A company employee generates a series of five-digit product
codes in accordance with the following rules:
The codes use the digits 0, 1, 2, 3, and 4, and no others.
Each digit occurs exactly once in any code.
The second digit has a value exactly twice that of the
first digit.
The value of the third digit is less than the value of the
fifth digit.
Any of the following pairs could be the third and
fourth digits, respectively, of an acceptable product
code, EXCEPT:
A 0, 1
B 0, 3
C 1, 0
D 3, 0
(E) 3, 4
My answer is just checking to see if I'm correct.
To find the correct answer, we need to analyze the given rules and eliminate the pair that does not meet those criteria.
According to the given rules:
1. The codes use the digits 0, 1, 2, 3, and 4, and no others.
2. Each digit occurs exactly once in any code.
3. The second digit has a value exactly twice that of the first digit.
4. The value of the third digit is less than the value of the fifth digit.
Let's evaluate each answer choice based on these rules:
A) 0, 1:
- 0 is the first digit, and 1 is the second digit. The rule is satisfied.
- However, the value of the third digit is not specified in this pair.
- We cannot determine if the value of the third digit is less than the value of the fifth digit.
- This pair cannot be eliminated based on the given information.
B) 0, 3:
- 0 is the first digit, and 3 is the second digit. The rule is satisfied.
- Again, the value of the third digit is not specified.
- We cannot determine if the value of the third digit is less than the value of the fifth digit.
- This pair cannot be eliminated based on the given information.
C) 1, 0:
- Again, 1 is the first digit, and 0 is the second digit. The rule is satisfied.
- Once more, the value of the third digit is not specified.
- We cannot determine if the value of the third digit is less than the value of the fifth digit.
- This pair cannot be eliminated based on the given information.
D) 3, 0:
- 3 is the first digit, and 0 is the second digit. The rule is satisfied.
- The value of the third digit is 0, which is indeed less than the value of the fifth digit.
- This pair satisfies all the given rules.
E) 3, 4:
- Once again, 3 is the first digit, and 4 is the second digit. The rule is satisfied.
- The value of the third digit is 4, which is not less than the value of the fifth digit (also 4 in this case).
- This pair violates the given rule that the value of the third digit is less than the value of the fifth digit.
- Therefore, this pair can be eliminated.
Based on this analysis, the answer is (E) 3, 4, as it violates the rule that the value of the third digit must be less than the value of the fifth digit.
To determine which pair of digits could NOT be the third and fourth digits of an acceptable product code, let's analyze the given rules.
Rule 1: The codes use the digits 0, 1, 2, 3, and 4, and no others.
Rule 2: Each digit occurs exactly once in any code.
Rule 3: The second digit has a value exactly twice that of the first digit.
Rule 4: The value of the third digit is less than the value of the fifth digit.
Now let's evaluate each of the answer choices:
(A) 0, 1:
- The third digit (0) is less than the fourth digit (1).
- This pair could be the third and fourth digits of an acceptable product code.
(B) 0, 3:
- The third digit (0) is less than the fourth digit (3).
- This pair could be the third and fourth digits of an acceptable product code.
(C) 1, 0:
- The third digit (1) is greater than the fourth digit (0).
- This pair could NOT be the third and fourth digits of an acceptable product code.
(D) 3, 0:
- The third digit (3) is greater than the fourth digit (0).
- This pair could NOT be the third and fourth digits of an acceptable product code.
(E) 3, 4:
- The third digit (3) is less than the fourth digit (4).
- This pair could be the third and fourth digits of an acceptable product code.
Based on the analysis, the pair that could NOT be the third and fourth digits of an acceptable product code is (C) 1, 0. So the correct answer is option C.