Free Arizona Math Practice Test — LicenseIQ

Question 1

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

Accepted Answer

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

Question 2

A buyer purchases a $275,000 home with an 80% LTV loan and pays 2.5 discount points. What do the points cost?

Accepted Answer

Loan = $275,000 x 0.80 = $220,000; points = $220,000 x 0.025 = $5,500. ($6,875 wrongly applies points to the price.)

Question 3

Under an open listing, the seller owes a commission to:

Accepted Answer

Open listings are non-exclusive; only the procuring broker is paid, and the owner owes nothing for a self-sale.

Question 4

A broker received a 4.2% commission totaling $12,600. What was the sale price?

Accepted Answer

Sale price = commission / rate = $12,600 / 0.042 = $300,000.

Question 5

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?

Accepted Answer

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.

Question 6

Four buyers in a single transaction each obtain a $12,000 judgment against the same salesperson for fraud. Assuming all other requirements are met, what is the most the Recovery Fund will pay in total for this transaction?

Accepted Answer

The judgments total 4 x $12,000 = $48,000, but A.R.S. §32-2186(B) caps payment at $30,000 per transaction regardless of the number of claimants. The $90,000 per-licensee cap does not raise the per-transaction limit.

Question 7

An owner-occupied home has an LPV of $320,000. The combined tax rate is $9.00 per $100 of assessed value. Using a 10% assessment ratio, what is the annual tax?

Accepted Answer

Assessed value = $320,000 x 10% = $32,000. Tax = ($32,000 / 100) x $9.00 = 320 x 9 = $2,880.

Question 8

A landowner divides a ranch into eight parcels of 40 acres each and offers them for sale. Under Arizona law these are:

Accepted Answer

Unsubdivided lands are six or more parcels, each 36 acres or more but less than 160 acres. Forty-acre parcels fall in that range.

Question 9

Which of the following is a letter of concern issued by the Arizona Commissioner?

Accepted Answer

Under A.R.S. §32-2153(F), a letter of concern advises a licensee that conduct does not presently warrant disciplinary action but should be modified or discipline may follow. It is not itself discipline.

Question 10

An ad describes a 38,000-square-foot lot as a 'one-acre homesite.' Under Arizona rules this is:

Accepted Answer

R4-28-502(H) permits the term 'acre' only for land equal to 43,560 square feet. 38,000 is 0.87 acre (38,000 / 43,560 = 0.872).

Question 11

A seller wants to net $250,000 after paying a 6% commission and $6,000 in other closing costs. To the nearest dollar, what must the sale price be?

Accepted Answer

Net + other costs = $256,000, which equals 94% of the price (100% - 6%). Price = $256,000 / 0.94 = $272,340.43, about $272,340. Adding 6% to $256,000 ($271,360) understates the price.

Question 12

An investment property with NOI of $63,000 sells for $900,000. What is the capitalization rate?

Accepted Answer

Cap rate = NOI / value = $63,000 / $900,000 = 0.07 = 7%.

Question 13

A lender offers a 95% LTV loan. The buyer has $18,000 for the down payment. What is the maximum purchase price?

Accepted Answer

At 95% LTV the down payment is 5% of price. Price = $18,000 / 0.05 = $360,000; loan = $342,000.

Question 14

A seller says, 'I will pay any broker a 5% commission if they bring me a buyer.' This promise creates a(n):

Accepted Answer

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.

Question 15

Under Arizona's Commissioner's Rules, a licensee owes a fiduciary duty to the client and must also:

Accepted Answer

R4-28-1101(A) says the licensee owes a fiduciary duty to the client, must protect and promote the client's interests, and must deal fairly with all other parties. Fair dealing is not equal representation.

Question 16

A lender approves a $276,000 loan and the buyer wants to keep an 80% LTV. What is the maximum purchase price?

Accepted Answer

Purchase price = loan / LTV = $276,000 / 0.80 = $345,000. ($220,800 wrongly multiplies by 0.80.)

Question 17

When competing brokerages agree to charge the same commission rate, they commit:

Accepted Answer

Agreeing on commissions among competitors is illegal price fixing under the Sherman Antitrust Act; commissions must be set independently and are always negotiable.

Question 18

An Arizona salesperson is convicted of a misdemeanor. Within what period must the salesperson notify the Commissioner in writing?

Accepted Answer

R4-28-301(F) requires written notice to the Commissioner within 10 days of a misdemeanor or felony conviction, along with supporting documentation. Waiting until renewal is a common wrong assumption.

Question 19

On a $250,000 loan, how much is 2 discount points?

Accepted Answer

1 point = 1% of the loan. 2 points = 0.02 x $250,000 = $5,000.

Question 20

An 8-unit building rents for $1,100 per unit per month with 5% vacancy. Annual operating expenses are $28,320 (excluding debt service). At an 8% capitalization rate, what is the value?

Accepted Answer

PGI = 8 x $1,100 x 12 = $105,600; less 5% vacancy = $100,320; NOI = $100,320 - $28,320 = $72,000; value = $72,000 / 0.08 = $900,000.

Question 21

A house is L-shaped: one section is 40 ft by 30 ft and the other is 20 ft by 15 ft. At $185 per square foot, what is the estimated cost to build?

Accepted Answer

Area = (40 x 30) + (20 x 15) = 1,200 + 300 = 1,500 sq ft; 1,500 x $185 = $277,500.

Question 22

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?

Accepted Answer

$20,000 x 0.50 = $10,000 to the buyer's broker.

Question 23

An Arizona salesperson has completed 3 hours each in Agency Law, Contract Law, Commissioner's Standards, Fair Housing, and Disclosure, plus 9 hours of General Real Estate. What must she still complete to renew?

Accepted Answer

She has 15 + 9 = 24 hours, but she is missing the required 3-hour minimum in Real Estate Legal Issues. Every one of the six mandatory categories must be met; elective hours cannot substitute. The Broker Management Clinic applies to designated brokers.

Question 24

When the Commissioner orders payment from the Recovery Fund on account of a licensee, the licensee's license is:

Accepted Answer

A.R.S. §32-2188(I) provides that the license is automatically terminated when payment is authorized, and the person cannot be relicensed until the amount paid plus interest is repaid and the judgment is satisfied.

Question 25

A developer divides a 180-acre tract into equal parcels. Which division would create subdivided lands (rather than unsubdivided lands) under A.R.S. §32-2101?

Accepted Answer

180 / 6 = 30 acres each. Six or more lots under 36 acres is subdivided land. 180 / 5 = 36 acres gives only five parcels, which is not a subdivision, and 180 / 4 = 45 acres gives only four.

Arizona real estate math practice test

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

2. A buyer purchases a $275,000 home with an 80% LTV loan and pays 2.5 discount points. What do the points cost?

3. Under an open listing, the seller owes a commission to:

4. A broker received a 4.2% commission totaling $12,600. What was the sale price?

5. 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?

6. Four buyers in a single transaction each obtain a $12,000 judgment against the same salesperson for fraud. Assuming all other requirements are met, what is the most the Recovery Fund will pay in total for this transaction?

7. An owner-occupied home has an LPV of $320,000. The combined tax rate is $9.00 per $100 of assessed value. Using a 10% assessment ratio, what is the annual tax?

8. A landowner divides a ranch into eight parcels of 40 acres each and offers them for sale. Under Arizona law these are:

9. Which of the following is a letter of concern issued by the Arizona Commissioner?

10. An ad describes a 38,000-square-foot lot as a 'one-acre homesite.' Under Arizona rules this is:

11. A seller wants to net $250,000 after paying a 6% commission and $6,000 in other closing costs. To the nearest dollar, what must the sale price be?

12. An investment property with NOI of $63,000 sells for $900,000. What is the capitalization rate?

13. A lender offers a 95% LTV loan. The buyer has $18,000 for the down payment. What is the maximum purchase price?

14. A seller says, 'I will pay any broker a 5% commission if they bring me a buyer.' This promise creates a(n):

15. Under Arizona's Commissioner's Rules, a licensee owes a fiduciary duty to the client and must also:

16. A lender approves a $276,000 loan and the buyer wants to keep an 80% LTV. What is the maximum purchase price?

17. When competing brokerages agree to charge the same commission rate, they commit:

18. An Arizona salesperson is convicted of a misdemeanor. Within what period must the salesperson notify the Commissioner in writing?

19. On a $250,000 loan, how much is 2 discount points?

20. An 8-unit building rents for $1,100 per unit per month with 5% vacancy. Annual operating expenses are $28,320 (excluding debt service). At an 8% capitalization rate, what is the value?

21. A house is L-shaped: one section is 40 ft by 30 ft and the other is 20 ft by 15 ft. At $185 per square foot, what is the estimated cost to build?

22. 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?

23. An Arizona salesperson has completed 3 hours each in Agency Law, Contract Law, Commissioner's Standards, Fair Housing, and Disclosure, plus 9 hours of General Real Estate. What must she still complete to renew?

24. When the Commissioner orders payment from the Recovery Fund on account of a licensee, the licensee's license is:

25. A developer divides a 180-acre tract into equal parcels. Which division would create subdivided lands (rather than unsubdivided lands) under A.R.S. §32-2101?

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