High School Practice Problems: Logic
HL-37) Answer: $30
The number of two-dollar bills I need to pay for a purchase is 9 more than the number of five-dollar bills I need to pay for the same purchase. What is the cost of the purchase? Explain your answer in detail.
HL-36) Answer: 5
A group of 21 people went to the county fair with 9 people on a stagecoach and 3 people in each buggy. On the return trip, 4 people rode in each buggy. How many people returned on the stagecoach? Explain your answer in detail.
HL-35) Answer: Donna Drucker, AT&T, +$500; Susan Callahan, GE, +$400; Bobby Robinson, Kodak,+$200; Hannah Smith, Pfizer, -$200
Mrs. Callahan and three of her friends have formed an investment club. Each of them picked one favorite stock and invested $3,000 in it. At the end-of-year party and meeting of the club, it turned out that three of the four members had made a profit and only one had lost money. From the clues, determine each person's full name, how much each person lost or gained, and the name of the stock each invested in. Hannah did not invest in General Electric. Susan, whose last name is neither Robinson nor Drucker, made $100 less than Donna. Two people made more money than the person who invested in Kodak. The person who invested in Pfizer was the only one to lose money. Donna made $500, which was the most profit made by anyone. Ms. Robinson did not invest in AT&T but the person who did made the most money. Mrs. Smith lost $200 and Bobby made $200. Explain your answer in detail.
HL-34) Answer: 23
If a kindergarten teacher places her children 4 on each bench, there will be 3 children who will not have a place. However, if 5 children are placed on each bench, there will be 2 empty places. What is the smallest number of children the class could have? Explain your answer in detail.
HL-33) Answer: 5 containers: 54, 56, 58, 59, 62 lbs.
A recycling plant was packaging aluminum cans in containers. They packed five containers and weighed them in pairs. The weights were 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 pounds. what were the weights of the individual containers? Explain your answer in detail.
HL-32) Answer: 26
The members of an Olympiad team contributed a total of $1.69 for refreshments for their weekly practice. Each member contributed the same amount and paid for his or her share in five coins. How many nickels were contributed by all of the members? Explain your answer in detail.
HL-31) Answer: 10 minutes
A circular track is 1000 yards in circumference. Cyclists A, B, and C start at the same place and time, and race around the track at the following rates per minute: A at 700 yards, B at 800 yards, and C at 900 yards. What is the least number of minutes it must take for all three to be together again? Explain your answer in detail.
HL-30) Answer: 4 hours
Three water pipes are used to fill a swimming pool. The first pipe alone takes 8 hours to fill the pool, the second pipe alone takes 12 hours to fill the pool, and the third pipe alone takes 24 hours to fill the pool. If all three pipes are opened at the same time, how long will it take to fill the pool? Explain your answer in detail.
HL-29) Answer: 6 days
A group of 12 girl scouts had enough food to last for 8 days when they arrived in camp. However, 4 more scouts joined them without the amount of food being increased. How long will the food last if each scout is given the same daily ration as originally planned? Explain your answer in detail.
HL-28) Answer: 1976
Person A was born on January 15, 1948. Person B was born on January 15, 1962. If both are alive now, in what year was person A twice as old as person B? Explain your answer in detail.
HL-27) Answer: 720
A twelve-hour clock loses I minute every hour. Suppose it shows the correct time now. What is the least number of hours from now when it will again show the correct time? Explain your answer in detail.
HL-26) Answer: 1560
A and B are two different numbers selected from the first forty counting numbers, I through 40 inclusive. What is the largest value that (AxB) / (A-B) can have? Explain your answer in detail.
HL-25) Answer: 43 went swimming
There are 125 juniors participating in the Junior-Day Olympics: 59 played football, 49 played baseball, 42 participated in the races, 20 participated in the races and played baseball, 29 participated in the races and played foot-ball, 31 played both football and baseball, and 12 entered all three events. Those who did not participate in any of these three events went swimming. How many went swimming? Explain your answer in detail.
HL-24) Answer: 3
During a school year, a student was given an award of 25 cents for each math test he passed and was fined 50 cents for each math test he failed. At the end of the school year, the student had passed 7 times as many tests as he had failed, and received $3.75. How many tests did he fail? Explain your answer in detail. -
HL-23) Answer: 8 days
Twelve people purchased supplies for a ten-day camping trip with the understanding that each of the twelve will get equal daily shares. They are then joined by three more people, but make no further purchases. How long will the supplies then last if the original daily share for each person is not changed? Explain your answer in detail.
HL-22) Answer: 6
A total of fifteen pennies are put into four piles so that each pile has a different number of pennies. What is the smallest possible number of pennies that could be in the largest pile? Explain your answer in detail.
HL-21) Answer: 20
In the "magic-square" below, five more numbers can be placed in the boxes so that the sum of the three numbers in each row, in each column, and in each diagonal is always the same. What value should X have? Explain your answer in detail.
15 |
- |
35 |
50 |
- |
- |
25 |
X |
- |
HL-20) Answer: Friday
Suppose five days before the day after tomorrow was Wednesday. What day of the week was yesterday? Explain your answer in detail.
HL-19) Answer: 312132 or 231213
Arrange the digits 1, 1, 2, 2, 3, 3, as a six-digit number in which the 1s are separated by one digit, the 2s are separated by two digits, and the 3s are separated by three digits. There are two answers. Find one. Explain your answer in detail.
HL-18) Answer: Glenn – tennis; Harry – soccer; Kim - baseball
Glen, Harry, and Kim each have a different favorite sport among tennis, baseball, and soccer. Glen does not like baseball or soccer. Harry does not like baseball. Name the favorite sport of each person. Explain your answer in detail.
HL-17) Answer: 15
In the "magic square" below, the four numbers in each column, in each row, and in each of the two diagonals, have the same sum. What value should N have? Explain your answer in detail.
- |
- |
7 |
12 |
N |
4 |
9 |
- |
- |
5 |
16 |
3 |
8 |
11 |
- |
- |
HL-16) Answer: 56
I am less than 6 feet tall but more than 2 feet tall. My height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. What is my height in inches? Explain your answer in detail.
HL-15) Answer: 7953
In the addition problem below, different letters represent different digits. It is also given that N is 6 and T is greater than 1. What four-digit number does T H I S represent? Explain your answer in detail.
T H I S
+ I S
K E E N
HL-14) Answer: $1.15
The cost of a book is $1 and a whole number of cents. The total cost of six copies of the book is less than $8. However, the total cost of seven copies of the same book at the same price per book is more than $8. What is the least a single copy of the book could cost? Explain your answer in detail.
HL-13) Answer: 15 days
A work crew of 3 people requires 3 weeks and 2 days to do a certain job How long would it take a work crew of 4 people to do the same job if each person of both crews works at the same rate as each of the others? Note: each week contains six work-days. Explain your answer in detail.
HL-12) Answer: 9 feet
A dog takes 3 steps to walk the same distance for which a cat takes 4 steps. Suppose 1 step of the dog covers 1 foot. How many feet would the cat cover in taking 12 steps? Explain your answer in detail.
HL-11) Answer: 7 (Unless you allow “some” 13-cent stamps to mean zero of them!)
Carol spent exactly $1 for some 5-cent stamps and some 13-cent stamps. How many 5-cent stamps did she buy? Explain your answer in detail.
HL-10) Answer: 15 cents
Ann gave Betty as many cents as Betty had. Betty then gave Ann as many cents as Ann then had. At this point, each had 12 cents. How much did Ann have at the beginning? Explain your answer in detail.
HL-9) Answer: 13
In a group of 30 high school students, 8 take French, 12 take Spanish and 3 take both languages. How many students of the group take neither French nor Spanish? Explain your answer in detail.
HL-8) Answer: 17
A study of 50 high school students showed that exactly 25 of them took Biology, exactly 20 of them took Chemistry, and exactly 12 of them took both subjects. How many of the 50 students took neither Biology nor Chemistry? Explain your answer in detail.
HL-7) Answer: 5
I have a drawer which contains 40 socks in the following numbers and colors: 12 tan, 9 brown, 11 gray, and 8 blue. Suppose I am blindfolded. What is the fewest number of socks I must pick from the drawer to be absolutely certain that I have two socks of the same color among those I have picked? Explain your answer in detail.
HL-6) Answer: 7
A container has 10 red disks, 10 white disks, and 10 blue disks, all of the same size. Suppose I am blindfolded when I pick disks from the container. What is the least number of disks I must pick in order to be absolutely certain that there are three disks of the same color among those I have picked? Explain your answer in detail.
HL-5) Answer: 95 cents
Eric has just three types of coins in his change-purse: nickels, dimes, and quarters. The purse contains more dimes than quarters, and more quarters than nickels and there are seven coins in all. What is the total value of the seven coins? Explain your answer in detail.
HL-4) Answer: 87
In the XYZ contest, a school may enter 1, 2, 3, or, at most, 4 teams. Suppose 347 teams are entered in the XYZ contest. What is the smallest number of schools that could have entered the XYZ contest? Explain your answer in detail.
HL-3) Answer: Sunday or Monday
June has 30 days. One year, June had exactly four Sundays. On which two days of the week could June 30 not have occurred that year? Explain your answer in detail.
HL-2) Answer: 7
Barbara has 20 coins consisting of nickels and dimes. If the nickels were dimes and the dimes were nickels, she would have 30 cents more than she has now. How many dimes did she have to begin with? Explain your answer in detail.
HL-1) Answer: $165
Two cash registers of a store had a combined total of $300. When the manager transferred $1 5 from one register to the other register, each register then had the same amount. How much did the register with the larger amount have before the transfer was made? Explain your answer in detail.