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Sample LUMS LCAT Practice Questions

Try these sample questions to review concepts for the LUMS LCAT exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 98+ question experience with AI tutoring.

1If 4(2x - 3) - 3(x + 1) = 2x + 9, what is the value of x?
A.6
B.7
C.8
D.9
Explanation: Distributing the constants on the left side gives 8x - 12 - 3x - 3 = 2x + 9, which simplifies to 5x - 15 = 2x + 9. Subtracting 2x from both sides yields 3x - 15 = 9. Adding 15 to both sides gives 3x = 24, so dividing by 3 results in x = 8.
2Which of the following represents the solution set for the inequality -3x + 7 >= 22?
A.x <= -5
B.x >= -5
C.x <= 5
D.x >= 5
Explanation: Subtracting 7 from both sides of the inequality gives -3x >= 15. When dividing both sides by a negative number (-3), the inequality sign must be reversed, yielding x <= -5.
3In the system of equations below, what is the value of x + y? 2x + 3y = 19 3x - y = 12
A.7
B.8
C.9
D.11
Explanation: Multiplying the second equation by 3 gives 9x - 3y = 36. Adding this to the first equation eliminates y: 11x = 55, which yields x = 5. Substituting x = 5 into 3x - y = 12 gives 15 - y = 12, so y = 3. Therefore, x + y = 5 + 3 = 8.
4For which value of the constant k will the system of equations below have infinitely many solutions? 3x - 5y = 12 kx - 15y = 36
A.3
B.6
C.9
D.-9
Explanation: A system of two linear equations has infinitely many solutions if the two equations are multiples of each other, representing the same line. Multiplying the first equation by 3 gives 9x - 15y = 36. Comparing this directly to kx - 15y = 36 shows that k must equal 9.
5A ride-hailing service charges a base fee of 150 PKR plus 45 PKR for each kilometer traveled. If a customer paid 690 PKR for a ride, what was the total distance traveled in kilometers?
A.10
B.12
C.14
D.15
Explanation: The total fare can be modeled by the linear equation 150 + 45d = 690, where d is the distance in kilometers. Subtracting 150 from 690 gives 540 PKR for the mileage charge. Dividing 540 by 45 yields d = 12 kilometers.
6What is the sum of all solutions to the equation |3x - 4| = 17?
A.4/3
B.8/3
C.14/3
D.6
Explanation: Splitting the absolute value equation into two cases gives 3x - 4 = 17 or 3x - 4 = -17. For the first case, 3x = 21, so x = 7. For the second case, 3x = -13, so x = -13/3. The sum of the solutions is 7 + (-13/3) = 21/3 - 13/3 = 8/3.
7Which inequality represents the set of all real numbers x such that |2x + 5| < 13?
A.-9 < x < 4
B.x < -9 or x > 4
C.-4 < x < 9
D.-9 <= x <= 4
Explanation: The inequality |2x + 5| < 13 expands to the compound inequality -13 < 2x + 5 < 13. Subtracting 5 from all three parts gives -18 < 2x < 8. Dividing by 2 yields -9 < x < 4.
8What are the roots of the quadratic equation 2x^2 - 7x - 15 = 0?
A.x = -5 and x = 3/2
B.x = 5 and x = -3/2
C.x = 5 and x = 3/2
D.x = -5 and x = -3/2
Explanation: Factoring by grouping, we seek factors of (2)(-15) = -30 that sum to -7, which are -10 and 3. Rewriting gives 2x(x - 5) + 3(x - 5) = (2x + 3)(x - 5) = 0. Setting each factor to zero yields x = -3/2 and x = 5.
9For what positive value of k does the equation x^2 - 6x + k = 0 have exactly one distinct real solution?
A.3
B.6
C.9
D.36
Explanation: A quadratic equation ax^2 + bx + c = 0 has exactly one distinct real solution when its discriminant Delta = b^2 - 4ac equals 0. Here, (-6)^2 - 4(1)(k) = 0, which gives 36 - 4k = 0. Solving for k yields k = 9.
10What is the maximum value of the quadratic function f(x) = -2x^2 + 12x - 11?
A.3
B.7
C.11
D.18
Explanation: The vertex of a parabola f(x) = ax^2 + bx + c occurs at x = -b / (2a) = -12 / (-4) = 3. Substituting x = 3 into the function yields f(3) = -2(3)^2 + 12(3) - 11 = -18 + 36 - 11 = 7. Because the leading coefficient a = -2 is negative, the parabola opens downward, making 7 the maximum value.

About the LUMS LCAT Exam

Independent English-language MCQs by OpenExamPrep for LCAT mathematics, reading and writing skills. Official samples cover algebra, advanced mathematics, data analysis, geometry/trigonometry, information and ideas, text structure and English conventions. Eligibility depends on the chosen school's secondary-qualification and subject requirements; consult the undergraduate criteria and equivalence rules. LCAT is an MCQ assessment, while application essays, references and any requested interview are separate admission work. This bank is neither an official paper nor a substitute for that work.

Exam sponsor: Lahore University of Management Sciences (LUMS). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

English-language paper-based MCQs in two verbal and two mathematics sections; calculators are not allowed. Undergraduate applicants may use SAT, ACT or LCAT as specified. Law applicants also require HEC LAT; the SBASSE subject test listed for graduate admissions is not a universal undergraduate requirement.

Time Limit

Four 40-minute sections: 160 minutes of testing; allow approximately three hours for the administered session.

Passing Score

No universal LCAT pass mark published in the reviewed guidance; admission is competitive and considers the full application.

Exam / Certification Fees

LCAT PKR 6,500, separate from undergraduate application processing of PKR 11,500 for local applicants or USD 200 for international applicants; follow the issued voucher.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

Mathematics sections; subdomain weights not confirmed

Algebra and Advanced Mathematics

Equations, functions, quadratics and algebraic structure.

Mathematics sections; subdomain weights not confirmed

Problem Solving, Data and Geometry

Ratios, probability, statistics, geometry and trigonometry.

Verbal sections; subdomain weights not confirmed

Reading

Information, ideas, evidence, inference and text structure.

Verbal sections; subdomain weights not confirmed

Writing and Language

Standard English conventions and expression of ideas.

Preparing for the LUMS LCAT Exam

What You Need to Know

  • Passing score: No universal LCAT pass mark published in the reviewed guidance; admission is competitive and considers the full application.
  • Assessment: English-language paper-based MCQs in two verbal and two mathematics sections; calculators are not allowed. Undergraduate applicants may use SAT, ACT or LCAT as specified. Law applicants also require HEC LAT; the SBASSE subject test listed for graduate admissions is not a universal undergraduate requirement.
  • Time limit: Four 40-minute sections: 160 minutes of testing; allow approximately three hours for the administered session.
  • Exam / certification fees: LCAT PKR 6,500, separate from undergraduate application processing of PKR 11,500 for local applicants or USD 200 for international applicants; follow the issued voucher. Official sources

Using Our Practice Resources

  • Work through all 98 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

LUMS LCAT: Suggested Study Strategy

1Use official samples to understand the skill domains.
2Practise mathematics without calculators.
3Prepare application writing and any requested interview separately.

Frequently Asked Questions

Is LCAT only for the business school?

No. LUMS lists it as an undergraduate testing option across schools. Check additional requirements, including LAT for law.

Are calculators permitted?

No. Practise the mathematics skills without a calculator.