Sample PSAT Questions---Math2--Quantitative Compar

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question 6 of 13


(from the October 17, 1998 test)

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Correct Answer: C

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question 7 of 13


(from the October 17, 1998 test)

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Correct Answer: D
Explanation: The value of y 6 in column A could be 0 or a positive number, it is never negative. The value of y 5 in column B could be 0, a positive number, or a negative number. If y = , then y 6 > y 5. However, if y = , then y 6 < y 5. Since a relationship cannot be determined from the information given, the answer to this problem is (D).

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question 8 of 13


(from the October 20, 1998 test)

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Correct Answer: A
Explanation: Since the average of the three positive numbers r, s,  and t  equals v, it follows that  = v  or r  + s + t  = 3v. Since v  is positive, 3v  > 2v   so the answer to this problem is (A) -- the quantity in column A is greater than the quantity in column B.

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question 9 of 13


(from the October 20, 1998 test)

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Explanation: Since the height of  is y  and its base is x , the area of the triangle is  xy . However, it is given that the area of  is 2y 2. Therefore, 2y 2 =  xy . and thus 4y  = x . Since the quantities in columns A and B are equal, the answer to this problem is (C).

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question 10 of 13

Column A Column B
Y represents one of the digits 0 through 9, inclusive.
The number that results after 8.4Y3 has been rounded to the nearest tenth
The number that results after 8.Y92 has been rounded to the nearest tenth


(from the October 12, 1999 test)

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Correct Answer: D
Explanation: In column A, the number that results after 8.4Y3 has been rounded to the nearest tenth is either 8.4 or 8.5, depending on what digit Y represents. In column B, the result when 8.Y92 is rounded to the nearest tenth could be several different numbers, depending on what digit Y represents. If Y = 1, then the number in column A is 8.4 and the number in column B is 8.2. In this case, the number in column A is greater than the number in column B. If Y = 8, then the number in column A is 8.5 and the number in column B is 8.9. In this case, the number in column B is greater than the number in column A. Since a relationship cannot be determined from the information given, the answer to this question is (D).

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question 11 of 13

Column A Column B

qr
qs


(from the October 12, 1999 test)

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Correct Answer: A
Explanation: Although the coordinates are not given for q, r, or s, you do know from the figure that q and r are negative numbers and s is a positive number. Therefore, the product of q and r in column A will be positive (negative x negative = positive) and the product of q and s in column B will be negative (negative x positive = negative). The answer to this question is (A) since the quantity in column A will always be greater than the quantity in column B.

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question 12 of 13

Column A Column B
A circle with center O and radius 1 lies in a plane.
Point P is not in the plane, and PO is perpendicular to the plane.
C is a point on the circle.  
The length of PC
The length of PO


(from the October 16, 1999 test)

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Correct Answer: A
Explanation: Since PO is perpendicular to the plane, the shortest distance from P to the plane is the length of PO. Therefore, the length of PC is greater than the length of PO.

Another way to arrive at this conclusion is to notice that PC is the hypotenuse of a right triangle with legs PO and OC. The hypotenuse of a right triangle is always greater than either of the legs. Since the quantity in column A is greater than the quantity in column B, the correct answer is (A).