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D
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Difficulty:
85%
(hard)
Question Stats:
46% (03:49) correct
54%
(03:01)
wrong
based on 13
sessions
History
Date
Time
Result
Not Attempted Yet
The provincial income tax that Leonor pays is \(p\%\) of the first $42,000 of her annual income plus \((p+3)\%\) of any amount above $42,000. The provincial tax Leonor pays is \((p+0.75)\%\) of her annual income. What is her annual income?
(A) $48,000
(B) $52,000
(C) $54,000
(D) $56,000
(E) $60,000
(A) $48,000
(B) $52,000
(C) $54,000
(D) $56,000
(E) $60,000
![The provincial income tax that Leonor pays is [m]p\%[/m] of](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "The provincial income tax that Leonor pays is [m]p\%[/m] of"){kind=icon}
26 Apr 2026, 01:17
Kudos
Bookmarks
This is a nice Word Problems / Algebra setup. The concept being tested is building a tax equation with two different rates and then equating it to a single blended rate.
Let x = Leonor's annual income (and x > $42,000, since she's paying the higher bracket rate too).
1. Tax formula from the brackets: p% of $42,000 + (p+3)% of (x - 42,000)
2. Tax formula from the blended rate: (p + 0.75)% of x
Set them equal and divide everything by 0.01 to drop the percentage notation:
42000p + (p+3)(x - 42000) = (p + 0.75)x
3. Expand the left side:
42000p + px - 42000p + 3x - 126000 = px + 0.75x
The 42000p terms cancel:
px + 3x - 126000 = px + 0.75x
4. The px terms cancel too:
3x - 126000 = 0.75x
2.25x = 126000
x = 56,000
Answer is D.
The trap most people fall into here is getting intimidated by the variable p and assuming you can't solve without knowing its value. But when you expand and simplify, p completely cancels out. That's the whole trick. If you spent time trying to find p or trying to substitute answer choices into the p term, you burned time for nothing.
I'd actually flag this type as a "two-rate blended average" problem. They show up on GMAT Focus in both PS and Data Sufficiency, and the algebra almost always collapses neatly if you're patient with the expansion.
Let x = Leonor's annual income (and x > $42,000, since she's paying the higher bracket rate too).
1. Tax formula from the brackets: p% of $42,000 + (p+3)% of (x - 42,000)
2. Tax formula from the blended rate: (p + 0.75)% of x
Set them equal and divide everything by 0.01 to drop the percentage notation:
42000p + (p+3)(x - 42000) = (p + 0.75)x
3. Expand the left side:
42000p + px - 42000p + 3x - 126000 = px + 0.75x
The 42000p terms cancel:
px + 3x - 126000 = px + 0.75x
4. The px terms cancel too:
3x - 126000 = 0.75x
2.25x = 126000
x = 56,000
Answer is D.
The trap most people fall into here is getting intimidated by the variable p and assuming you can't solve without knowing its value. But when you expand and simplify, p completely cancels out. That's the whole trick. If you spent time trying to find p or trying to substitute answer choices into the p term, you burned time for nothing.
I'd actually flag this type as a "two-rate blended average" problem. They show up on GMAT Focus in both PS and Data Sufficiency, and the algebra almost always collapses neatly if you're patient with the expansion.
