Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic?
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Answer: E — 9 pounds.
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Hint 1
24 hamburgers is 3 times as many as 8, so the meat triples.
In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?
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Answer: B — About 700.
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Hint 1
Births per day = 24/8 = 3. Net growth per day = 3 − 1 = 2. Multiply by 365.
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Approach: net per day × 365
Births per day: 24/8 = 3. Net daily growth: 3 − 1 = 2.
On February 13 The Oshkosh Northwester listed the length of daylight as 10 hours and 24 minutes, the sunrise was 6:57 AM, and the sunset as 8:15 PM. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?
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Answer: C — 1/8.
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Hint 1
Peter ate 1 full slice + half a slice = 1.5 slices out of 12.
A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?
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Answer: E — 88 square inches.
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Hint 1
Outer dimensions add 2 inches on each of two sides ⇒ 4 inches in each direction. Subtract the photo area.
Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she could have made on the third test?
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Answer: B — 92.
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Hint 1 of 2
Total points needed = 4 × 95 = 380. Subtract the first two scores to find what's left for tests 3 + 4.
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Hint 2 of 2
To minimize the 3rd test, maximize the 4th (cap = 100).
A shop advertises everything is "half price in today's sale." In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage off the original price?
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Answer: D — 60%.
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Hint 1
Multiply the surviving fractions: 50% × 80% = 40% of original. Customer saves 100% − 40%.
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Approach: multiply remaining fractions
After 50% off: 0.5 of original. After 20% off that: 0.5 × 0.8 = 0.4 of original.
The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?
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Answer: C — 139 birds.
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Hint 1
If every animal had 4 legs, you'd see 800 legs. The shortage (800 − 522) comes from the 2-leg birds, each missing 2 legs.
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Approach: leg-shortage shortcut
If all 200 had 4 legs: 200 · 4 = 800 legs.
Actual: 522 ⇒ shortage = 800 − 522 = 278 legs.
Each bird is short 2 legs ⇒ birds = 278 / 2 = 139.
Jamar bought some pencils costing more than a penny each at the school bookstore and paid $1.43. Sharona bought some of the same pencils and paid $1.87. How many more pencils did Sharona buy than Jamar?
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Answer: C — 4 more pencils.
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Hint 1
Working in cents: the price (in cents) divides both 143 and 187. Take their gcd; since price > 1 cent, only one option survives.
In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of 21 conference games were played during the 2012 season, how many teams were members of the BIG N conference?
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Answer: B — 7 teams.
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Hint 1
Round-robin: number of games = C(N, 2) = N(N − 1)/2.
Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?
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Answer: C — 87431.
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Hint 1
Higher place values dominate. To maximize the sum, put the two biggest digits in the ten-thousands place (one each), the next two in the thousands place, etc.
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Approach: split digits into matched pairs by place value
Pair digits by descending size for each place: {9, 8}, {7, 6}, {5, 4}, {3, 2}, {1, 0}.
Each number gets one from each pair. So the digits of each number (left to right) come from {9, 8}, {7, 6}, {5, 4}, {3, 2}, {1, 0}.
Only 87431 matches: 8∈{9,8}, 7∈{7,6}, 4∈{5,4}, 3∈{3,2}, 1∈{1,0}. ✓
A square with an integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?
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Answer: B — Side 4.
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Hint 1 of 2
Lower bound: total area ≥ 10 (each piece has integer side ≥ 1). So side ≥ √10 ⇒ side ≥ 4.
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Hint 2 of 2
Upper bound: find an explicit dissection of a 4×4 square into 10 integer-side squares, with 8 of them 1×1.
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Approach: lower bound + explicit construction
Side ≥ 4: total area is at least 10 (each of 10 pieces ≥ 1), so side2 ≥ 10 ⇒ side ≥ 4.
Construction for side 4: cover the top half (a 4×2 strip) with two 2×2 squares; tile the bottom half (4×2 strip) with 8 unit squares. Total: 2 + 8 = 10 squares, eight of area 1. ✓
What is the correct ordering of the three numbers 519, 721, and 923, in increasing order?
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Answer: B — 5/19 < 7/21 < 9/23.
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Hint 1
Each fraction is of the form (n)/(n + 14) for n = 5, 7, 9. Write as 1 − 14/(n + 14). Bigger denominator on the subtracted piece ⇒ bigger overall fraction.
Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?
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Answer: D — 50 square feet.
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Hint 1
Total surface area is 6 × 102. Split it into the green and the white parts.
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Approach: total surface area − green
Total: 6 · 100 = 600 sq ft. Green covers 300, so white covers 300.
Six congruent white squares share that 300: each is 300 / 6 = 50 sq ft.
The star fits snugly inside a square. What about the leftover regions in the corners?
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Hint 2 of 2
Inside a 4×4 square, the four corner 'bite' regions are exactly the four arcs that originally made up the circle — so they total to the circle's area.
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Approach: fit the star and circle pieces in a 4x4 square
Inscribe the star in a 4×4 square (its four points touch the four sides). The square's area is 16.
The four regions outside the star but inside the square are precisely the four arc-pieces from the circle — together their area equals the circle's area π(2)2 = 4π.
The big square is sliced by the small square into 4 congruent right triangles plus the small square. Total leftover area = 5 − 4 = 1, split equally among the 4 triangles.
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Hint 2 of 2
Each triangle has legs a and b, area (1/2)ab.
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Approach: leftover area gives ab
Big square area 5 = small square area 4 + total triangle area ⇒ triangles total 1.
By symmetry, the 4 triangles are congruent, each with area 1/4. Each has legs a and b, area (1/2)ab.
