CLEP COLLEGE COMPOSITION 2026 EXAM
QUESTIONS AND FULL SOLUTIONS 100%
CORRECT
◉ Triangle DEF (not shown) is similar to ABC shown, with angle B
congruent to angle E and angle C congruent to angle F. The length of
side DE is 6 cm. If the area of ABC is 5 square centimeters, what is
the area of DEF ? Answer: 45cm^2
◉ m is an odd integer. For each of the following numbers, check if
the number is odd. Answer: 2m-1
2m+1
m^2 + m + 1
◉ Which of the following statements is NOT true for all real
numbers a and b ? Answer: a^3 - b^3 = (a+b^2) (a^2-b)
◉ For any positive integers a and b, the operation ^ is defined as
a^b=(2a-1)^b-1 . What is the value of (2^2)^3? Answer: 25
◉ A company manufactures electronic components that each must
weigh from 29.5 grams to 30.5 grams, inclusive. Which of the
,following inequalities describes all acceptable weights x, in grams,
for each component? Answer: |30-x| <= 0.5
◉ Assume that x is the standard deviation of the set of the nonzero
numbers {a, b, c, d, e} For each of the following sets, indicate which
sets must have a standard deviation equal to x. Answer: {a+2, b+2,
c+2, d+2, e+2}
{a-2, b-2, c-2, d-2, e-2}
◉ When Bill makes a sandwich, he may choose from among 3 kinds
of rolls, 4 varieties of meat, and 2 types of sliced cheese. If he
chooses one roll, one meat, and one type of cheese, how many
different kinds of sandwiches can he make? Answer: 24
◉ 3x-4>=0 Answer: [4/3, infinity)
◉ Which of the following statements about an event A are true?
I. The probability that the event A will occur can be less than 0.
II. The probability that the event A will occur can be equal to 1.
, III. The sum of the probability that event A will occur and the
probability that event A will not occur is equal to 1. Answer: II and
III only
◉ The difference between the mean and the median of the numbers
27, 27, 29, 32, and 35 is Answer: 1
◉ In a class with 50 students, 25 of the students are female, 15 of
the students are mathematics majors, and 10 of the mathematics
majors are female. If a student in the class is to be selected at
random, what is the probability that the student selected will be
female or a mathematics major or both? Answer: 0.6
◉ On an exam for a class with 32 students, the mean score was 67.2
points. The instructor rescored the exam by adding 8 points to the
exam score for every student. What was the mean of the scores on
the rescored exam? Answer: 75.2
◉ A new computer graphics company employs 10 programmers.
The company decides to expand into digital animation and needs to
transfer 3 of the programmers into the new department. How many
different combinations of 3 programmers can be chosen to transfer
to the new department? Answer: 120
◉ The faces of a fair cube are numbered 1 through 6; the probability
of rolling any number from 1 through 6 is equally likely. If the cube is
QUESTIONS AND FULL SOLUTIONS 100%
CORRECT
◉ Triangle DEF (not shown) is similar to ABC shown, with angle B
congruent to angle E and angle C congruent to angle F. The length of
side DE is 6 cm. If the area of ABC is 5 square centimeters, what is
the area of DEF ? Answer: 45cm^2
◉ m is an odd integer. For each of the following numbers, check if
the number is odd. Answer: 2m-1
2m+1
m^2 + m + 1
◉ Which of the following statements is NOT true for all real
numbers a and b ? Answer: a^3 - b^3 = (a+b^2) (a^2-b)
◉ For any positive integers a and b, the operation ^ is defined as
a^b=(2a-1)^b-1 . What is the value of (2^2)^3? Answer: 25
◉ A company manufactures electronic components that each must
weigh from 29.5 grams to 30.5 grams, inclusive. Which of the
,following inequalities describes all acceptable weights x, in grams,
for each component? Answer: |30-x| <= 0.5
◉ Assume that x is the standard deviation of the set of the nonzero
numbers {a, b, c, d, e} For each of the following sets, indicate which
sets must have a standard deviation equal to x. Answer: {a+2, b+2,
c+2, d+2, e+2}
{a-2, b-2, c-2, d-2, e-2}
◉ When Bill makes a sandwich, he may choose from among 3 kinds
of rolls, 4 varieties of meat, and 2 types of sliced cheese. If he
chooses one roll, one meat, and one type of cheese, how many
different kinds of sandwiches can he make? Answer: 24
◉ 3x-4>=0 Answer: [4/3, infinity)
◉ Which of the following statements about an event A are true?
I. The probability that the event A will occur can be less than 0.
II. The probability that the event A will occur can be equal to 1.
, III. The sum of the probability that event A will occur and the
probability that event A will not occur is equal to 1. Answer: II and
III only
◉ The difference between the mean and the median of the numbers
27, 27, 29, 32, and 35 is Answer: 1
◉ In a class with 50 students, 25 of the students are female, 15 of
the students are mathematics majors, and 10 of the mathematics
majors are female. If a student in the class is to be selected at
random, what is the probability that the student selected will be
female or a mathematics major or both? Answer: 0.6
◉ On an exam for a class with 32 students, the mean score was 67.2
points. The instructor rescored the exam by adding 8 points to the
exam score for every student. What was the mean of the scores on
the rescored exam? Answer: 75.2
◉ A new computer graphics company employs 10 programmers.
The company decides to expand into digital animation and needs to
transfer 3 of the programmers into the new department. How many
different combinations of 3 programmers can be chosen to transfer
to the new department? Answer: 120
◉ The faces of a fair cube are numbered 1 through 6; the probability
of rolling any number from 1 through 6 is equally likely. If the cube is
