Question

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?
(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

1. Given that the average height of the students in class X is 120 cm, but given no information about the average height of the students in class Y, the desired ratio cannot be determined; NOT sufficient.
2. Given that the average height of the students in class X and class Y combined is 126 cm, the ratio of the averages of the individual classes cannot be determined. For example, if class X consists of 10 students, each of whom has height 120 cm, and class Y consists of 10 students, each of whom has height 132 cm, then the average height of the students in class X and class Y combined iscm and the ratio of the averages of the individual classes is . However, if class X consists of 10 students, each of whom has height 120 cm and class Y consists of 20 students, each of whom has height 129 cm, then the average height of the students in class X and class Y combined is cm and the ratio of the averages of the individual classes is ; NOT sufficient.

• Taking (1) and (2) together is of no more help than either (1) or (2) taken separately because the same examples used to show that (2) is not sufficient include the information from (1).
• The correct answer is E; both statements together are still not sufficient.