Deductive Reasoning – Test 2 (UK)

A pizza restaurant is trying to develop a new menu item. They have two sauce choices; Red or white sauce. They want to put two toppings on their new pizza, but the toppings must meet the following conditions:

• Pineapple can only go on a red sauce pizza.
• Chicken can only go on white sauce pizza.
• Spinach can be selected only as an accompaniment to chicken.
• Black olives can only go on red sauce pizza.
• Bacon can go on both red and white sauce pizza.
• The new pizza must have at least one meat and one vegetable/fruit topping.

Which of the following combinations would not be possible to be listed on the menu as is given the above guidelines?

Membership in the US House of Representatives is determined by state population. The Senate has two votes for each state. Since there are two houses, both large states and small states are satisfied. This system was set into the Constitution in 1787, when the “great compromise” listened to the plans from both Virginia and New Jersey to decide how the new US congress would be assembled.

Applying logic to the passage above, which of the following statements is true?

Claire, Lucy & Miles all recently took trips to Italy. Collectively, they visited Venice, Florence, Milan, Rome and Orvieto. The cities each visited must be consistent with the following guidelines:

• Each city was visited by at least one person.
• Only one person visited Orvieto.
• Claire did not visit Orvieto.
• Each person took only one trip and traveled to between one and three of the cities.
• Each person that went to Florence also went to Milan.
• Each person that went to Orvieto also went to Rome.
• The person who went to Venice did not go to Rome.
• Lucy and Claire went to the same three cities.

Which person/persons visited Rome?

Claire, Lucy & Miles all recently took trips to Italy. Collectively, they visited Venice, Florence, Milan, Rome and Orvieto. The cities each visited must be consistent with the following guidelines:

• Each city was visited by at least one person.
• Only one person visited Orvieto.
• Claire did not visit Orvieto.
• Each person took only one trip and traveled to between one and three of the cities.
• Each person that went to Florence also went to Milan.
• Each person that went to Orvieto also went to Rome.
• The person/persons who went to Venice did not go to Rome.
• Lucy and Claire went to the same three cities.

If everyone went to Orvieto (instead of just one person), how many cities would Lucy have ended up visiting during her trip?

Noel is an upcoming year 10 student, and the counsellors are working hard to configure her schedule. She is qualified to take honours history and honours English, but needs to be in regular maths. She is required to take chemistry and health class, and this leaves one schedule slot open for an elective. Her schedule must be consistent with the following guidelines:

• English Class Offerings
  • Honours: offered 1^st and 4^th periods
  • Regular: offered 2^nd and 3^rd periods
• History Class Offerings
  • Honours: offered 1^st and 5^th periods
  • Regular: offered 3^rd and 4^th periods
• Maths Class Offerings
  • Honours: offered 2^nd period
  • Regular: offered 1^st, 3^rd and 6^th periods
• Science Class Offerings
  • Chemistry: offered 1^st, 4^th and 6^th periods
• Health Class Offered 4^th, 5^th and 6^th periods

Which of the following schedules for Noel is invalid given the guidelines?

You own a bar and are working on making the bartender schedule for the week. You have four bartenders in your staff; Joe, Jeremy, Debbie, and Victoria.  You must meet the following scheduling requirements:

• You are open from 2:00pm to 2:00am, and have to have at least one bartender working at all times.
• You split the schedule into two shifts: 2:00-9:00pm, and 9:00pm-2:00am.
• On Friday and Saturday, you must have two bartenders on to accommodate the larger number of customers.
• Joe works a double shift on Friday, works second shift on Saturday, and never works on Sunday.
• Debbie can only work first shifts, but works every week day.
• Jeremy is a full-time student and can only work weekends (beginning Friday second shift).
• Victoria does not work first shifts after working second shifts.

Which two bartenders will be on during first shift on Fridays?

You own a bar and are working on making the bartender schedule for the week. You have four bartenders in your staff; Joe, Jeremy, Debbie, and Victoria.  You must meet the following scheduling requirements:

• You are open from 2:00pm to 2:00am, and have to have at least one bartender working at all times.
• You split the schedule into two shifts: 2:00-9:00pm, and 9:00pm-2:00am.
• On Friday and Saturday, you must have two bartenders on to accommodate the larger number of customers.
• Joe works a double shift on Friday, works second shift on Saturday, and never works on Sunday.
• Debbie can only work first shifts on week days, but works every weekday first shift.
• Jeremy is a full-time student and can only work weekends (beginning Friday second shift).
• Victoria does not work first shifts after working second shifts.
• Joe and Victoria typically split weekday second shifts.

Which of the following options is invalid given the scheduling requirements?

After the last day of the season, there was a three way tie at the top of the basketball league standings. The Hawks, Wildcats, and Tigers all finished with the same record 8-2. Here are the league tiebreaker rules:

• In the event of a tie in terms of final record- head to head results will determine who finishes higher in the standings.
• In the event of a three way tie, the record against the other top teams will be considered the tiebreaker.
• If the teams are still tied, point differential in the games between the other two teams will be used to break the tie.

Many coaches in the league are very unhappy with this tiebreaker rule because they feel in encourages poor sportsmanship. Which of the following statements best encompasses these coaches’ arguments?

You are going with your family to a big football game. You are part of a group of 7 in total (Mum, Dad, Grandfather, 3 Siblings and you). You bought tickets last minute, and unfortunately, cannot all sit together.  You have a group of 4 together in section 204, 2 together in section 105, and 1 seat in section 117.

You must decide who occupies what seats based on the following requirements:

• You and your Dad have been going to games together for years, and must sit together.
• Your 3 siblings are not enthusiastic football fans, and are more interested in the social aspect of going to the game.
• Your Grandfather is older and may need help navigating the stadium, so should not be sent to sit alone.
• An adult chaperone must be with each of your 3 siblings, but not necessarily with you.

Who should sit alone in section 117?

BINGS are more talented than VALYS

OKOYS are less talented than FENTER

VALYS are more talented than FRANS

FRANS are more talented than FENTER, but less talented than BINGS

OKOYS are less talented than VALYS

Statement: BINGS are the most talented.

Five friends (Max, Lindsay, Franz, Henry & Karen) are taking a road trip in a car that seats 5 people. The car has a driver’s seat and passenger’s seat in front, and a single row backseat with 2 regular sized seats and a smaller middle seat. The way you sit in the car must meet the following requirements:

• Max cannot drive because he doesn’t have his driving license.
• Lindsay has motion sickness and cannot sit in the backseat.
• Franz is too big to fit in the middle seat.
• Henry insists on not driving because he wants to be able to eat in the car more easily.

How many of the friends are eligible to drive based on the requirements above?

At your secondary school’s local art competition, the final five paintings in the competition are as follows: a landscape, a self-portrait, a basket of fruit, a religious painting, and a city-scape. The five artists are Carrie, Isabel, Jonas, Giovanni, and Minnie. Carrie painted the basket of fruit. The city-scape is in the middle and is displayed next to Giovanni’s painting and is in between the self-portrait and the basket of fruit. Minnie did not paint the landscape, and her painting is only next to one other painting. Isabel did not paint the city-scape.

Who painted the religious painting?

Johnny makes £15/hour at his job.

Louis makes £2/hour less than Johnny.

Johnny is a till assistant, while Louis is a sales assistant.

Evaluate the logical validity of this statement:

Sales assistant are valued higher than till assistants.