A teacher tells the class: "Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer." Ben thinks of 6 and gives his answer to Sue. What should Sue's answer be?
Show hint (soft nudge)
Compute Ben's answer first, then feed it into Sue's steps.
At Clover View Junior High, half of the students go home on the school bus, one fourth go home by automobile, and one tenth go home on their bicycles. The rest walk home. What fractional part of the students walk home?
Show hint (soft nudge)
Add the three known fractions over a common denominator (20).
An American traveling in Italy wishes to exchange American dollars for Italian lire. If 3000 lire = $1.60, how much lire will the traveler receive for $1.00?
A jacket and a shirt originally sold for 80 dollars and 40 dollars, respectively. During a sale Chris bought the 80-dollar jacket at a 40% discount and the 40-dollar shirt at a 55% discount. The total amount saved was what percent of the total of the original prices?
Show hint (soft nudge)
Find the dollars saved on each item.
Show hint (sharpest)
Compare the total saved to the total original price of $120.
Show solution
Savings: 40% of $80 = $32, and 55% of $40 = $22, for $54 saved.
A lucky year is one in which at least one date, written as month/day/year, has the property that the month times the day equals the last two digits of the year. For example, 1956 is lucky because 7/8/56 has 7 × 8 = 56. Which of the following is NOT a lucky year?
Show hint (soft nudge)
For each year, try to write its last two digits as month × day with a valid month (1–12) and day.
Show hint (sharpest)
94 has very few factor pairs.
Show solution
90 = 9 × 10, 91 = 7 × 13, 92 = 4 × 23, 93 = 3 × 31 — all have a month from 1–12 with a real day.
But 94 = 2 × 47 only (besides 1 × 94), and no month 1–12 pairs with a valid day, so 1994 is not lucky.
A team won 40 of its first 50 games. How many of the remaining 40 games must this team win so that it will have won exactly 70% of its games for the season?
Show hint (soft nudge)
The season has 50 + 40 = 90 games; find 70% of that.
Show hint (sharpest)
Subtract the 40 wins already in hand.
Show solution
70% of the 90 games is 63 wins needed for the season.
Already having 40, the team must win 63 − 40 = 23 more.
Students from three middle schools worked on a summer project. Seven students from Allen school worked for 3 days, four students from Balboa school worked for 5 days, and five students from Carver school worked for 9 days. The total amount paid for the students' work was $774. Assuming each student received the same amount for a day's work, how much did the students from Balboa school earn altogether?
Show hint (soft nudge)
Count total student-days across all schools.
Show hint (sharpest)
Find the pay per student-day, then multiply by Balboa's student-days.
Diana and Apollo each roll a standard die, obtaining a number at random from 1 to 6. What is the probability that Diana's number is larger than Apollo's number?
Show hint (soft nudge)
By symmetry, 'Diana larger' and 'Apollo larger' are equally likely.
Show hint (sharpest)
Subtract the ties first, then split the rest in half.
Show solution
Of the 36 outcomes, 6 are ties, leaving 30 where one is larger.
By symmetry half of those favor Diana: 15/36 = 5/12.
A plastic snap-together cube has a protruding snap on one side and receptacle holes on the other five sides. What is the smallest number of these cubes that can be snapped together so that only receptacle holes are showing?
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Every cube's single snap must be plugged into another cube's hole.
Show hint (sharpest)
Arrange the cubes so each snap points into the next one.
Show solution
Each cube has one snap that must be hidden inside a neighbor's hole.
Four cubes in a square ring, each snap pointing into the next, hide all four snaps, leaving only holes outside — and fewer than four can't absorb every snap. So 4.
Buses from Dallas to Houston leave every hour on the hour. Buses from Houston to Dallas leave every hour on the half hour. The trip from one city to the other takes 5 hours. Assuming the buses travel on the same highway, how many Dallas-bound buses does a Houston-bound bus pass on the highway (not in the station)?
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A Houston-bound bus is on the road for a 5-hour window; it passes any oncoming bus whose own road-window overlaps.
Show hint (sharpest)
Count the Dallas departure times whose 5-hour trips overlap that window on the highway.
Show solution
Say the bus leaves Houston at 12:30 and reaches Dallas at 17:30. It meets every Dallas-bound bus already on the road or that sets out before it arrives.
Those are the Dallas buses leaving from 8:00 through 17:00 — 10 of them — all passed on the highway.
