William buys a bus ticket every day, Monday to Friday, for $2.50. The bus company has just introduced a card which can be bought to get a discount on all bus fares. Each card is valid for 1 week. William has worked out that he will pay exactly the same amount if he gets the card as he will if he continues to buy tickets at the normal price. Which of the following could be the price and discount for the card?
Correct answer: D. $10 for the card and a discount of 80% on ticket prices
- A. $5 for the card and a discount of 10% on ticket prices
- B. $5 for the card and a discount of 50% on ticket prices
- C. $10 for the card and a discount of 50% on ticket prices
- D. $10 for the card and a discount of 80% on ticket prices
Explanation
William buys a bus ticket every day from Monday to Friday, so he buys 5 tickets per week. If he continues to buy tickets at the normal price, he will spend:5 tickets/week × $2.50/ticket = $12.50/weekSince William has worked out that he will pay exactly the same amount if he gets the card, we can set up an equation to solve for the cost of the card and the discount on ticket prices:(cost of card) + [(discounted ticket price) × (cost of 5 tickets per week)]Let's try each option:Option A: $5 for the card and a discount of 10% on ticket prices:The cost of the card is $5. The discount on ticket prices is 10%, which reduces the price to $2.25 per ticket.= $5 + ($2.25 x 5) = $16.25/weekOption B: $5 for the card and a discount of 50% on ticket prices:The cost of the card is $5. The discount on ticket prices is 50%, which reduces the price to $1.25 per ticket.= $5 + ($1.25 x 5) = $11.25/weekOption C: $10 for the card and a discount of 50% on ticket prices:The cost of the card is $10. The discount on ticket prices is 50%, which reduces the price to $1.25 per ticket.= $10 + ($1.25 × 5) = $16.25/weekOption D: $10 for the card and a discount of 80% on ticket prices:The cost of the card is $10. The discount on ticket prices is 80%, which reduces the price to $0.50.= $10 + ($0.50 x 5) = $12.50/weekThis is the same as the cost of buying tickets at the normal price, so option D could be correct
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? support@testustad.com
About Quantitative Reasoning
Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
Practise Quantitative Reasoning
625 free Quantitative Reasoning MCQs from Analytical and Logical Reasoning, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Analytical and Logical Reasoning questions like this
Analytical and Logical Reasoning is on 27 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Quantitative Reasoning questions
In a restaurant recently, I received the following bill:Starter $7.00Main Course $20.75Dessert $9.75Drink $4.50Service Charge $5.25TOTAL $47.25What percentage of the cost of the food and drink had been added to the bill as service charge?
The price for hiring a car is determined by the number of days for which it is to be hired and the number of people who will be using it. The table below shows the prices for groups of up to 5 people hiring cars for up to 7 days.Patrick is part of a group of 5 people on a holiday for 5 days. They will be going on outings each day, and had planned to hire one car for all of them for all 5 days. However, two of the group will only be there for the first 3 days, so an alternative is to hire one car for this period and another for the final two days. What will be the difference if they choose this alternative?
Four identical glasses are shown below. One glass is empty, and the other 3 glasses are ¼ full,1/2 full, and ⅘ full of water, respectively. If the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled?
Gemma is on a coach trip. After a short sleep she has woken up just in time to see this sign on the side of the motorway.The last thing she remembers seeing before she fell asleep is this sign:How far has the coach travelled while Gemma has been asleep?
Monthly sales of new cars in Illyria are always highest in March and September. At the end of each month, the sales figures from the 1st January up to the end of the month are recorded. These figures are then presented on a chart. Which of the four charts below could represent the car sales in lllyria?
What is the mode of this data set?