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41
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If cubical blocks in a display are stacked one on top of the other on a flat surface, what is the volume of the stack of blocks in cubic centimeters?
1.The volume of the top block is 8 cubic centimeters.
2.The height of the stack of blocks is 10 centimeters.
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42
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In the standard (x,y) coordinate plane, what is the slope of the line containing the distinct points P and Q ?
1.Both P and Q lie on the graph of |x| + |y|=1.
2.Both P and Q lie on the graph of |x + y| = 1.
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43
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What is the length of the hypotenuse of △ABC ?
(1)The lengths of the three sides of △ABC are consecutive even integers.
(2)The hypotenuse of △ABC is 4 units longer than the shorter leg.
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44
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In the figure above, B is on $$\overline {AC}$$ , D is on $$\overline {AE}$$ , $$\overline {AB}$$ has the same length as $$\overline {BC}$$ ,and ∠ ABD has the same measure as ∠ACE. Wliat is the length of $$\overline {DB}$$
1.The length of $$\overline {EC}$$ is 6.
2.The length of $$\overline {DE}$$ is 5.
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45
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In the figure above, what is the perimeter of △PQR ?
1.The length of segment PT is 2.
2.The length of segment RS is $$\sqrt{3}$$.
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46
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In the rectangular coordinate system, line k passes through the point (n, - 1). Is the slope of line k greater than zero?
1.Line k passes through the origin.
2.Line k passes through the point (1,n+ 2).
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47
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Patricia purchased x meters of fencing. She originally intended to use all of the fencing to enclose a square region, but later decided to use all of the fencing to enclose a rectangular region with length y meters greater than its width. In square meters, what is the positive difference between the area of the square region and the area of the rectangular region?
1. xy=256
2. y=4
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48
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In the figure above, points A, B, C, and D are collinear and AB , BC sand CD are semicircles with diameters $$d_1$$ cm, $$d_2$$ cm, and $$d_3$$ cm, respectively. What is the sum of the lengths of AB,BC,and CD,in centimeters?
1.$$d_1$$ : $$d_2$$ : $$d_3$$ is 3:2:1.
2.The length of $$\overline {AD}$$ is 48 cm.
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49
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In the figure above, segments $$\overline{RS}$$ and $$\overline{TU}$$ represent two positions of the same ladder leaning against the side $$\overline{SV}$$ of a wall. The length of $$\overline{TV}$$ is how much greater than the length of $$\overline{RV}$$ ?
1.The length of $$\overline{TU}$$ is 10 meters.
2.The length of $$\overline{RV}$$ is 5 meters.
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50
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If the lengths of the legs of a right triangle are integers, what is the area of the triangular region?
1.The length of one leg is $$\frac{3}{4}$$ the length of the other.
2.The length of the hypotenuse is 5.
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51
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Is the perimeter of a certain rectangular garden greater than 50 meters?
1.The two shorter sides of the garden are each 15 meters long.
2.The length of the garden is 5 meters greater than the width of the garden.
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52
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The top surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?
1.After the changes were made, the surface area was 70 square inches.
2.There was a 25 percent increase in one of the dimensions.
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53
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When opened and lying flat, a birthday card is in the shape of a regular hexagon. The card must be folded in half along 1 of its diagonals before being placed in an envelope for mailing. Assuming that the thickness of the folded card will not be an issue, will the birthday card fit inside a rectangular envelope that is 4 inches by 9 inches?
1.Each side of the regular hexagon is 4 inches long.
2.The area of the top surface (which is the same as the area of the bottom surface) of the folded birthday card is less than 36 square inches.
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54
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In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS ?
1.△QTRis equilateral.
2.Segments PT and TS have equal length.
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55
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The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft= 12 inches)
1.w = 3 inches
2.PQ=$$\sqrt{18}$$ inches
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56
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In quadrilateral ABCD, is angle BCD a right angle?
1.Angle ABC is a right angle.
2.Angle ADC is a right angle.
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57
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Sprinklers are being installed to water a lawn. Each sprinkler waters in a circle. Can the lawn be watered completely by 4 installed sprinklers?
(1)The lawn is rectangular and its area is 32 square yards.
(2)Each sprinkler can completely water a circular area of lawn with a maximum radius of 2 yards.
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58
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A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the account was opened. Once the balance reached $1,000,the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate?
1.The account earned exactly $25 in interest at the 2.5% rate.
2.The account was open for exactly three years.
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59
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Town X has 50,000 residents, some of whom were born in Town X. What percent of the residents of Town X were born in Town X ?
1.Of the male residents of Town X, 40 percent were not born in Town X.
2.Of the female residents of Town X, 60 percent were born in Town X.
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60
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A novelist pays her agent 15% of the royalties she receives from her novels. She pays her publicist 5% of the royalties, plus a yearly fee. Did the novelist pay more to her agent last year than she paid to her publicist?
1.The publicist 's yearly fee is $2,000.
2.The novelist earned an average of $3,500 in royalties last year on each of her novels.
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