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28 Jun 2026, 11:44
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
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Question Stats:
57% (03:22) correct
43%
(03:35)
wrong
based on 28
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Date
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Montse works for Gulliver’s Travel. Her income in any given month consists of a fixed salary plus p percent of any amount by which Gulliver’s monthly sales exceed T dollars. Three months ago, the company’s sales were $93,000, and her income was $2,725. Two months ago, the company’s sales were $76,000, and her income was $2,500. Last month, the company’s sales were $95,000, and her income was $2,755.
What is the value of T?
A. 77,000
B. 78,000
C. 79,000
D. 80,000
E. 82,000
What is the value of T?
A. 77,000
B. 78,000
C. 79,000
D. 80,000
E. 82,000
28 Jun 2026, 19:02
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Income rises by $30 when sales rise $2,000, or $15 for every $1,000. When sales are $76,000, or sales drop $17,000, income drops $225 (15 x 15) - if no limit T it would have dropped $ (15 x 17). So $2,000 above $76,000 is the limit T
29 Jun 2026, 00:10
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The key insight here is figuring out which months had sales above T and which didn't. Let me set up the equation first.
Income = F + p*(Sales - T), but only when Sales > T. When Sales <= T, income = F (just the fixed salary).
Notice the three income values: $2,725, $2,500, $2,755. The lowest is $2,500 (when sales were $76,000). That's suspicious -- if all three months had sales above T, then as sales rise, income should rise proportionally. But $76k gives less income than both $93k and $95k, which makes sense. What doesn't make sense is if $76k were above T, we'd expect a consistent slope.
Let me check: if all three months had sales above T:
From month A to month C: sales rise $2,000, income rises $30. So p = 30/2000 = 1.5%
From month A to month B: sales drop $17,000, income drops $225. So p = 225/17000 = 1.32%
These give different values of p -- contradiction. So NOT all months are above T.
The only month that could be at or below T is the lowest-sales month: $76,000 (month B). So that month, income = F = $2,500.
Now set up equations using months A and C (both above T):
Month A: $2,500 + p*(93,000 - T) = $2,725, so p*(93,000 - T) = 225
Month C: $2,500 + p*(95,000 - T) = $2,755, so p*(95,000 - T) = 255
Divide: (95,000 - T)/(93,000 - T) = 255/225 = 17/15
Cross multiply:
15*(95,000 - T) = 17*(93,000 - T)
1,425,000 - 15T = 1,581,000 - 17T
2T = 156,000
T = 78,000
Answer is B.
The trap is assuming all three months are above T. Once you check the slope consistency and find it doesn't hold, the logic unlocks immediately. Classic GMAT move -- always verify your assumptions first.
Income = F + p*(Sales - T), but only when Sales > T. When Sales <= T, income = F (just the fixed salary).
Notice the three income values: $2,725, $2,500, $2,755. The lowest is $2,500 (when sales were $76,000). That's suspicious -- if all three months had sales above T, then as sales rise, income should rise proportionally. But $76k gives less income than both $93k and $95k, which makes sense. What doesn't make sense is if $76k were above T, we'd expect a consistent slope.
Let me check: if all three months had sales above T:
From month A to month C: sales rise $2,000, income rises $30. So p = 30/2000 = 1.5%
From month A to month B: sales drop $17,000, income drops $225. So p = 225/17000 = 1.32%
These give different values of p -- contradiction. So NOT all months are above T.
The only month that could be at or below T is the lowest-sales month: $76,000 (month B). So that month, income = F = $2,500.
Now set up equations using months A and C (both above T):
Month A: $2,500 + p*(93,000 - T) = $2,725, so p*(93,000 - T) = 225
Month C: $2,500 + p*(95,000 - T) = $2,755, so p*(95,000 - T) = 255
Divide: (95,000 - T)/(93,000 - T) = 255/225 = 17/15
Cross multiply:
15*(95,000 - T) = 17*(93,000 - T)
1,425,000 - 15T = 1,581,000 - 17T
2T = 156,000
T = 78,000
Answer is B.
The trap is assuming all three months are above T. Once you check the slope consistency and find it doesn't hold, the logic unlocks immediately. Classic GMAT move -- always verify your assumptions first.
