Free Pennsylvania Math Practice Test — LicenseIQ

Question 1

A buyer purchases a $300,000 home with a $60,000 down payment. What is the loan-to-value (LTV) ratio?

Accepted Answer

Loan = $300,000 - $60,000 = $240,000; $240,000 / $300,000 = 80% LTV. (20% is the down payment percentage.)

Question 2

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 3

When a broker appoints one salesperson to represent the seller and another salesperson in the same office to represent the buyer, this is:

Accepted Answer

Designated agency assigns separate agents within one brokerage; the broker is still a dual agent and written consent is required.

Question 4

A candidate passed the national portion of the salesperson exam on March 10, 2025 and the state portion on May 5, 2025. To use both scores, the completed license application must be received by the Commission no later than approximately:

Accepted Answer

Each part must be passed within 3 years before a properly completed application is submitted. The earlier score, the national portion on March 10, 2025, expires first, so the deadline is about March 10, 2028. Using the state date is tempting, but the national score would be stale by then.

Question 5

A house with only one bathroom and very small closets in a market expecting more suffers from:

Accepted Answer

Functional obsolescence is outdated design or layout inside the property. External obsolescence comes from outside the property and is usually incurable.

Question 6

A Philadelphia condo sells for $280,000. How much of the total transfer tax goes to the CITY?

Accepted Answer

City rate 3.578%: $280,000 × 0.03578 = $10,018.40. $2,800 is the state's 1%, $12,818.40 is the combined total, and $9,178.40 uses the old 3.278% city rate.

Question 7

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?

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Members of the State Real Estate Commission are appointed by the:

Accepted Answer

The Governor appoints the Commission's members. The Secretary of the Commonwealth heads the Department of State but does not appoint the Commission, and a trade association has no appointment power.

Question 10

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 11

A complaint of housing discrimination must be filed with the Pennsylvania Human Relations Commission within:

Accepted Answer

PHRC requires complaints within 180 days. One year is the federal HUD deadline under the Fair Housing Act.

Question 12

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 13

A borrower pays $4,500 for 1.5 discount points. What is the loan amount?

Accepted Answer

Loan = cost of points / points as a percentage = $4,500 / 0.015 = $300,000.

Question 14

A home sells for $520,000 with a 5% commission. The listing broker pays 2.5% to the buyer's broker and splits the listing side 60/40 with the listing salesperson (salesperson gets 60%). How much does the listing salesperson earn?

Accepted Answer

Total = $520,000 x 0.05 = $26,000. Buyer broker gets 2.5% = $13,000, leaving $13,000 for the listing side. Salesperson = $13,000 x 0.60 = $7,800.

Question 15

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 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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 19

A seller complains that the 6% commission she negotiated and signed was too high. What can the State Real Estate Commission do about the rate itself?

Accepted Answer

Pennsylvania has no Commission-set commission rate. Fees are negotiated between the broker and consumer, and the agreement must say so. The Commission disciplines licensees for violations, but it does not award civil damages or set fee schedules.

Question 20

A buyer's agent is paid by the listing broker out of the seller's commission. Whom does the buyer's agent represent?

Accepted Answer

The Consumer Notice states that a buyer's agent works exclusively for the buyer even if the seller pays the fee, and RELRA §606.1(d) confirms that payment alone does not create agency.

Question 21

A new highway interchange built next to a residential subdivision lowers home values. This is:

Accepted Answer

Loss in value caused by factors outside the property boundaries is external obsolescence.

Question 22

A Pennsylvania salesperson may lawfully accept a commission for a sale from:

Accepted Answer

RELRA §604(a)(12) prohibits a salesperson or associate broker from accepting compensation from anyone other than the employing broker. All pay flows through the broker.

Question 23

When the Commission disciplines a licensee based solely on discipline imposed in another state, it may NOT:

Accepted Answer

Section 604(a)(30) allows discipline based on discipline in another jurisdiction, but the Commission cannot impose a fine based solely on that ground.

Question 24

After a hearing, the State Real Estate Commission may impose a civil penalty on an unlicensed person practicing real estate of up to:

Accepted Answer

RELRA §305 authorizes a civil penalty of up to $1,000 on a licensee who violates the Act or on anyone practicing without a license, in addition to any criminal penalty. $500 is the criminal first-offense fine cap.

Question 25

A salesperson named Katherine wants to advertise as 'Kate.' Under Commission rules, she must:

Accepted Answer

Section 35.305(b) requires licensees who want to use and advertise a first-name nickname to include it on their license or biennial renewal application.

Pennsylvania real estate math practice test

1. A buyer purchases a $300,000 home with a $60,000 down payment. What is the loan-to-value (LTV) ratio?

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

3. When a broker appoints one salesperson to represent the seller and another salesperson in the same office to represent the buyer, this is:

4. A candidate passed the national portion of the salesperson exam on March 10, 2025 and the state portion on May 5, 2025. To use both scores, the completed license application must be received by the Commission no later than approximately:

5. A house with only one bathroom and very small closets in a market expecting more suffers from:

6. A Philadelphia condo sells for $280,000. How much of the total transfer tax goes to the CITY?

7. 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?

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

9. Members of the State Real Estate Commission are appointed by the:

10. 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?

11. A complaint of housing discrimination must be filed with the Pennsylvania Human Relations Commission within:

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

13. A borrower pays $4,500 for 1.5 discount points. What is the loan amount?

14. A home sells for $520,000 with a 5% commission. The listing broker pays 2.5% to the buyer's broker and splits the listing side 60/40 with the listing salesperson (salesperson gets 60%). How much does the listing salesperson earn?

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

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

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

18. 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?

19. A seller complains that the 6% commission she negotiated and signed was too high. What can the State Real Estate Commission do about the rate itself?

20. A buyer's agent is paid by the listing broker out of the seller's commission. Whom does the buyer's agent represent?

21. A new highway interchange built next to a residential subdivision lowers home values. This is:

22. A Pennsylvania salesperson may lawfully accept a commission for a sale from:

23. When the Commission disciplines a licensee based solely on discipline imposed in another state, it may NOT:

24. After a hearing, the State Real Estate Commission may impose a civil penalty on an unlicensed person practicing real estate of up to:

25. A salesperson named Katherine wants to advertise as 'Kate.' Under Commission rules, she must:

Sources