Sample Questions

The following sample questions in the three major content clusters are illustrative of the types of questions that appear on the ELM test. Remember that the actual test will have 50 questions. Five of these questions are included for field-testing purposes and will not count toward your score.

The topic code following each sample question is keyed to the list of topics given in the Topics on the ELM Test.

  1. Unless otherwise specified, the denominators of algebraic expressions appearing in these problems are assumed to be nonzero.
  2. Figures that accompany problems are drawn as accurately as possible EXCEPT when it is stated that the figure is not drawn to scale.
  3. The Geometry Reference Formulas will be printed inside the front cover of the ELM test book.

Geometry Formulas

Sample Questions 1–15


The pilots of an airline have signed a new two-year contract. For the first year of the new contract, current salaries will be reduced by 25 percent. For the second year, these reduced salaries will be further reduced by 10 percent. What percent of their current salaries will the pilots earn during the second year of the new contract?

  1. 35%
  2. 65%
  3. 67.5%
  4. 72.5%
  5. 75%

Topic — Understand and use percent in context


The number of atoms of platinum (Pt) in the universe is estimated to be 1.4 times the number of atoms of silicon (Si) in the universe. The number of atoms of silver (Ag) in the universe is estimated to be 0.33 times the number of atoms of silicon in the universe. Based on these estimates, the number of atoms of platinum in the universe is approximately how many times the number of atoms of silver in the universe?

  1. 0.24
  2. 0.46
  3. 1.07
  4. 1.73
  5. 4.24

Topic — Carry out basic arithmetic calculations

image of a starfish


In the picture above, the perimeter of the starfish is 30 centimeters. This original picture is to be enlarged in both dimensions to an image that is similar to the original picture. If the area of the enlarged image is 9 times the area of the original picture, what is the perimeter in centimeters of the starfish in the enlarged image?

  1. 30
  2. 90
  3. 180
  4. 270
  5. 2,430

Topic — Calculate the ratio of corresponding geometric measurements of similar figures


Abraham's physics class has 40 students, and his class had an average (arithmetic mean) score of 75 on the midterm. Anita’s physics class has 20 students, and her class had an average score of 81 on the same midterm. What was the average score of all the students in both physics classes on the midterm?

  1. 77
  2. 77.5
  3. 78
  4. 78.5
  5. 79

Topic — Interpret and calculate the arithmetic mean


The average price of gas increased by 10 percent during one year. If x represents the average price of gas at the beginning of the year and if y represents the average price of gas at the end of the year, which of the following is true?

  1. x = 0.1y
  2. y = 0.1x
  3. y = x + 0.1
  4. y = 1.1x
  5. x = 1.1y

Topic — Express relationships among quantities using variables


Over the last thirty years, the speed of microprocessors has become approximately 4 times faster every 3 years. Based on this information, microprocessors made today are approximately how many times as fast as microprocessors made 9 years ago?

  1. 4 ?3
  2. 34
  3. 42
  4. 43

Topic — Interpret and use ratio and proportion in context


As a scooter salesman, Gerardo keeps track of how many scooters he sells each week. In his first four weeks on the job, he sold 9, 4, 7, and 6 scooters. In his fifth week, he sold k scooters. If the median number of scooters sold per week for the five weeks is equal to 7, which of the following must be true?

  1. k ≤ 4
  2. k ≤ 7
  3. k ≥ 7
  4. k ≤ 9
  5. k ≥ 9

Topic — Interpret and calculate the median


  1. 2-10
  2. 2-7
  3. 23
  4. 27
  5. 210

Topic — Use properties of exponents


Right circular cylinder A has radius r and height h. Right circular cylinder B has radius 2r and height What is the ratio of the volume of cylinder A to the volume of cylinder B?

  1. 1 to 1
  2. 1 to 2
  3. 2 to 1
  4. 2 to

Topic — Solve geometric problems using the properties of basic geometric figures


An airline overbooks a certain flight by selling 20 percent more tickets than the total number of seats for people. The airline sold 180 tickets for the flight. How many people with tickets will not have a seat on the flight?

  1. 20
  2. 24
  3. 28
  4. 30
  5. 36

Topic — Understand and use percent in context


  1. 5

Topic — Simplify algebraic expressions


The rectangular floor of a closet is 3 times as long as it is wide. If the distance from one corner of the floor to the opposite corner of the floor is 10 feet, what is the area of the floor in square feet?

  1. 25
  2. 30
  3. 50
  4. 10

Topic — Solve geometric problems using the properties of basic geometric figures


Topic — Solve linear equations


Which of the following is a factor of 16x3y + 4x2 y2 - 42xy3

  1. 2x + 3y
  2. 2x + 7y
  3. 4x + 3y
  4. 4x – 3y
  5. 4x + 7y

Topic — Perform polynomial arithmetic (add, subtract, multiply, divide and factor)


The rear wheel on a certain cyclist’s bike has a circumference of 2,108 millimeters.
The cyclist rode in a 200-kilometer race without the rear wheel slipping. Of the following, which best estimates the number of complete revolutions of the rear wheel during the race? (1 kilometer = 106 millimeters)

  1. Slightly less than 10,000 revolutions
  2. Slightly less than 100,000 revolutions
  3. Slightly more than 100,000 revolutions
  4. Slightly less than 1,000,000 revolutions
  5. Slightly more than 1,000,000 revolutions

Topic — Use estimation appropriately

Answers to Sample Questions on the ELM test

  1. C
  2. E
  3. B
  4. A
  5. D
  6. D
  7. C
  8. E
  9. B
  10. D
  11. D
  12. B
  13. E
  14. E
  15. B