[分享] Sample PSAT/NMSQT Questions---The Math Sect

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Regular Multiple Choice

Directions: Solve each problem. Then decide which is the best of the choices given and fill in the corresponding oval on the answer sheet.

hint:Here are some general hints for answering Regular Multiple-Choice questions.

Look at the answer choices before you begin to work on each question.


Read each question carefully, even if it looks like a question you don't think you can answer. Don't let the form of the question keep you from trying to answer it.


If your answer isn't among the choices, try writing it in a different form. You may have the same answer in a different mathematical format.
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question 1 of 13

If n  is an odd integer, which of the following is even?


(A) 2n  + 1
(B) n (n  + 2)
(C) n  + (n  - l)
(D) (n  - 2)(n  + 2)
(E) 2(n  + l)
(from the October 1996 test)

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Correct Answer: E
Explanation: Look at all the answer choices before beginning to plug in numbers and compute results. You will see that (E), 2(n + l), must always be even because the number resulting from n + 1 is multiplied by 2.
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question 2 of 13

During 30 minutes of a certain exercise, a person burns 200 calories. At this rate, what is the number of 30-minute exercise sessions necessary for this person to burn 3,600 calories?


(A) 600
(B) 540
(C) 120
(D) 18
(E) 12
(from the October 14, 1997 test)

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Correct Answer: D

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question 3 of 13


If 0 < a  < b  < c  < d  < e  in the equation above, then the greatest increase in S  would result from adding 1 to the value of which variable?

(A) a
(B) b
(C) c
(D) d
(E) e
(from the October 14, 1997 test)

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Correct Answer: A

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question 4 of 13


(from the October 18, 1997 test)

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Correct Answer: A

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question 5 of 13

If m and p are positive integers and (m + p) x m is even, which of the following must be true?


(A) If m  is odd, then p  is odd.
(B) If m  is odd, then p  is even.
(C) If m  is even, then p  is even.
(D) If m  is even, then p  is odd.
(E) m  must be even.
(from the October 18, 1997 test)

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Correct Answer: A
Explanation: If m is even, then the expression (m + p) x m will always be even and it cannot be determined whether p is even or odd. This eliminates choices (C) and (D). If m is odd, then (m + p) x m will be even only when m + p is even and m + p will be even only when p is odd. The correct answer is (A) since the truth of statement (A) also eliminates choices (B) and (E).question 6 of 13

If xy  = 2 and xy 2 = 8, what is the value of x ?


(A)1/2
(B) 2
(C) 4
(D) 8
(E) 16
(from the October 17, 1998 test)

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Correct Answer: A
Explanation: Substituting xy  = 2 into the equation xy2 = 8, you will obtain (xy)y = 2y = 8, thus y = 4. To find x, substitute y = 4 into one of the two original equations to obtain x = . The answer to this problem is (A).

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question 7 of 13


In the incomplete table above, the sum of the three integers in each row, column, and diagonal is the same. If the numerical values in four of the blocks are as shown, what is the value of w ?

(A) -6
(B) -5
(C) 2
(D) 5
(E) 8
(from the October 17, 1998 test)

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Correct Answer: C
Explanation: Since the sum of the integers in each row, column, and diagonal is the same, it follows that w  - 2 + a  = 3 + a  - 3. Thus w  - 2 = 0 so that w  = 2. The answer to this problem is (C).

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question 8 of 13

If n  is an odd integer, which of the following must be an odd integer?


(A) n - 1
(B) n + 1
(C) 2n
(D) 3n + 1
(E) 4n + 1
(from the October 20, 1998 test)

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Correct Answer: E
Explanation: If n is an odd integer, both one more and one less than n  will be even integers, eliminating choices (A) and (B). Any even multiple of n  will be an even integer, eliminating choice (C). However, 4n  is even, making 4n +1 an odd integer. The answer to this problem is (E). Note that 3n  + 1 is even if n  is odd and it is odd if n  is even. Since the question asks, "Which of the following MUST be an odd integer," (D) cannot be the correct answer.

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question 9 of 13

A 19-liter mixture consists by volume of 1 part juice to 18 parts water. If x liters of juice and y  liters of water are added to this mixture to make a 54-liter mixture consisting by volume of 1 part juice to 2 parts water, what is the value of x ?


(A) 17
(B) 18
(C) 27
(D) 35
(E) 36
(from the October 20, 1998 test)