Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer?
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Answer: B — 15.
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Hint 1
First recover the original number, then divide by 2.
Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day?
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters?
Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school?
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Answer: D — 8 minutes.
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Hint 1
Running 3x as fast takes 1/3 the time for the same distance.
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Approach: scale time by speed
Walking half: 6 min. Running the other half (3x speed): 6/3 = 2 min.
The sales tax rate in Bergville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its $90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up $90.00 and adds 6% sales tax, then subtracts 20% from this total. Jill rings up $90.00, subtracts 20% of the price, then adds 6% of the discounted price for sales tax. What is Jack's total minus Jill's total?
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Answer: C — $0.
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Hint 1
Multiplication is commutative: order of factors doesn't change the product.
Big Al the ape ate 100 delicious yellow bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. How many delicious bananas did Big Al eat on May 5?
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Answer: D — 32.
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Hint 1
Five-term arithmetic sequence with common difference 6. Middle term = average = 100/5 = 20.
The Little Twelve Basketball League has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many games are scheduled?
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Answer: B — 96.
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Hint 1 of 2
Intra-division pairs per division: C(6, 2) = 15; each pair plays twice. Two divisions.
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Hint 2 of 2
Inter-division: 6 × 6 = 36, no doubling.
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Approach: count intra-division and inter-division separately
A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be 5 socks of the same color?
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Answer: D — 13.
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Hint 1
Worst case: 4 of each color (12 socks) without yet getting 5 of one color.
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Approach: pigeonhole on the worst case
After 12 socks, possible to have 4 red, 4 white, 4 blue (no color has 5).
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
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Answer: A — 6 turns.
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Hint 1
After k turns, Alice is at +5k and Bob is at −9k (mod 12). They coincide when 5k ≡ −9k (mod 12) ⇒ 14k ≡ 0 (mod 12).
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.
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Answer: E — MLS (best M, then L, then S).
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Hint 1
Set the small price to $1 and the large size to 10 oz. Derive the rest, then compute price per oz.
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Approach: anchor sizes, compute unit prices
Small: $1, 5 oz (large is twice the small ⇒ small = 5 oz).
Medium: $1.50 (50% more than small), 8 oz (20% less than 10 oz large).
A certain calculator has only two keys [+1] and [×2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed "9" and you pressed [+1], it would display "10." If you then pressed [×2], it would display "20." Starting with the display "1," what is the fewest number of keystrokes you would need to reach "200"?
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Answer: B — 9 keystrokes.
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Hint 1 of 2
Work backwards. If the current number is even, the last move was likely ×2 (divide by 2). If odd, the last was +1 (subtract 1).
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Hint 2 of 2
Each step backwards corresponds to one keystroke forward.
