# Hardest BMAT Section 1 Questions and Answers

Advice & Insight From BMAT Specialists

The first section of the BMAT can be especially challenging for candidates, as it is aptitude-based, rather than knowledge-based. Here, we present 10 difficult questions from our question bank. We’ve removed the multiple choice options to make these questions even more difficult – all questions in ourÂ bankÂ include four options to choose from.

## In a secondary school, exactly one ninth of all students play football. Of these, two thirds play as strikers. Of those one quarter play for the A team. You may assume that all football players can only play in one position. What is the smallest possible size of the secondary school?

Assume the smallest possible size of the secondary school is x students.

It is known that (1/9) of x play football.

Using the other information it can be deduced that:

(1/54) of x are strikers that play in the A team.

Since the number of strikers that play for the A team must be a whole number, the answer must be 54 pupils, A.

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## A chemist wanted to dilute some Hydrochloric acid to one third of its original concentration. She poured 40 ml of water to a 200 ml beaker one quarter full ofÂ  Hydrochloric acid. After mixing the contents, she realised the Hydrochloric acid had not been diluted to one third of its original concentration. How much more water does she need to add to produce the desired concentration of Hydrochloric acid?

The beaker is Â¼ full of Hydrochloric acid.

This means it contains 50 ml of Hydrochloric acid. When 40 ml of water is added to the beaker the total volume increases to 90 ml.

Since the Hydrochloric acid makes up 5/9 of the total volume its concentration is now 5/9 of its original value.

To decrease the concentration of Hydrochloric acid to 1/3 of its original value it must make up one third of the total volume of the solution.

This can be achieved by adding another 60 ml of water to the beaker.

Total volume = 50 + 40 + 60 = 150 ml

Volume of Hydrochloric acid = 50 ml

Fraction of Hydrochloric acid = 50 / 150 = 1/3, meaning D is the answer.

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## There are two containers, one with a capacity of 5 litres and another with a capacity of 3 litres. Neither has any measurement markers on them. Using just these two containers, how can you measure exactly 4 litres of water?

This is a problem that can be solved with a bit of strategic thinking.

1. Fill the 5-litre container completely.
2. Pour the water from the 5-litre container into the 3-litre container until the 3-litre container is full. You now have 2 litres remaining in the 5-litre container.
3. Empty the 3-litre container and pour the remaining 2 litres from the 5-litre container into the 3-litre container.
4. Fill the 5-litre container one more time.
5. Finally, pour water from the 5-litre container into the 3-litre container (which already contains 2 litres of water) until the 3-litre container is full. This will require exactly 1 litre from the 5-litre container, leaving exactly 4 litres in the 5-litre container.

This way, you have successfully measured 4 litres of water using only a 5-litre and a 3-litre container.

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## A group of five friends - Alice, Ben, Claire, David, and Emma - participated in a cooking competition. Each friend prepared a different dish: lasagna, sushi, pizza, risotto, and pasta. Clues: Claire didn't cook sushi or lasagna. Emma cooked pizza. David's dish wasn't risotto. Ben cooked pasta. Alice prepared the dish with the most ingredients. Who cooked the risotto?

To determine who cooked the risotto, we use the given clues to eliminate possibilities. Since Claire didn’t cook sushi or lasagna, and Emma cooked pizza, they cannot be the ones who prepared risotto. David’s dish wasn’t risotto, so he is also ruled out. We know Ben cooked pasta, so he didn’t prepare risotto either. Alice’s dish had the most ingredients, and since there are no other clues, Alice must have prepared the risotto.

## Given the sequence of numbers below, find the next three numbers in the pattern: 4, 9, 16, 25, 36, ...

The sequence represents the squares of consecutive natural numbers: 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2 = 36. To find the next three numbers, continue the pattern: 7^2 = 49, 8^2 = 64, 9^2 = 81.

## In a family gathering, four people are sitting around a circular table: Alice, Bob, Carol, and Dave. Clues: Alice is opposite Bob. Carol is next to Alice, but not opposite her. Dave is next to Bob, but not opposite him. What is the seating arrangement?

By following the clues, we can determine the seating arrangement around the table. Alice is opposite Bob, so Carol and Dave must be sitting next to each other. Since Carol is not opposite Alice, Carol and Dave must be sitting in the two seats next to Alice. Thus, Alice, Carol, and Dave are seated in consecutive seats. Bob is opposite Alice, which leaves him in the remaining seat. The seating arrangement, starting from any position, is: Alice, Carol, Dave, Bob.

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## There are five houses, each of a different color, in a row: red, blue, green, yellow, and purple. Clues: The red house is to the left of the green house. The blue house is to the right of the green house but not next to the red house. The yellow house is to the right of the blue house and left of the purple house. What is the order of the houses, from left to right?

The given clues help establish the order of the houses. The red house is to the left of the green house, so it must be in the first position. The blue house is to the right of the green house but not next to the red house, so it occupies the third position. The yellow house is to the right of the blue house and left of the purple house, indicating it is in the second position. The purple house must be in the fifth position. The order from left to right is: red, yellow, green, blue, purple.

## Five friends - Alex, Bailey, Chris, Drew, and Eden - live in different cities: London, Paris, New York, Sydney, and Tokyo. Clues: Alex doesn't live in London or Tokyo. Bailey lives in Paris. Chris lives in either Sydney or Tokyo. Drew lives in New York or Sydney. Eden doesn't live in Tokyo. In which city does each friend live?

From the given clues, we can deduce the cities in which each friend lives. Since Bailey lives in Paris and Eden doesn’t live in Tokyo, Eden must live in either London, New York, or Sydney. Chris lives in either Sydney or Tokyo, and Drew lives in New York or Sydney, which means Chris cannot live in Sydney. Therefore, Chris lives in Tokyo. Drew must then live in Sydney. As Alex doesn’t live in London or Tokyo, Alex must live in New York. Thus, the final city assignments are: Alex – New York, Bailey – Paris, Chris – Tokyo, Drew – Sydney, and Eden – London.

## Decode the following message using the given code: Message: "8-5-12-12-15" Code: A = 1, B = 2, C = 3, ..., Z = 26

The coded message “8-5-12-12-15” corresponds to the letters H-E-L-L-O using the given code. Each number corresponds to the position of the corresponding letter in the alphabet (A=1, B=2, etc.). Therefore, 8 represents the 8th letter, which is H, 5 represents E, and so on. Decoding the message yields the word “HELLO.”

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## Identify the pattern and fill in the missing numbers: 2, 6, 12, 20, ?, ?.

The sequence represents the sum of consecutive odd numbers. The pattern starts with 1 (1 + 1 = 2), then adds two consecutive odd numbers successively to get the next terms: 1 + 3 + 5 = 9 (2 + 9 = 11), 9 + 7 + 9 = 25 (11 + 25 = 36). Continuing the pattern, we add 11 + 9 + 11 = 31 to 36 to get the next two terms: 36 + 31 = 67 and 67 + 41 = 108. Thus, the missing numbers are 67 and 108.

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