Roberta was born in 1967, and so in 1976 she was nine years old.

Roberta was born in 1967, and so in 1976 she was nine years old. It is clear from this example that the last two digits of a person’s birth year will be the same as the last two digits of the year of that person’s ninth birthday, except that the position of the digits will be reversed.

It fails to consider birth years like 2000 --> 2009, 1976 --> 1985, 1944 --> 1953, etc.

A. The generalization is valid only for those birth years that do not end in two zeroes. Not True

B. The example does not exhibit the same principle as is expressed in the generalization based on it. Not True, the example does echibit the principle discussed

C. The generalization is valid only for those birth years in which the last digit is one greater than the second-to-last digit. This is the case. Those are the only cases, where the above generalisation works

D. The example cannot be shown to be correct unless the truth of the generalization is already presupposed. Doesn't make sense

E. The generalization is valid only for those birth years in which the last digit is greater than five. Doesn't work for 1976, not true

OFFICIAL EXPLANATION

The generalization is only true for some birth years. A good criticism of the generalization would show when the generalization is not true. C does just that and thus is the correct answer.

A is incorrect. It is false that the generalization holds for all years that do not end in two zeros. For example, 1970 is a birth year that does not end in two zeros. However, 1970 plus nine equals 1979, and hence this is a case for which the generalization is not valid. Since this answer choice is false, it cannot be a good criticism of the assertions.

The second answer choice is also incorrect. In the example, the last two digits of the person’s birth year-67-are the same as the last two digits of the year of the person’s ninth birthday-76-except reversed. Thus, the example does in fact exhibit the same principle as the generalization.

The fourth answer choice is incorrect. The difference between 1976 and 1967 is nine. The correctness of the first statement depends only on this fact and the fact that Roberta was born in 1967 and was still alive in 1976. Thus, the truth of the generalization is not presupposed.

The last answer choice is also incorrect. Consider birth year 1923. a person born in 1923 would have been nine in 1932 and the generalization holds. So E is false.