Deductive Reasoning – Test 1 (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.

If the restaurant decides to make their new pizza with white sauce, what ingredient must be on the pizza?

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.

After doing extensive market research, the owner decides that the new pizza must contain bacon. Which of the following combinations is acceptable given the guidelines listed above?

Members of the US House of Representatives serve in short, two year terms. Members of the more selective United States Senate serve in longer, six year terms. There are no term limits for members of either house, but they must be continually re-elected when their terms end.

Which of the following statements is NOT 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 travelled 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.

Which of the following statements is supported by the passage and guidelines?

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

Given the scheduling requirements, which class that is offered during first period could Noel not take at that time so as not to ruin her other scheduling requirements?

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 1st and 4th periods
• Regular: offered 2nd and 3rd periods

History Class Offerings

• Honours: offered 1st and 5th periods
• Regular: offered 3rd and 4th periods

Math Class Offerings

• Honours: offered 2nd period
• Regular: offered 1st, 3rd and 6th periods

Science Class Offerings

• Chemistry: offered 1st, 4th and 6th periods

Health Class Offered 4th, 5th and 6th periods
Elective Offerings

• Band
  • 3rd Period
• Current Events
  • 2nd, 3rd, 4th Period
• Yearbook
  • 2nd Period
• Newspaper
  • 6th Period
• Musical Theatre
  • 6th Period
• Graphic Design
  • 1st Period

Noel calls the school and insists on being in band class, even if it means that the requirements and guidelines for her schedule of other classes would be broken. If Noel is in band, which scheduling guideline would have to be broken?

You own a bar and are working on making the bartender schedule for the week. You have four bartenders on 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.

Given the scheduling requirements listed above, which bartender likely works the most hours consistently?

A FILO is more expensive and higher quality than a HARMY. A VERTUN is the same price as a FILO, but is of similar quality as a HARMY. A NEWKIRK is the best quality and most expensive.  

Statement: The smartest purchase is a NEWKIRK 

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.

GAME RESULTS:

• Hawks defeated Tigers 45-30
• Wildcats defeated Hawks 50-49
• Tigers defeated Wildcats 38-35

According to the tiebreaker rules, which team finished third in the standings?

You are going with your family to the big homecoming football game. You are part of a group of 7 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. They would prefer to sit together.
• 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.

If your Grandfather insisted on sitting with your Mum, Is there a way to arrange the seats without violating one of the previous guiding principles?

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

Which of the following is the LEAST talented, based on the logic above?

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.

Which of the following backseat combinations meets all the requirements?

At your high 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.

How many possible display combinations exist that meet all the requirements listed above?

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.

Johnny has been working at the company for 5 years, and Louis is in his first week.

Jennifer is a sales assistant who started at the same time as Johnny, and she makes £20/hour.

Which conclusion below in INVALID given the information you’ve been given?