District of Columbia real estate math practice test
25 questions with answers and explanations · 2026
1. A seller says, 'I will pay any broker a 5% commission if they bring me a buyer.' This promise creates a(n):
Answer & explanation
Answer: D. In a unilateral contract only one party is bound (to pay if the act is performed); the other party has no obligation to act. Most real estate contracts are bilateral.
2. On a $250,000 loan, how much is 2 discount points?
Answer & explanation
Answer: A. 1 point = 1% of the loan. 2 points = 0.02 x $250,000 = $5,000.
3. A borrower pays $4,500 for 1.5 discount points. What is the loan amount?
Answer & explanation
Answer: C. Loan = cost of points / points as a percentage = $4,500 / 0.015 = $300,000.
4. An owner offered tenants a building at $4,000,000. Which third-party contract price would require the owner to comply anew with TOPA?
Answer & explanation
Answer: D. Restart is required when the third-party price is more than 10% below the tenant price, meaning below $3,600,000. $3,560,000 is 11% below. $3,640,000 is 9% below, and the other prices are closer still.
5. How many members sit on the DC Board of Real Estate (the DC Real Estate Commission)?
Answer & explanation
Answer: A. §47-2853.06(h) creates a 9-member Board: 3 brokers, 2 salespersons, 2 property managers, 1 real estate attorney, and 1 consumer. 7 is a common board size elsewhere, but it is not DC's.
6. A listing where the seller may sell themselves without owing commission, but only the listing broker among agents is protected, is:
Answer & explanation
Answer: B. In an exclusive agency listing, the seller pays no commission on a self-sale, but the listing broker is protected if any broker sells it. (Reclassified to section 6 / CORE.)
7. An investor buys a rental house for $350,000; the land is valued at $75,000. Using straight-line depreciation over 27.5 years, the annual depreciation deduction is:
Answer & explanation
Answer: C. Only the building depreciates: $350,000 - $75,000 = $275,000; $275,000 / 27.5 = $10,000. Using the full price gives $12,727 (wrong).
8. The seller of a rental property collected $1,800 rent for the month on the 1st. Closing is on the 10th, and the seller owns the day of closing (30-day month). What is the rent proration?
Answer & explanation
Answer: C. Daily rent = $1,800 / 30 = $60. Buyer owns days 11-30 = 20 days. 20 x $60 = $1,200, credited to the buyer because the seller collected rent for days the buyer will own.
9. A commercial space of 2,400 rentable square feet is quoted at $27 per square foot per year. What is the monthly rent?
Answer & explanation
Answer: B. Annual rent = 2,400 x $27 = $64,800; monthly = $64,800 / 12 = $5,400. Commercial rates are quoted per square foot per YEAR.
10. On the $20,000 commission above, the listing broker keeps 50% and pays 50% to the buyer's broker. How much does the buyer's broker receive?
Answer & explanation
Answer: D. $20,000 x 0.50 = $10,000 to the buyer's broker.
11. A residential property sells for $520,000. What is the combined DC recordation and transfer tax?
Answer & explanation
Answer: D. At $400,000 or more, each tax is 1.45%: 0.0145 × 520,000 = $7,540, and two taxes total $15,080. $11,440 wrongly uses 1.1% for both.
12. A buyer purchases a $275,000 home with an 80% LTV loan and pays 2.5 discount points. What do the points cost?
Answer & explanation
Answer: A. Loan = $275,000 x 0.80 = $220,000; points = $220,000 x 0.025 = $5,500. ($6,875 wrongly applies points to the price.)
13. A broker received a 4.2% commission totaling $12,600. What was the sale price?
Answer & explanation
Answer: C. Sale price = commission / rate = $12,600 / 0.042 = $300,000.
14. A lender approves a $276,000 loan and the buyer wants to keep an 80% LTV. What is the maximum purchase price?
Answer & explanation
Answer: A. Purchase price = loan / LTV = $276,000 / 0.80 = $345,000. ($220,800 wrongly multiplies by 0.80.)
15. A lender offers a 95% LTV loan. The buyer has $18,000 for the down payment. What is the maximum purchase price?
Answer & explanation
Answer: A. At 95% LTV the down payment is 5% of price. Price = $18,000 / 0.05 = $360,000; loan = $342,000.
16. A buyer contracts to buy a home for $300,000, but it appraises at $290,000. The lender offers 75% LTV. What is the maximum loan?
Answer & explanation
Answer: B. LTV is applied to the LESSER of price or appraised value: $290,000 x 0.75 = $217,500. Using the $300,000 price ($225,000) is the common mistake.
17. A house with only one bathroom and very small closets in a market expecting more suffers from:
Answer & explanation
Answer: C. Functional obsolescence is outdated design or layout inside the property. External obsolescence comes from outside the property and is usually incurable.
18. Under the Code of Ethics, commission disputes between REALTORS associated with different firms are generally resolved through:
Answer & explanation
Answer: B. Article 17 requires REALTORS to mediate or arbitrate contractual and specific non-contractual disputes with other REALTORS through the association.
19. An investment property with NOI of $63,000 sells for $900,000. What is the capitalization rate?
Answer & explanation
Answer: C. Cap rate = NOI / value = $63,000 / $900,000 = 0.07 = 7%.
20. A rectangular parcel measures 330 feet by 660 feet. How many acres does it contain?
Answer & explanation
Answer: D. Area = 330 x 660 = 217,800 sq ft; 217,800 / 43,560 = 5 acres.
21. An escrow holder must notify the Commission of the financial institution's name and address and the escrow account number within how many calendar days?
Answer & explanation
Answer: B. §42-1704(b)(1) requires notice within 14 calendar days. Seven days is the deadline for depositing funds.
22. A residential condo sells for $360,000. What is the seller's DC transfer tax?
Answer & explanation
Answer: A. Residential property under $400,000 is taxed at 1.1%, and 0.011 × 360,000 = $3,960. $7,920 is the combined recordation and transfer tax.
23. A licensee is found by the DC Commission on Human Rights to have violated the Human Rights Act. For licensing purposes, this is:
Answer & explanation
Answer: A. §47-2853.197(a)(33) makes a determined HRA violation a prohibited act.
24. A DC salesperson may accept a commission for licensed activity only from:
Answer & explanation
Answer: A. §47-2853.197(a)(6) restricts payment to the salesperson's broker as of the time the fee was earned.
25. A DC salesperson asks the broker to pay their commission to the salesperson's single-member LLC. Under the unlicensed-payment rule, this is:
Answer & explanation
Answer: C. §47-2853.197(a)(38)(B) allows payment, at the licensee's direction, to an entity comprised solely of licensees, excluding administrative and maintenance staff.
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