Critical Reasoning Questions and Answers


6)

Kurt is a student of Spanish. All students study either Latin or English, but some students of English do not study Latin because they do not think it is a useful thing to know. Students of Spanish never study English. Therefore, Kurt must think Latin is a useful thing to know.

Which of the following must be true for the conclusion above to be logically correct?


Explanation: 

The information given can be summarized as follows:
All students study either Latin or English.
Students of Spanish never study English.
Kurt is a student of Spanish and must therefore study Latin.

The statements are as follows:
A. Spanish is more useful than English.
B. All students who think Latin is useful study it.
C. All students of Latin think it is a useful thing to know.
D. Latin is more useful than Spanish.
E. All students who find Spanish difficult study English.

Considering each in turn:
A. Is not relevant
B. Initially this looks relevant but ‘All students who think Latin is useful study
it’ is not the same as saying all students who study Latin think it is useful.
Kurt might study Latin but not think it is useful. Therefore option B does not
support the conclusion.
C. The statement ‘All students of Latin think it is a useful thing to know’
supports the conclusion ‘Kurt must think Latin is a useful thing to know’.
D. Is not relevant
E. Is not relevant
Option C is the correct answer.

7)

Sabine earns more than Pedro. Sabine earns the same as Maria.
Antonio earns less than Maria. Valeria earns less than Sabine.
Pedro earns less than Valeria.

Who earns the least money?


Explanation:

Working through the statements gives the sequence.
Maria = Sabine > Antonio > Valeria > Pedro
Where > means ‘earns more than’.
Therefore Pedro earns the least money.
Option D is the correct answer.

8)

Richard paid more for his house than did Robert.
Robert paid less for his house than did John.
Derek paid more for his house than did Sarah.
Sarah paid the same amount for her house as did John.

If the above information is true, which of the following must also be true?


Explanation:

Working through the statements gives the sequences:
Richard > Robert
Derek > Sarah = John > Robert
Where > means ‘paid more for house than’

Considering the options:
A. Richard paid more for his house than did Derek.
B. Derek paid more for his house than did Robert.
C. Richard paid more for his house than did John.
D. Sarah paid less for her house than did Richard.
E. Sarah paid less for her house than did Robert.

A. May not be true.
B. Must be true.
C. May not be true.
D. May not be true.
E. Must be false.
Option B is the correct answer.

9)

An insurance policy covering flood damage to stock pays 80% of the costs for the first $1,000 and all of the cost thereafter up to a total of $5,000. Following a claim, the claimant had to pay an additional $1,000 to replace damaged stock. How much was the stock worth?


Explanation:

If the claimant had to pay an additional $1,000, then the insurance company must have paid out 80% of $1,000 plus $5,000.
This means the insurance company paid out $5,800.
The claimant paid an additional $1,000 making the stock worth a total of $6,800.
Option D is the correct answer.

10)

What percentage of all the marbles in the bag were black?

Statement 1 - The ratio of black to white marbles in the bag was 20 : 1.
Statement 2 - There were 5 white marbles in the bag.

Which of the statements above make it possible to answer the question.


Explanation: 

Statement 1 gives the ratio of black and white marbles, but does not tell us the total number of marbles in the bag. So this statement alone is not sufficient to answer the question.
Statement 2 gives the number of white marbles in the bag. So this statement alone is not sufficient to answer the question.
At first sight it may appear that the total number of marbles can be calculated using both statements together like this: White Marbles = 5. Black Marbles = 5 x 20 = 100. Therefore total number of marbles = 105.

However there one critical piece of information missing. It is impossible to say whether there are only black and white marbles in the bag. There may in fact be other colors.

Hence the two statements together are also not sufficient to answer the question.
Since none of the two statements are sufficient to answer the question on their own, and an answer cannot be obtained by combining the two statements as well.

Option E is the correct answer.
This question is more of a ‘trick’ question than most of those you will find in critical reasoning tests. However it has been included to illustrate the importance of not making assumptions when answering these types of question.