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SAT Quantitative test chapters These questions closely resemble real test questions collected by students from 2000 to 2003 The answers and explanations were written by leading Test preparation professionals RealTestQuestions.com is a private initiative to bring students real actual test questions answered For any questions log on to www.realtestquestions.com Have a good SAT/PSAT exam chapters of Quantitative comparison questions (12 questions each): Every question answered and explained Chapter 1:  A:   B: 2  The best answer is A Simplify each of the expressions    80     54    45 Column B can be written as: , which is smaller than one     80 Column A can be written as: and thus smaller than column A A: The distance from checkpoint A to nest C B: 100 miles AI: A group of airplanes fly an hour north from checkpoint A to checkpoint B at an average speed of 80 miles per hour and then another hour west from checkpoint B to checkpoint C at an average speed of 30 miles per 30 minutes The best answer is C Draw a sketch of the path; you can see that the planes form a right triangle with three corners: A, B and C The distance from A to C can be calculated using the Pythagoras principle as followed: AC = 80  (2  30)  100 miles and therefore the answer is C A: 11  17  17  11 B:  17  11 17  11 The best answer is C Remember the expression: (X + Y)(X – Y) = X2 – Y Now use this formula in both cases to get: A =  17   112 = 17 – 121 = -104 B=  17  2  11 = -104 and therefore both columns are equal 4 A: 0.8      5 X B: AI: X is a positive integer greater than zero The best answer is D When X=0, column A equals to zero but in all the other cases it doesn’t and therefore the answer cannot be determined A: X – 100Y B: AI: X and Y are both negative integers The best answer is D We don’t know if X is greater than Y or the opposite and therefore we cannot determine if the expression given in column A is negative or positive AI: Last year, the American economy was much weaker than today A: The price of a car last year B: The price of a car today The best answer is D We are not economists and therefore the data about the economy has no correlation to the changing price of a car The relationship cannot be determined from the information given A: The surface area of the entire cube in feet squared B: 36 feet squared AI: One of the faces of a cube has an area of feet squared The best answer is C If one of the faces is feet squared, the total surface area of the cube is simply x (there are faces to a cube) = 36 feet squared and so both columns are equal A: The perimeter of the rectangle B: 16R AI: Two circles with a radius of R are blocked inside a rectangle The best answer is B According to the figure, one side of the rectangle is equal to 4R and the other is equal to 2R The perimeter of the rectangle is therefore 2(4R + 2R) = 12R 16R > 12R and so the answer is B A: + 72 + 73 + B: The best answer is B Don’t try to solve these columns, instead compare 75 = x 74 = 74 + 74 + 74 + 74, which is definitely greater than column A 10 A: X B: X AI: -4 < X < -2 The best answer is A Take a representative number: X = -3 Column A = and column B = and therefore the answer is A 11 A: (X + Y) B: (X – Y) AI: X , Y  The best answer is D Simplify both columns and subtract common items A = X + 2XY + Y2 B = X - 2XY + Y2 Compare between 2XY to -2XY There is no room to compare since we don’t know if X and Y are positive or negative 12 A: 15X B: 14Y AI: X > Y The best answer is A If X > Y than 15X is definitely greater than 14Y and so the answer is A Chapter 2: A: 25 percent of 480 B: 120 The best answer is C 25% of 480 is simply 480/4 = 120, which is equal to column B and so the answer is C A: The digit in the thousands place of the rounded number B: AI: The number 273,666 is to be rounded to the nearest thousand The best answer is A The number is rounded to 274,000 since > The digit in the thousands place is and so column A is greater than column B A: 14% of 14 B: 15% of 15 The best answer is B Don’t calculate, compare 15 is greater than 14 and therefore 15% of 15 must be greater than 14% of 14 If you’ll calculate you will see that A = 1.96 and 2.25 A: The amount of money that the computer store received from the computer sales B: $12,500 AI: A computer store sold more than half of its computers for $800 and the rest were sold for $650 The best answer is D Since the question says that more than half were sold for $800, the answer cannot be determined because it is not specific enough We don’t know how many computers were sold in each price and so the right answer is D A: XZ + Y B: ZX + X AI: X = and Y = The best answer is A It doesn’t matter what is the value of XZ, it can be subtracted from both columns anyway XZ is added with the value of Y in column A and with the value of X in column B, since Y > X column A is greater A: ABC B: A2BC AI: B = and C = 12 The best answer is D Since we don’t know the value of A, the answer cannot be determined Take A=2 and A=1 as two examples: For A=2, column B is greater and for A=1, the columns are equal Since there is more then one answer, the right answer is D A: A B: B AI: A < B2 The best answer is D Take two sets of numbers, for example: A=1, B=2 and A=1, B=-2 In the first case A > B and in the second case A < B Since there is more then one answer, the right answer is D A: X o B: 200o AI: The angles of a quadrilateral are 54.5o, 13.6o, 67.2o and Xo The best answer is A The sums of all the angles in a quadrilateral are 360 degrees Write the equation: 360 = 54.5 + 13.6 + 67.2 + X Round each of the angles up: 55, 14 and 68  X = 223o, which is a lot greater than 200o and so the answer is A A: X B: 2.5 AI: 10 < X + 3Y < 20 and Y = 3X The best answer is B Replace 3X with Y in the inequality: 10 < X + 3(3X) < 20  10 < X + 9X < 20  10 < 10X < 20 divide all by 10 to get: < X < and so 2.5 is out of the range and column B is greater 10 8 21 B:  17 A: The best answer is B Column A = 1/21 = 2/42 and column B = 2/17 The denominator of B is smaller and so column B is greater than column A B 11 A C A: The length of the curved path from A to C B: 50 AI: The radius of the circle is 25 The best answer is A Angle ABC lies on the diameter of the circle since it is equal to 90o and therefore a straight line from A to C would equal 50 Since any curved line is greater than any straight line between the same two points, the curved path is greater than 50 12 Let {X, Y} be defined as the set of all prime numbers between X and Y, excluding X and Y For example: {0, 4} include 1, and A: A B: B AI: A is in {6, 11} B is in {10, 17} The best answer is B A can only be and B can be 11 or 13 Therefore B is greater than A Chapter 3: A: The number of convertible cars B: 36 AI: All the convertible cars in the dealership are also red There are 40 red cars in the dealership The best answer is D Let’s take two number of convertible cars that would satisfy the conditions above: 38 and 25 In the first case (38) there are 38 convertible cars in the dealership which are also red and the rest of the red cars (40 – 38 = 2) are not convertible In the second case (25) there are 25 convertible cars in the dealership which are also red and the rest of the cars (40 – 25 = 15) are not convertible Since there is a different answer every time, the right answer is D A: X + Y – Z B: AI: X = 1433, Y = 737 and Z = 2160 The best answer is A Calculate the expression in column A: X + Y – Z = 1433 + 737 – 2160 = 2170 – 2160 = 10 10 > and so column A is greater A: The factorial of X B: The factorial of Y divided by the factorial of X AI: X = and Y = The best answer is B The factorial of X (3) is 3! = x x = The factorial of Y (6) is 6! = x x x x x If we divide the factorial of Y by the factorial of X, the result would be x x = 120 120 > and so column B is greater than column A A: 7/19 B: 11/30 The best answer is B Since A/B = 0, A must be zero since it is the only variable that can nullify the equation A x B is therefore and so column B is greater 12 A: X B: X AI: Four times X equals less than (X + 5) The best answer is B Write the following equation: 4X = (X + 5) –  4X = X –  3X = -2  X = -2/3  X2 = 4/9 4/9 > -2/3 and therefore column B is greater Chapter 4: A: 88% of the number of cookies that Ray sold B: 44% of the number of cookies that Mary sold AI: Ray sold twice as much cookies as Mary The best answer is A Let’s say that Ray sold 200 cookies and Mary 100 Column A = 176 cookies while column B = only 44 cookies and therefore column A is greater A: 60% of Jane’s money B: 20% of Natalie’s money AI: Natalie has three times more money than Jane The best answer is C Let’s say that Jane has $100 and so Natalie has $300 Column A = 60% of 100 is $60 Column B = 20% of 300 is $60 and so the columns are equal A: 17 X  17 X  B: 17 X  17 X AI: X > The best answer is B Column A is simply  1 Column B is simply 1   and therefore this column is greater 1 A: X2 X4 X8 B: X  X 10  X AI: X > The best answer is D Column A can be simplified to: X2 X4 X8  X2 X4X4  X2X4  X6  X3 Column B can be simplified to: X  X 10  X  X3X5 X  X  X  X If X is a fraction column A is greater, otherwise column B is greater Since there is more than one answer, the right answer is D A: Z B: 2Z AI: X = 14 – Y + Z Y+Z=6–X The best answer is A Rewrite the equations: X + Y – Z = 14 and X + Y + Z = Subtract the first equation from the second: 2Z = – 14 = -8  Z = -4 Column A= -4 and column B= -8 and so column A is greater A: The probability of drawing a ball with stripes B: The probability of drawing a ball with out stripes AI: A jar contains red balls with blue stripes, orange balls, black balls with yellow stripes and black and white balls The best answer is A There are 4+5+8+2 = 19 balls in total There are 4+8 = 12 balls with stripes and so the probability of pulling a striped ball is 12/19 and the probability of pulling a ball with out stripes is 7/19 and so column A is greater A: R B: S AI: The absolute value of R is smaller than S The best answer is B We can write the additional information as R  S The only way that this inequality be true is if R < S and so column B is greater A: Q B: P AI: The absolute value of Q is greater than P The best answer is D We can write the additional as Q  P Take two sets of numbers: Q=-3, P=2 and Q=3, P=2, they both fulfill the inequality yet they give different answers and so the right answer is D Yo M N Xo A: X o B: Y o AI: Line N is parallel to M The best answer is D We know that line M and N are parallel yet no information was specified on the other two lines and so the answer cannot be determined 10 A: The cost of a desk B: The cost of a chair AI: chairs and desks cost $120 The best answer is D Let the price of one chair be X and the price of one desk be Y All we know is that 3X + 2Y = 120 We have two unknowns and only one equation and therefore the answer cannot be determined 11 A: F B: 15 AI: 4.5  F 3.5 The best answer is A F = 4.5 x 3.5 = (9/2) x (7/2) = 63/4 = 15.75, which is greater than 15 and so column A is greater 12 2Y o Xo Yo A: 50 o B: X AI: Y = X The best answer is A Sum up the angles in the triangle: X+Y+2Y = 180  X+X+2X = 180  X=45o and so column A is greater Chapter 5: A: P – Q B: Q – P AI: P is a prime number between and inclusive Q is a prime number between and 12 inclusive The best answer is B The range of P is 2 The best answer is D Column A can be written as A2 x 0.25 = A0.5 Column B can be written as A4 x 0.5 = A2 Pick up two numbers: A=0.5 and A=2 For A=0.5, column A is greater and for A=2, column B is greater Since there is more than one answer, the right answer is D A: 1/X – 1/3 B: 1/3 AI: X is an integer smaller than The best answer is D X can be one of the following: or If X=1, – 1/3 = 2/3 and so column A is greater If X=2, ½ - 1/3 = 1/6 and so column B is greater Since there in more than one answer, the right answer is D A( 2,5) B ( X ,5) AI: The length of line segment AB is 14 A: X B: 14 The best answer is A If the line segment is 14 in length, the X coordinate of point B should be + 14, which is 16 and so column A is greater than column B A: The increase in the volume of a cylinder A when its height is increased by a foot B: The increase in the volume of a cylinder B when its height is increased by a foot The best answer is D Let’s take two examples of cylinders: The first is when cylinder A and B are identical- the increase in the height will increase their volumes in the same manner and column A will equal column B The second is if the radius of the first cylinder is times bigger than that of the second cylinder If we increase the height in both cylinders, the cylinder with the larger radius will grow by much more since the volume is calculated using the radius squared AI: 3M + 32 = 388 – 7M A: 100 B: 3M The best answer is B Solve the equation: 3M + 32 = 388 – 7M  10M = 356  M = 35.6  3M = x 35.6 = a number that is larger than 100 and so column B is greater AI: Mark and Jim both have a basketball card collection The number of cards in Mark’s album is 10 less than 12 times the number of cards in Jim’s album A: The number of cards in Mark’s album B: The number of cards in Jim’s album The best answer is A Take the critical case: Jim has only one card and so Mark has 11 less than 12, thus two cards only, which is greater than the number if cards that Jim has For any other number, Mark will have many more cards than Jim has and so A is the right answer AI: Julia and Catharine collect antique furniture The number of antique items in Catharine’s collection is less than times the number in Julia’s antique collection A: The number of antique items in Julia’s collection B: The number of antique items in Catharine’s collection The best answer is D If Julia has only one item in her collection, Catherine will have less than 4, which is also and so column A will equal column B For every other number of items, column B is greater and so the right answer in this case is D 10 AI: X is times Y Y is ¼ of Z Z is times W W is ½ of S A: S B: X The best answer is B X = 3Y = 3(Z/4) = ¾(Z) = ¾(5W) = 15W/4 = 15(S/2)/4 = 15S/8 Cross multiply to get: 8X = 15S and so X > S and column B is greater 11 AI: ¼ < X < 1/6 1/5 < Y < 1/7 A: X B: Y The best answer is D There are certain values in which X=Y, for example 2/11 Since X=Y in some numbers and in other numbers, X is greater than Y, the right answer is D 12 AI: A 100 liters aquarium is currently one fifth full A: The number of liters required to make the aquarium half full B: 40 liters The best answer is B If the aquarium is 1/5 full, it contains 100/5 = 20 liters In order to make it half full, 30 liters should be added to the aquarium 30 < 40 and so column B is greater SAT Quantitative test chapters These questions closely resemble real test questions collected by students from 2000 to 2003 The answers and explanations were written by leading Test preparation professionals RealTestQuestions.com is a private initiative to bring students real actual test questions answered For any questions log on to www.realtestquestions.com Have a good SAT/PSAT exam chapters of grid questions (12 questions each): Every question answered and explained Chapter 1: A determinant of [a, b, c, d] is defined as (a x d – b x c) What is the value of the determinant of [2.5, 2, 1, 5]? According to the rules of the determinant in the question, the result of the determinant of [2.5, 2, 1, 5] = (2.5 x – x 1) = 10.5 The mathematical function #(X, Y, Z) is defined as (X – Y 2)/ Z2 #(7, 5, 6) = ? Use the pattern in the question #(7, 5, 6) = (49 – 25)/36 = 24/36 = 2/3 2.25 grams of sugar can be found in a can of Juicy-juice How many grams of sugar can be found in a dozen cans? If one can consists of 2.25 grams, a dozen (12) cans consists of 12 x 2.25 = 27 grams of sugar The local race track is miles long How long is the track in kilometers assuming that mile = 1.6 kilometers? The transition is mile = 1.6 kilometers miles = x 1.6 kilometers, which is 9.6 kilometers A cake recipe requires tablespoons of chocolate powder How many teaspoons of chocolate powder should you put in the cake assuming that teaspoon is 1/3 tablespoon? According to the question, one tablespoon is three teaspoons 23 69 We require         teaspoons      4  4 If 0.2X = 15, what is the value of X ? 10 Solve the equation: 0.2X = 15  X = 15/0.2 = 15 x 10/2 = 75 X/10 = 75/10 = 7.5 If 0.66X = – 0.34X, what is the value of X ? ... therefore 2(4R + 2R) = 12R 16R > 12R and so the answer is B A: + 72 + 73 + B: The best answer is B Don’t try to solve these columns, instead compare 75 = x 74 = 74 + 74 + 74 + 74 , which is definitely... 13.6o, 67 .2o and Xo The best answer is A The sums of all the angles in a quadrilateral are 360 degrees Write the equation: 360 = 54.5 + 13 .6 + 67 .2 + X Round each of the angles up: 55, 14 and 68 ... Stock''s value from 69 to 72 25 20 20 15 10 16 15 12 1 969 1 970 1 971 1 972 AI: The value of a certain stock is presented in the graph The value has decreased by S percent from 1 971 to 1 972 and increased