Mrs. orlof teaches two history classes, one in the morning and one in the afternoon. yesterday she gave the same test to both classes. anyone who failed the test must take a retest. since a greater percentage of students who took the morning test failed the test than students who took the afternoon test, more of orlof's morning history students than afternoon history students will have to take the retest. the conclusion above is not necessarily valid because

The conclusion assumes that a greater number of students failed the morning test compared to the evening test. A greater percentage of the morning class could easily mean a smaller number of total students in that class. For example, suppose the morning class has 10 students while the evening class has 20 students. So if one student failed in each class, 10% of the morning class students (1/10 * 100%) and 5% of the evening class students (1/20 * 100%) would have failed. Percentages merely indicate a proportion of the whole, not the absolute number.