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19 Feb 2026, 06:10
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:58) correct
37%
(02:58)
wrong
based on 93
sessions
History
Date
Time
Result
Not Attempted Yet
Three freelance designers, Luca, Sophie, and Marta, receive monthly retainers that total €9,700. Luca spends 70% of his retainer, Sophie spends 75%, and Marta spends 60%. At the end of the month, their savings are in the ratio 9:8:14. What is Marta’s monthly retainer?
A. €3,000
B. €3,200
C. €3,500
D. €3,700
E. €4,000
A. €3,000
B. €3,200
C. €3,500
D. €3,700
E. €4,000
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19 Feb 2026, 11:01
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The concept being tested here is ratio-to-variable translation — turning a savings ratio into a set of equations you can solve simultaneously. This is a classic Fractions and Ratios setup that looks messier than it actually is.
The common trap: students work with spending percentages (70%, 75%, 60%) instead of first converting to savings percentages. If you set up equations using how much they spend rather than how much they save, you'll go in circles.
Step 1 — Convert spending percentages to savings percentages.
- Luca spends 70% → saves 30% of his retainer
- Sophie spends 75% → saves 25% of her retainer
- Marta spends 60% → saves 40% of her retainer
Step 2 — Set up the ratio equation.
Let the retainers be L (Luca), S (Sophie), and M (Marta). Their savings are in the ratio 9 : 8 : 14, so:
0.3L : 0.25S : 0.4M = 9 : 8 : 14
Set each fraction equal to a constant k:
- 0.3L / 9 = k → L = 30k
- 0.25S / 8 = k → S = 32k
- 0.4M / 14 = k → M = 35k
Step 3 — Use the total retainer constraint.
L + S + M = €9,700
30k + 32k + 35k = 9,700
97k = 9,700 → k = 100
Step 4 — Solve for Marta's retainer.
M = 35k = 35 × 100 = €3,500
Answer: C (€3,500)
Quick sanity check: L = €3,000, S = €3,200, M = €3,500. Total = €9,700 ✓
Savings: Luca saves €900, Sophie saves €800, Marta saves €1,400 → ratio = 9 : 8 : 14 ✓
Takeaway: When a problem gives you spending percentages but a savings ratio, always flip to savings percentages first — then let a single constant k tie all three retainers together. The total constraint gives you k directly.
The common trap: students work with spending percentages (70%, 75%, 60%) instead of first converting to savings percentages. If you set up equations using how much they spend rather than how much they save, you'll go in circles.
Step 1 — Convert spending percentages to savings percentages.
- Luca spends 70% → saves 30% of his retainer
- Sophie spends 75% → saves 25% of her retainer
- Marta spends 60% → saves 40% of her retainer
Step 2 — Set up the ratio equation.
Let the retainers be L (Luca), S (Sophie), and M (Marta). Their savings are in the ratio 9 : 8 : 14, so:
0.3L : 0.25S : 0.4M = 9 : 8 : 14
Set each fraction equal to a constant k:
- 0.3L / 9 = k → L = 30k
- 0.25S / 8 = k → S = 32k
- 0.4M / 14 = k → M = 35k
Step 3 — Use the total retainer constraint.
L + S + M = €9,700
30k + 32k + 35k = 9,700
97k = 9,700 → k = 100
Step 4 — Solve for Marta's retainer.
M = 35k = 35 × 100 = €3,500
Answer: C (€3,500)
Quick sanity check: L = €3,000, S = €3,200, M = €3,500. Total = €9,700 ✓
Savings: Luca saves €900, Sophie saves €800, Marta saves €1,400 → ratio = 9 : 8 : 14 ✓
Takeaway: When a problem gives you spending percentages but a savings ratio, always flip to savings percentages first — then let a single constant k tie all three retainers together. The total constraint gives you k directly.
27 Feb 2026, 04:15
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Bunuel
GMAT Club Official Solution:
Let L, S, M be the retainers.
Savings:
Luca saves 30% so savings = 0.30L
Sophie saves 25% so savings = 0.25S
Marta saves 40% so savings = 0.40M
Given savings ratio 9:8:14, set
0.30L = 9k
0.25S = 8k
0.40M = 14k
Solve each:
L = 9k/0.30 = 9k/(3/10) = 9k * 10/3 = 30k
S = 8k/0.25 = 8k/(1/4) = 8k * 4 = 32k
M = 14k/0.40 = 14k/(2/5) = 14k * 5/2 = 35k
Total retainer:
30k + 32k + 35k = 97k = 9700
So k = 100
Marta’s retainer:
M = 35k = 3500 euros.
Answer: C.
