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Utah real estate math practice test

25 questions with answers and explanations · 2026

1. Which form is NOT one of the forms approved by the Utah Real Estate Commission and the Attorney General?

Answer & explanation

Answer: D. R162-2f-401f lists the REPC, addenda, financing and lead-paint forms, and the all-inclusive trust deed and note. Listing agreements are not on the list.

2. 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.

3. 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.

4. 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.

5. Commissions owed to a Utah principal broker must be moved from the trust account to the operating account within:

Answer & explanation

Answer: A. R162-2f-403a(13) treats failure to transfer within 60 days as commingling. Thirty days is a plausible but incorrect guess.

6. A Utah sales agent's seller client refuses to pay the commission. Who may sue the seller to collect?

Answer & explanation

Answer: A. 61-2f-409 lets only the principal broker or affiliated entity sue. An agent may sue only the principal broker the agent is or was affiliated with.

7. A home sells for $400,000 with a 5% total commission. What is the total commission?

Answer & explanation

Answer: B. $400,000 x 0.05 = $20,000.

8. Under the Utah REPC, property taxes and HOA dues are prorated as of:

Answer & explanation

Answer: A. REPC Section 4.1 prorates as of the Settlement Deadline in Section 24(d). Possession date is a common but incorrect guess.

9. A buyer purchases a home for $425,000 with a loan of $361,250. What is the LTV?

Answer & explanation

Answer: B. LTV = loan / price = $361,250 / $425,000 = 0.85 = 85%. (15% is the down payment percentage.)

10. 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.)

11. A Utah sales agent may lawfully receive a commission check directly from a title insurance agent when:

Answer & explanation

Answer: C. 61-2f-305 allows payment through a title insurance agent following the principal broker's written instructions. Otherwise agents accept compensation only from their principal broker, and client consent does not substitute.

12. A listing agreement in which the broker earns a commission regardless of who sells the property is a(n):

Answer & explanation

Answer: B. In an exclusive right-to-sell listing, the listing broker earns a commission no matter who procures the buyer, even the owner. (Reclassified to section 6 / CORE.)

13. A rectangular lot is 100 ft by 150 ft. How many square feet is it?

Answer & explanation

Answer: C. Area = length x width = 100 x 150 = 15,000 square feet. (250 is the sum of two sides.)

14. How many members serve on the Utah Real Estate Commission?

Answer & explanation

Answer: B. 61-2f-103 creates a five-member Commission appointed by the governor with Senate consent. Three is tempting because three members make a quorum, but the Commission has five members.

15. 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.

16. Under R162-2f-401l, an inducement gift from a licensee to a buyer is permissible and not illegal commission sharing if it:

Answer & explanation

Answer: D. The rule conditions inducement gifts on compliance with applicable loan underwriting guidelines. It sets no dollar cap.

17. Buyer debits: $389,000 price, $525 escrow fee, $3,875 loan costs. Buyer credits: $4,000 earnest money, $311,200 new loan, $2,500 seller concession, $1,137 tax proration. Cash due from the buyer at closing is:

Answer & explanation

Answer: D. Debits total $393,400 and credits total $318,837, so $393,400 − $318,837 = $74,563. $76,837 counts the tax proration as a debit instead of a credit.

18. A broker earned a $15,750 commission on a $450,000 sale. What was the commission rate?

Answer & explanation

Answer: A. Rate = commission / sale price = $15,750 / $450,000 = 0.035 = 3.5%.

19. A salesperson earns $6,000 on a $150,000 sale. What was the commission rate?

Answer & explanation

Answer: B. Rate = commission / sale price = $6,000 / $150,000 = 0.04 = 4%.

20. A home sells for $389,000. The seller pays a 5% commission, a $212,600 mortgage payoff, $1,200 attorney fee, $1,950 transfer tax and $600 in other costs. What are the seller's net proceeds?

Answer & explanation

Answer: D. Commission = $389,000 x 0.05 = $19,450. Total costs = $19,450 + $212,600 + $1,200 + $1,950 + $600 = $235,800. Net = $389,000 - $235,800 = $153,200.

21. A borrower paid $3,150 in points on a $210,000 loan. How many points were paid?

Answer & explanation

Answer: A. Points = cost / loan = $3,150 / $210,000 = 0.015 = 1.5 points (1 point = 1% of the loan).

22. A primary residence worth $600,000 is in an area with a combined tax rate of 0.0105. The annual tax is:

Answer & explanation

Answer: C. Taxable value is $600,000 × 0.55 = $330,000, and $330,000 × 0.0105 = $3,465. $6,300 ignores the exemption.

23. 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%.

24. Annual taxes of $4,380 are unpaid. The Settlement Deadline is March 15 (not a leap year), and the seller is responsible through March 15. Using a 365-day year, the proration is:

Answer & explanation

Answer: B. Jan 31 + Feb 28 + Mar 15 = 74 days, and $4,380 ÷ 365 = $12 per day, so 74 × $12 = $888. Because taxes are unpaid, the seller pays the buyer. $876 uses 73 days, leaving off the settlement day.

25. A 275-gallon heating oil tank costs $168 to fill at $4.20 per gallon. The buyer will credit the seller for the oil remaining in the tank. What is the credit?

Answer & explanation

Answer: C. Gallons needed = $168 / $4.20 = 40; remaining = 275 - 40 = 235 gallons; credit = 235 x $4.20 = $987.

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