Each day Maria must work 8 hours. This does not include the 45 minutes she takes for lunch. If she begins working at 7:25 A.M. and takes her lunch break at noon, then her working day will end at
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Answer: C — 4:10 P.M.
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Hint 1 of 2
Find how much she works before lunch, then how much is left.
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Hint 2 of 2
Don't forget the 45-minute lunch pushes the afternoon back.
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Approach: split the workday around lunch
From 7:25 to noon she works 4 h 35 min, leaving 8 h − 4 h 35 min = 3 h 25 min.
Lunch ends at 12:45, and 3 h 25 min later is 4:10 P.M.
A shopper buys a 100-dollar coat on sale for 20% off. An additional 5 dollars are taken off the sale price by using a discount coupon. A sales tax of 8% is paid on the final selling price. The total amount the shopper pays for the coat is
Last summer 100 students attended basketball camp. Of those, 52 were boys and 48 were girls. Also, 40 students were from Jonas Middle School and 60 were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School?
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Answer: B — 32.
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Hint 1 of 2
Make a boys/girls by Jonas/Clay table and fill it in.
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Hint 2 of 2
Find the Clay girls first, then the Clay boys.
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Approach: fill in a two-way table
Girls from Clay = 48 − 20 = 28.
Clay has 60 students, so boys from Clay = 60 − 28 = 32.
Two children at a time can play pairball. For 90 minutes, with only two children playing at a time, five children take turns so that each one plays the same amount of time. The number of minutes each child plays is
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Answer: E — 36.
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Hint 1 of 2
Two children play at once, so there are 2 × 90 child-minutes of play available.
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Hint 2 of 2
Share those equally among the five children.
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Approach: total child-minutes, shared equally
Two play at a time for 90 minutes: 2 × 90 = 180 child-minutes.
The perimeter of one square is 3 times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?
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Answer: E — 9.
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Hint 1 of 2
Perimeter scales with the side, so the sides are in the same 3 : 1 ratio.
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Hint 2 of 2
Area scales with the side squared.
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Approach: area scales as the square of the side ratio
Pauline can shovel snow at the rate of 20 cubic yards for the first hour, 19 cubic yards for the second, 18 for the third, and so on, always shoveling one cubic yard less per hour than the previous hour. If her driveway is 4 yards wide, 10 yards long, and covered with snow 3 yards deep, then the number of hours it will take her to shovel it clean is closest to
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Answer: D — 7.
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Hint 1 of 2
First find the total volume of snow: 4 × 10 × 3.
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Hint 2 of 2
Add 20 + 19 + 18 + … until you reach that volume.
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Approach: accumulate the decreasing hourly amounts
The snow is 4 × 10 × 3 = 120 cubic yards.
Running totals: 20, 39, 57, 74, 90, 105, 119 — after 7 hours she's at 119, just shy of 120, so the time is closest to 7 hours.
Distance from home rises while going out, stays flat while shopping, then falls coming back.
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Hint 2 of 2
Because the speed changes (gentle in city, steep on highway), each side of the graph bends rather than staying a single straight line.
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Approach: match each changing-speed leg to the graph's slope
Going out, distance rises gently (city) then steeply (highway), so the climb curves and gets steeper; it stays flat for the hour at the mall; coming home it falls steeply (highway) then gently (city).
Graph B shows these two different slopes on each side — the straight-sided trapezoid (A) would mean a single constant speed each way.
A gumball machine contains 9 red, 7 white, and 8 blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is
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Answer: C — 10.
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Hint 1 of 2
Imagine the worst luck: as many gumballs as possible without four of any color.
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Hint 2 of 2
That's three of each color; the next one must make a fourth.
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Approach: worst case, then one more
You could draw 3 red, 3 white, 3 blue — 9 gumballs — with no color yet reaching four.
The 10th gumball must complete a set of four, so the answer is 10.
A 2 by 2 square is divided into four 1 by 1 squares. Each small square is painted green or red. In how many ways can this be done so that no green square shares its top or right side with a red square? (There may be from zero to four green squares.)
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Answer: B — 6.
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Hint 1 of 2
The rule means: anything directly above or to the right of a green square must also be green.
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Hint 2 of 2
So the green squares must form an 'up-and-right' staircase region.
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Approach: green region must be closed upward and rightward
If a square is green, the squares above it and to its right can't be red, so they're green too.
The green sets that satisfy this are: none, just the top-right, top-right + top-left, top-right + bottom-right, those three together, and all four — 6 ways.
