518
Coach:
340 + 2 * 80 * 0.80 = 340 + 128 = 468
So Marco’s lowest cost is also with the Library Plan.
Answer: Yes
• Lena would spend less with the Coach Plan than Marco would spend with the Plus Plan.
Lena expects 6 sessions.
Coach ($340, 20% discount and 2 free sessions): 340 + 4 * 80 * 0.80 = 340 + 256 = 596
Marco expects 4 sessions.
Plus ($230, 10% discount and no free sessions): 230 + 4 * 80 * 0.90 = 230 + 288 = 518
Lena’s cost with the Coach Plan is 596, which is greater than Marco’s cost with the Plus Plan.
Answer: No
• Viktor and Sofia would each have the lowest yearly cost with the Immersion Plan.
Viktor expects 10 sessions.
Library: 120 + 10 * 80 = 920
Plus: 230 + 10 * 80 * 0.90 = 950
Coach: 340 + 8 * 80 * 0.80 = 852
Pro: 480 + 5 * 80 * 0.70 = 760
Immersion: 650 + 2 * 80 * 0.60 = 746
Viktor’s lowest cost is with the Immersion Plan.
Sofia expects 14 sessions. Since Immersion is already the lowest-cost plan at 10 sessions and has the lowest cost for each additional paid session, increasing the number of sessions from 10 to 14 cannot make another plan become cheaper than Immersion. Therefore, Sofia’s lowest cost is also with the Immersion Plan.
Answer: Yes
Correct answer:
Elsa and Marco would each have the lowest yearly cost with the Library Plan. Yes
Lena would spend less with the Coach Plan than Marco would spend with the Plus Plan. No
Viktor and Sofia would each have the lowest yearly cost with the Immersion Plan. Yes
====================
2. Based on the Prior-Year Plan Data, by how much did the plan with the highest total revenue exceed the plan with the second-highest total revenue?
Total revenue is found by adding annual plan-fee revenue and revenue from paid private coaching.
• Library:
Annual plan-fee revenue = 800 * 120 = 96,000
Total revenue = 96,000 + 48,000 = 144,000
• Plus:
Annual plan-fee revenue = 300 * 230 = 69,000
Total revenue = 69,000 + 78,000 = 147,000
• Coach:
Annual plan-fee revenue = 220 * 340 = 74,800
Total revenue = 74,800 + 96,800 = 171,600
• Pro:
Annual plan-fee revenue = 140 * 480 = 67,200
Total revenue = 67,200 + 120,400 = 187,600
• Immersion:
Annual plan-fee revenue = 70 * 650 = 45,500
Total revenue = 45,500 + 100,800 = 146,300
The highest total revenue is from the Pro Plan: 187,600.
The second-highest total revenue is from the Coach Plan: 171,600.
Difference:
187,600 - 171,600 = 16,000
Correct answer: $16,000
====================
3. Based on the Prior-Year Plan Data, select Yes if the statement is supported by the information provided. Otherwise, select No.
• Paid private-coaching revenue exceeded annual plan-fee revenue in exactly 4 of the 5 plans.
Compare paid private-coaching revenue with annual plan-fee revenue for each plan.
Library:
Annual plan-fee revenue = 800 * 120 = 96,000
Paid private-coaching revenue = 48,000
Paid private-coaching revenue did not exceed annual plan-fee revenue.
Plus:
Annual plan-fee revenue = 300 * 230 = 69,000
Paid private-coaching revenue = 78,000
Paid private-coaching revenue exceeded annual plan-fee revenue.
Coach:
Annual plan-fee revenue = 220 * 340 = 74,800
Paid private-coaching revenue = 96,800
Paid private-coaching revenue exceeded annual plan-fee revenue.
Pro:
Annual plan-fee revenue = 140 * 480 = 67,200
Paid private-coaching revenue = 120,400
Paid private-coaching revenue exceeded annual plan-fee revenue.
Immersion:
Annual plan-fee revenue = 70 * 650 = 45,500
Paid private-coaching revenue = 100,800
Paid private-coaching revenue exceeded annual plan-fee revenue.
So the statement is true for exactly 4 of the 5 plans.
Answer: Yes
• The plan with the highest annual fee also generated the highest total revenue.
The highest annual fee is for the Immersion Plan: 650.
But from Q2, the highest total revenue is from the Pro Plan: 187,600.
So the plan with the highest annual fee did not generate the highest total revenue.
Answer: No
• The median number of students per plan was greater than the mean number of students per plan.
The numbers of students in ascending order are:
70, 140, 220, 300, 800
Median = 220
Mean = (800 + 300 + 220 + 140 + 70)/5 = 306
The median, 220, is not greater than the mean, 306.
Answer: No
Correct answer:
Paid private-coaching revenue exceeded annual plan-fee revenue in exactly 4 of the 5 plans. Yes
The plan with the highest annual fee also generated the highest total revenue. No
The median number of students per plan was greater than the mean number of students per plan. No
====================
Takeaway
In GMAT math-related MSR questions, do not default to full exact calculation. Exact calculation is needed only when estimation or logical comparison cannot decide the answer safely. Often, you can estimate, approximate, or skip calculation entirely when the structure of the numbers already shows which result must be larger, smaller, or sufficient. The goal is to use the least amount of calculation needed to reach a reliable answer.
What This Question Tests
This question tests math-related GMAT MSR skills, including interpreting information from multiple tabs, applying stated rules correctly, combining numerical information from different sources, and making efficient calculation decisions. It also tests comparison of quantities, evaluation of Yes/No statements, and basic statistical reasoning such as mean and median.
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