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04 Mar 2026, 20:00
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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:
95%
(hard)
Question Stats:
40% (02:10) correct
60%
(02:20)
wrong
based on 67
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A contractor was hired to build a house for $132,000, consisting of payments for material, labor, taxes, and regulatory adherence. The taxes were calculated as x% of the total cost of materials and labor. The cost of regulatory adherence was y% of the total cost of material, labor, and taxes. How much did the contractor charge to cover regulatory adherence?
(1) x = 10
(2) y = 20
(1) x = 10
(2) y = 20
05 Mar 2026, 01:35
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Nice layered word problem. Let me set it up cleanly.
Key Concept: Cascading Percentages in Data Sufficiency — when the total anchors the system
Define variables:
- M+L = combined cost of materials and labor
- Taxes = x% of (M+L)
- Regulatory adherence = y% of (M+L+Taxes)
- Total = (M+L) + Taxes + Regulatory = $132,000
Expressing everything in terms of M+L:
- Taxes = (x/100)(M+L)
- M+L+Taxes = (M+L)(1 + x/100)
- Regulatory = (y/100) × (M+L)(1 + x/100)
- Total = (M+L)(1 + x/100)(1 + y/100) = 132,000
So: Regulatory = Total × (y/100) / (1 + y/100) = 132,000 × (y/100) / (1 + y/100)
Notice: once we have the grand total of $132,000 fixed, we only need y to calculate regulatory adherence — because the total already folds in all the materials, labor, and taxes underneath.
Statement (1) alone: x = 10
Tells us the tax rate. But without y, we can't find regulatory adherence. Insufficient.
Statement (2) alone: y = 20
Regulatory = 132,000 × (0.20 / 1.20) = 132,000 × (1/6) = $22,000
This alone is sufficient — we don't need x at all.
Answer: B
The common trap: Students assume you need x first to find the materials+labor base, then apply y on top. But the $132,000 total already includes everything — so regulatory adherence as a share of the sub-total is directly calculable from the grand total and y alone. x becomes irrelevant.
Takeaway: In cascading-percentage Data Sufficiency problems, check whether the final total anchors the system — if it does, you may only need the last percentage in the chain, not every rate.
Key Concept: Cascading Percentages in Data Sufficiency — when the total anchors the system
Define variables:
- M+L = combined cost of materials and labor
- Taxes = x% of (M+L)
- Regulatory adherence = y% of (M+L+Taxes)
- Total = (M+L) + Taxes + Regulatory = $132,000
Expressing everything in terms of M+L:
- Taxes = (x/100)(M+L)
- M+L+Taxes = (M+L)(1 + x/100)
- Regulatory = (y/100) × (M+L)(1 + x/100)
- Total = (M+L)(1 + x/100)(1 + y/100) = 132,000
So: Regulatory = Total × (y/100) / (1 + y/100) = 132,000 × (y/100) / (1 + y/100)
Notice: once we have the grand total of $132,000 fixed, we only need y to calculate regulatory adherence — because the total already folds in all the materials, labor, and taxes underneath.
Statement (1) alone: x = 10
Tells us the tax rate. But without y, we can't find regulatory adherence. Insufficient.
Statement (2) alone: y = 20
Regulatory = 132,000 × (0.20 / 1.20) = 132,000 × (1/6) = $22,000
This alone is sufficient — we don't need x at all.
Answer: B
The common trap: Students assume you need x first to find the materials+labor base, then apply y on top. But the $132,000 total already includes everything — so regulatory adherence as a share of the sub-total is directly calculable from the grand total and y alone. x becomes irrelevant.
Takeaway: In cascading-percentage Data Sufficiency problems, check whether the final total anchors the system — if it does, you may only need the last percentage in the chain, not every rate.
08 Mar 2026, 07:00
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ExpertsGlobal5
Explanation:
Let the material cost be M.
Let the labor cost be L.
Let the taxes be T.
Let the regulatory adherence cost be R.
Since the contractor was hired to build a house for $132,000: M + L + T + R = 132,000 (Equation I)
Since taxes were calculated as x% of the total cost of materials and labor: T = x(M + L) / 100 (Equation II)
Since regulatory adherence cost was y% of the total cost of material, labor, and taxes: R = y(M + L + T) / 100 (Equation III)
We need to find whether the value of R can be determined.
Statement (1)
x = 10
From Equation II:
T = x(M + L) / 100
T = 10(M + L) / 100
T = (M + L) / 10
10T = M + L
Substituting the above equation into Equation I does not help determine the value of R. Hence, Statement (1) is insufficient.
Statement (2)
y = 20
From Equation III:
R = y(M + L + T) / 100
R = 20(M + L + T) / 100
R = (M + L + T) / 5
5R = M + L + T
Substituting the above value of (M + L + T) into Equation I:
M + L + T + R = 132,000
5R + R = 132,000
It is possible to determine with certainty the value of R. Hence, Statement (2) is sufficient.
B is the correct answer choice.
