Regents Prep: Math A
Multiple-Choice Questions
Regents Prep Math A: Topical Multiple-Choice Question Archive
Use of Topical Archive Multiple-Choice Questions
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Mathematical Reasoning: Question 1 of 20
The statement "If x is divisible by 8, then it is divisible by 6" is false if x equals
  1. 6
  2. 14
  3. 32
  4. 48

Correct Answer Number: 3

Explanation: A sentence in "If....then..." form is called an implication. The only time when an implication is false is when the "If" part of the sentence is true and the "then" part of the sentence is false. The number 32 makes the first part of the statement true and the second part of the statement false.

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Mathematical Reasoning: Question 2 of 20
In a class of 50 students, 18 take music, 26 take art, and 2 take both art and music. How many students in the class are not enrolled in either music or art?
  1. 6
  2. 8
  3. 16
  4. 24

Correct Answer Number: 2

Explanation: Draw a Venn diagram (circles) to represent the students taking art and music. The circles will overlap. The circle for art contains 26 students. The circle for music contains 18 students. Since 2 students take BOTH art and music (place 2 in the area where the circles overlap), the remainder of the art circle contains 24 students and the remainder of the music circle contains 16 students. Adding all values (24 + 16 + 2) gives a total of 42 students. Of the class of 50 students, 8 do not take art or music.

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Mathematical Reasoning: Question 3 of 20
What is true about the statement "If two angles are right angles, the angles have equal measure" and its converse "If two angles have equal measure then the two angles are right angles"?
  1. The statement is true but its converse is false.
  2. The statement is false but its converse is true.
  3. Both the statement and its converse are false.
  4. Both the statement and its converse are true.

Correct Answer Number: 1

Explanation: All right angles have 90 degrees, therefore they are all equal in measure. However, two angles can be equal in measure (each being 30 degrees), but they are not necessarily right angles.

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Mathematical Reasoning: Question 4 of 20
Mary says "The number I am thinking is divisible by 2 or it is divisible by 3". This statement is false if the number Mary is thinking of is
  1. 6
  2. 8
  3. 11
  4. 15

Correct Answer Number: 3

Explanation: This sentence contains the word "or" (disjunction). A disjunction is only false if BOTH conditions are false. The only number that is not divisble by 2 and is not divisible by 3 is 11.

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Mathematical Reasoning: Question 5 of 20
"If Tom buys a red skateboard, then Amanda buys green in-line skates." Which statement below is logically equivalent?
  1. If Amanda does not buy green in-line skates, then Tom does not buy a red skateboard.
  2. If Tom does not buy a red skateboard, then Amanda does not buy green in-line skates.
  3. If Amanda buys green in-line skates, then Tom buys a red skateboard.
  4. If Tom buys a red skateboard, then Amanda does not buy green in-line skates.

Correct Answer Number: 1

Explanation: The original statement and its contrapositive are logically equivalent. Remember that the contrapositive is the "converse of the inverse" -- flip the "If ...then" sections AND insert "NOTs".

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Mathematical Reasoning: Question 6 of 20
Which statement represents the inverse of the statement "If it is snowing, then Skeeter wears a sweater."?
  1. If Skeeter wears a sweater, then it is snowing.
  2. If Skeeter does not wear a sweater, then it is not snowing.
  3. If it is not snowing, then Skeeter does not wear a sweater.
  4. If it is not snowing, then Skeeter wears a sweater.

Correct Answer Number: 3

Explanation: Remember: to form the INVERSE of a statement, insert "NOT" into the "If" and the "then" sections of the sentence.

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Mathematical Reasoning: Question 7 of 20
Which of the following is the converse of the statement: "If x>4, then x+2>5"?
  1. If x+2<5, then x<4.
  2. If x is not greater than 4, then x+2 is not greater than 5.
  3. If x+2>5, then x>4,
  4. If x+2 is not greater than 5, then x is not greater than 4.

Correct Answer Number: 3

Explanation: Remember: to form the CONVERSE of a statement, the "If" and the "then" sections of the statement switch places.

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Mathematical Reasoning: Question 8 of 20
Which statement is logically equivalent to "If Yoda cannot use a lightsaber, then he cannot help Luke win the battle."
  1. Yoda cannot use a lightsaber and he will help Luke win the battle.
  2. If Yoda can help Luke win the battle, then he can use a lightsaber.
  3. Yoda can use a lightsaber if and only if he can help Luke win the battle.
  4. Yoda cannot use a lightsaber and will not help Luke win the battle.

Correct Answer Number: 2

Explanation: A statement is logically equivalent to its contrapositive. To form the contrapositive, switch the "If" and "then" sections of the statement AND insert "NOTs" into each section. Notice in this situation, that inserting "NOTs" turns the thoughts positive (you are negating negative thoughts).

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Mathematical Reasoning: Question 9 of 20
If Shelly does not like John, what is the truth value of the statement "Shelly likes Mike and she likes John."?
  1. True
  2. False
  3. Shelly likes Peter.
  4. none of the above

Correct Answer Number: 2

Explanation: The statement in question contains the word "AND". A statement with "AND" is only true when BOTH conditions are true. The section "she likes John" is false, so the entire statement is false.

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Mathematical Reasoning: Question 10 of 20
When y = 3, which of the following is FALSE?
  1. y is prime and y is odd
  2. y is odd or y is even
  3. y is not prime and y is odd
  4. y is odd and 2y is even

Correct Answer Number: 3

Explanation: Remember what is TRUE: 3 is prime, odd and 2(3) is even.
Choice 1: T and T is TRUE
Choice 2: T or F is TRUE
Choice 3: F and T is FALSE
Choice 4: T and T is TRUE

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Mathematical Reasoning: Question 11 of 20
Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?
  1. Today is Sunday and Matt can play hockey.
  2. If Matt plays hockey, then today is not Sunday.
  3. Today is Sunday and Matt cannot play hockey.
  4. Today is not Sunday if and only if Matt plays hockey.

Correct Answer Number: 2

Explanation: Statements are logically equivalent to their contrapositives.

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Mathematical Reasoning: Question 12 of 20
The statement "x>5 or x<3" is true if x equals
  1. 1
  2. 3
  3. 4
  4. 5

Correct Answer Number: 1

Explanation: For "or" to be true, either (or both) of the conditions must be true. The only value that makes either of the conditions true is 1.

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Mathematical Reasoning: Question 13 of 20
What is the truth value of "4 is even and 8 is odd."?
  1. True
  2. False
  3. 24
  4. Cannot be determined.

Correct Answer Number: 2

Explanation: For "and" to be true, both conditions must be true. "4 is even" is true, but "8 is odd" is false.
T and F is FALSE

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Mathematical Reasoning: Question 14 of 20
The sentence "____ if and only if x + x = 3x" is TRUE. Which of the following could be used to fill in the blank?
  1. x + x = 2x
  2. 2x - x = 2x
  3. both 1 and 2 could be used
  4. neither 1 nor 2 could be used

Correct Answer Number: 2

Explanation: "if and only if" is TRUE when both conditions are the SAME truth value. Since "x + x = 3x" is false, the first condition must also be false. 2x - x = 2x is false.

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Mathematical Reasoning: Question 15 of 20
The inverse of the converse of a conditional statement is the _______________.
  1. converse
  2. inverse
  3. contrapositive
  4. none of the above

Correct Answer Number: 3

Explanation: The inverse will insert NOT into the statement.
The converse will switch the IF and THEN.
The contrapositive does both. The contrapositive is the inverse of the converse of the conditional statement.

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Mathematical Reasoning: Question 16 of 20
If Susan does not like spinach, what is the truth value of the statement "Susan likes ice cream and she like spinach."?
  1. True
  2. False
  3. Susan like pizza.
  4. none of the above

Correct Answer Number: 2

Explanation: "and" is only true when both conditions are TRUE. Since Susan does not like spinach, the second condition is false, making the entire statement false.

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Mathematical Reasoning: Question 17 of 20
Which of the following is an open sentence?
  1. A trapezoid is a four-sided polygon.
  2. Albany is a city in New York State.
  3. It was blue with white stripes.
  4. 5(20)+3=113

Correct Answer Number: 3

Explanation: An open sentence is a sentence in which you cannot determine whether it is true or false due to a lack of information. Answers 1 and 2 are true. Answer 4 is false. The truth of Answer 3 cannot be determined.

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Mathematical Reasoning: Question 18 of 20
"It has two pairs of opposite sides parallel." Which of the following make this open sentence true?
  1. parallelogram
  2. trapezoid
  3. rectangle
  4. both 1 and 3

Correct Answer Number: 4

Explanation: Parallelograms and rectangles have two pairs (sets) of parallel sides. A trapezoid has one pair (set) of parallel sides.

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Mathematical Reasoning: Question 19 of 20
Consider the sentence: x < 5
Which of the following integers makes this open sentence true?
  1. 4
  2. 5
  3. 6
  4. none of the above

Correct Answer Number: 1

Explanation: The only number less than 5 in the list of answers is 4.

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Mathematical Reasoning: Question 20 of 20
"If Deb and Sam go to the mall, then it is snowing."
Which statement below is logically equivalent?
  1. If Deb and Sam do not go to the mall, then it is not snowing.
  2. If Deb and Sam do not go to the mall, them it is snowing.
  3. If it is snowing, then Deb and Sam go to the mall.
  4. If it is not snowing, then Deb and Sam do not go to the mall.

Correct Answer Number: 4

Explanation: A statement is logically equivalent to its contrapositive.

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