Start with grouping the statements in all possible combinations and try to find an example for each group.
Statements II and III.
Practice makes perfect
We have been given the following three statements.
I. & Each of the two items that Val bought &costs more than $10.
II. & Val spent $34 on the two items.
III. & Neither of the two items that Val bought &costs more than $15.
In order to identify the two statements that contradict each other, we will first group the statements in all possible combinations.
Group A
Group B
Group C
I. Each of the two items that Val bought costs more than $10.
I. Each of the two items that Val bought costs more than $10.
II. Val spent $34 on the two items.
II. Val spent $34 on the two items.
III. Neither of the two items that Val bought costs more than $15.
III. Neither of the two items that Val bought costs more than $15.
Next, we will find an example for each group. If we cannot, this means that the two statements contradict each other. Let's start with Group A.
Group A
An example for Group A must be a pair of items such that each item costs more than $10 and, at the same time, their overall price is equal to $34. Let's say that Val has bought two books: Book A and Book B, each for $17. Let's check whether this example satisfies both statements.
Statement I: Since both books cost $17, each of them costs more than $10. âś“
Statement II: Since both books cost $17, the cost of buying two of them is $34. âś“
As we can see, our example with Book A and Book B satisfies both statements. Therefore, statements I and II do not contradict each other.
Group B
Let's continue with Group B. Each of the two items must cost more than $10 and, at the same time, neither can cost more than $15. This time, let's consider Book C and Book D, each of them costing exactly $15. Let's check whether this example satisfies both statements.
Statement I: Since both books cost $15, each of them costs more than $10. âś“
Statement III: Since both books cost $15, each of them costs not more than $15. âś“
As we can see, our example with Book C and Book D satisfies both statements. Therefore, statements I and III also do not contradict each other.
Group C
For the last group, we need two items such that their overall price is $34 and neither of them can cost more than $15. Now we will consider Book E and Book F, each for $15. Let's check whether this example satisfies both conditions.
Statement II: Since both books cost $15, the cost of buying two of them is $30, not $34. *
Statement III: Since both books cost $15, each of them costs not more than $15. âś“
We can see that one of the condition is not satisfied. Notice that the sum of two items, that costs at most $15 each, cannot be greater than 2*15=30 dollars.
Therefore, statements II and III contradict each other.
