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04 Mar 2026, 21:48
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (01:41) correct
27%
(01:07)
wrong
based on 60
sessions
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Jay's net income equals his gross income minus his deductions. By what percent did Jay's net income change as of December 31, when both his gross income and his deductions increased?
(1) Jay's gross income increased by 8 percent on December 31.
(2) Jay's deductions increased by 16 percent on December 31.
(1) Jay's gross income increased by 8 percent on December 31.
(2) Jay's deductions increased by 16 percent on December 31.
04 Mar 2026, 23:10
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When percentage increase or decrease is asked we need to be able to factor out income and deductions.
Both statements are clearly not enough individually as they dont tell about either deductions or income in one of them.
Combining both:
1.08x+1.16y = Net; and here we cant factor out completely, thus we cant say the percent increase or decrease.
INSUFFICIENT.
Answer: Option E
Both statements are clearly not enough individually as they dont tell about either deductions or income in one of them.
Combining both:
1.08x+1.16y = Net; and here we cant factor out completely, thus we cant say the percent increase or decrease.
INSUFFICIENT.
Answer: Option E
Bunuel
05 Mar 2026, 01:33
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This one catches a lot of people because the statements feel like they should be enough together. Let me show why they aren't.
Key Concept: Percent Change in Data Sufficiency — you need the base values, not just the percent changes
Set up the relationship:
Net = Gross − Deductions
Let original Gross = G and original Deductions = D.
So original Net = G − D.
Statement (1) alone: Gross increased by 8%
New Gross = 1.08G. But we have no information about what happened to deductions or what D is relative to G. Insufficient.
Statement (2) alone: Deductions increased by 16%
New Deductions = 1.16D. Same problem — we don't know G relative to D. Insufficient.
Both statements together:
New Net = 1.08G − 1.16D
Percent change in net = [(1.08G − 1.16D) − (G − D)] / (G − D)
= (0.08G − 0.16D) / (G − D)
This simplifies to: 0.08(G − 2D) / (G − D)
This expression depends on the ratio of G to D. Without knowing that ratio, you can't get a unique answer.
Quick check: if G = 100 and D = 20, percent change = (8 − 3.2)/80 = 6%. If G = 100 and D = 40, percent change = (8 − 6.4)/60 = 2.67%. Different ratios, different answers. Still insufficient.
Answer: E
The common trap: Students see two percent changes and think "two pieces of information for two variables — must be sufficient." The mistake is forgetting that percent change in net income depends on the ratio of deductions to gross income, which is a third unknown neither statement addresses.
Takeaway: In Data Sufficiency percent-change problems, always ask yourself whether you know the base values or just how they changed — knowing only the percent changes to components is rarely enough to find the percent change in a derived quantity.
Key Concept: Percent Change in Data Sufficiency — you need the base values, not just the percent changes
Set up the relationship:
Net = Gross − Deductions
Let original Gross = G and original Deductions = D.
So original Net = G − D.
Statement (1) alone: Gross increased by 8%
New Gross = 1.08G. But we have no information about what happened to deductions or what D is relative to G. Insufficient.
Statement (2) alone: Deductions increased by 16%
New Deductions = 1.16D. Same problem — we don't know G relative to D. Insufficient.
Both statements together:
New Net = 1.08G − 1.16D
Percent change in net = [(1.08G − 1.16D) − (G − D)] / (G − D)
= (0.08G − 0.16D) / (G − D)
This simplifies to: 0.08(G − 2D) / (G − D)
This expression depends on the ratio of G to D. Without knowing that ratio, you can't get a unique answer.
Quick check: if G = 100 and D = 20, percent change = (8 − 3.2)/80 = 6%. If G = 100 and D = 40, percent change = (8 − 6.4)/60 = 2.67%. Different ratios, different answers. Still insufficient.
Answer: E
The common trap: Students see two percent changes and think "two pieces of information for two variables — must be sufficient." The mistake is forgetting that percent change in net income depends on the ratio of deductions to gross income, which is a third unknown neither statement addresses.
Takeaway: In Data Sufficiency percent-change problems, always ask yourself whether you know the base values or just how they changed — knowing only the percent changes to components is rarely enough to find the percent change in a derived quantity.
