Pencil
Have a go at some questions.
Good luck!
Good luck!
Question 1
Which one of the following cannot be true?
John always shops at G. Bob shops at G on weekdays but at weekends she shops at S. Sam always shops at S for food but at F for all other goods. One of the three sees the other pair of shoppers coming out of one of the shops where they have both been buying food.
A. It’s a weekday.
B. It’s a weekend and the shop is S.
C. The shop is G and one of the pair of shoppers is Bob.
D. It’s a weekend and the shop is G.
E. It’s a weekend and neither of the pair of shoppers is John.
Which one of the following cannot be true?
John always shops at G. Bob shops at G on weekdays but at weekends she shops at S. Sam always shops at S for food but at F for all other goods. One of the three sees the other pair of shoppers coming out of one of the shops where they have both been buying food.
A. It’s a weekday.
B. It’s a weekend and the shop is S.
C. The shop is G and one of the pair of shoppers is Bob.
D. It’s a weekend and the shop is G.
E. It’s a weekend and neither of the pair of shoppers is John.
Question 1 Answer
Correct Answer: D
Explanation: One way of solving this problem is to look at each option and work out if it can be true.
Option A → This could be Sam seeing John and Bob coming out of G.
Option B → This could be John seeing Bob and Sam.
Option C → This could be Sam seeing John and Bob on a weekday.
Option D → Only John shops at G on a weekend, so this cannot be true.
Option E → This could be John seeing Bob and Sam coming out of S.
Correct Answer: D
Explanation: One way of solving this problem is to look at each option and work out if it can be true.
Option A → This could be Sam seeing John and Bob coming out of G.
Option B → This could be John seeing Bob and Sam.
Option C → This could be Sam seeing John and Bob on a weekday.
Option D → Only John shops at G on a weekend, so this cannot be true.
Option E → This could be John seeing Bob and Sam coming out of S.
Question 2
When I buy my favourite brand of coffee from the supermarket I normally have a choice of three jar sizes, small - 100 g; medium - 200 g; large - 400 g
At present, all three jars contain 25% extra for the normal price and, in addition, customers who buy a large jar get a small jar free. For customers who buy a large jar of coffee, what is the total extra percentage of coffee for the normal price of the large jar?
A. 33 1/3 %
B. 36%
C. 46 2/3 %
D. 50%
E. 56 1/4 %
F. 87 1/2 %
When I buy my favourite brand of coffee from the supermarket I normally have a choice of three jar sizes, small - 100 g; medium - 200 g; large - 400 g
At present, all three jars contain 25% extra for the normal price and, in addition, customers who buy a large jar get a small jar free. For customers who buy a large jar of coffee, what is the total extra percentage of coffee for the normal price of the large jar?
A. 33 1/3 %
B. 36%
C. 46 2/3 %
D. 50%
E. 56 1/4 %
F. 87 1/2 %
Question 2 Answer
Correct Answer: E
Explanation: This question requires the calculations to be made in the appropriate order.
Start with calculating the amount in each jar.
The 25% extra means that the large jar will contain 400 g × 1.25 = 500 g of coffee.
Similarly, the small jar will contain 100 g × 1.25 = 125 g of coffee.
Buying a large jar of coffee (500 g) also gets a small jar for free (125 g).
So, in total the customer will get 625 g.
If the special offers had not been in place, purchasing a large jar of coffee would get a customer 400 g.
Thus, customers obtain an additional 500 g + 125 g – 400 g = 225 g of coffee.
A customer will therefore get (225 / 400) × 100% = 56 1/4 % more coffee.
Correct Answer: E
Explanation: This question requires the calculations to be made in the appropriate order.
Start with calculating the amount in each jar.
The 25% extra means that the large jar will contain 400 g × 1.25 = 500 g of coffee.
Similarly, the small jar will contain 100 g × 1.25 = 125 g of coffee.
Buying a large jar of coffee (500 g) also gets a small jar for free (125 g).
So, in total the customer will get 625 g.
If the special offers had not been in place, purchasing a large jar of coffee would get a customer 400 g.
Thus, customers obtain an additional 500 g + 125 g – 400 g = 225 g of coffee.
A customer will therefore get (225 / 400) × 100% = 56 1/4 % more coffee.
Question 3
In a high-speed police chase, police drivers sometimes lose sight of the car they are chasing. But that’s no reason to give up. All they have to do is take the first left, and then the first left again. Pursued drivers are likely to keep taking turns as they come up, as this seems instinctively like the best way to lose someone who is following them. They are not going to turn right as this involves waiting and checking for oncoming traffic. Therefore, take a couple of left turns and the police car will soon have their criminal in sight once again!
Which of the following, if true, would strengthen this argument?
A. car chases tend to end with the pursued driver losing control of their vehicle.
B. Drivers in TV car chases tend to turn left rather than right when pursued.
C. Two left turns might take the criminal where they want to be going.
D. Police drivers are usually able to sustain faster average speeds over a length of time than other drivers.
E. Police drivers usually request overhead assistance from a helicopter when chasing criminals in cars.
In a high-speed police chase, police drivers sometimes lose sight of the car they are chasing. But that’s no reason to give up. All they have to do is take the first left, and then the first left again. Pursued drivers are likely to keep taking turns as they come up, as this seems instinctively like the best way to lose someone who is following them. They are not going to turn right as this involves waiting and checking for oncoming traffic. Therefore, take a couple of left turns and the police car will soon have their criminal in sight once again!
Which of the following, if true, would strengthen this argument?
A. car chases tend to end with the pursued driver losing control of their vehicle.
B. Drivers in TV car chases tend to turn left rather than right when pursued.
C. Two left turns might take the criminal where they want to be going.
D. Police drivers are usually able to sustain faster average speeds over a length of time than other drivers.
E. Police drivers usually request overhead assistance from a helicopter when chasing criminals in cars.
Question 3 Answer
Correct Answer: C
Explanation:
Option A & B → these are irrelevant. The issue of drivers losing control of the vehicle is irrelevant to which turns they will take whilst what happens in TV car chases may not necessarily be what happens in real life car chases. Thus, these are incorrect.
Option D → This is also irrelevant as further assistance is irrelevant to what direction the drivers being pursued will go.
Option E → This appears relevant, but does not affect how the argument’s reasoning leads on to its conclusion. The argument describes how pursued drivers will frequently wish to turn, and how left turns are easier and quicker, and then describes how this means police taking left turns will soon catch up to the criminals. The idea of criminals turning left because that leads to their destination is a separate point from this reasoning.
Option C → Strengthens the argument. It relates to the idea that even if the police follow the path of a criminal, if they wish to catch up they must surely travel at a faster speed. Thus, if C is true, the argument’s conclusion is much more solid.
Correct Answer: C
Explanation:
Option A & B → these are irrelevant. The issue of drivers losing control of the vehicle is irrelevant to which turns they will take whilst what happens in TV car chases may not necessarily be what happens in real life car chases. Thus, these are incorrect.
Option D → This is also irrelevant as further assistance is irrelevant to what direction the drivers being pursued will go.
Option E → This appears relevant, but does not affect how the argument’s reasoning leads on to its conclusion. The argument describes how pursued drivers will frequently wish to turn, and how left turns are easier and quicker, and then describes how this means police taking left turns will soon catch up to the criminals. The idea of criminals turning left because that leads to their destination is a separate point from this reasoning.
Option C → Strengthens the argument. It relates to the idea that even if the police follow the path of a criminal, if they wish to catch up they must surely travel at a faster speed. Thus, if C is true, the argument’s conclusion is much more solid.
Question 4
Which of the following sequences do not adhere to the same underlying mathematics?
A. 5, 13, 17, 29, 41
B. 17, 29, 37, 41, 53
C. 17, 29, 41, 53, 65
D. 29, 41, 53, 81, 97
Which of the following sequences do not adhere to the same underlying mathematics?
A. 5, 13, 17, 29, 41
B. 17, 29, 37, 41, 53
C. 17, 29, 41, 53, 65
D. 29, 41, 53, 81, 97
Question 4 Answer
Correct Answer: C
Explanation:
Do they all progress in 12’s? No. The numbers are all primes which are the sums of two squares.
Primes:2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,11 3Squares:1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256
Correct Answer: C
Explanation:
Do they all progress in 12’s? No. The numbers are all primes which are the sums of two squares.
Primes:2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,11 3Squares:1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256
Shooting Star
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