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.Statements (1) and (2) together are not sufficient.

Answer 1

Hint: In this type of problem, we have to analyze the two statements which are given, in the first statement desired ratio cannot be obtained so, not sufficient because information is not provided for Average height of Class Y. In the second statement if we consider two different sets of class X and Y which give the average height of X and Y are the same but its ratio changes hence, its Data is not sufficient. So, the correct option is E.

Complete step-by-step answer:
The needed ratio cannot be computed if the average height of the students in class X is 120 cm, but there is no information regarding the average height of the students in class Y; NOT adequate.
Given that the combined average height of students in classes X and Y is 126 cm, the ratio of the individual class averages cannot be computed. For example, if class X has ten students, each of whom is 120 cm tall, and class Y has ten students, each of whom is 132 cm tall, then the average height of the student in class X and class Y combined is \[\dfrac{10(120)+10(132)}{20}=126\,cm\] and the ratio of the individual class is \[\dfrac{120}{132}\] .
If, on the other hand, class X has ten students, each of whom is 120 cm tall, and class Y has twenty students, each of whom is 129 cm tall, then the average height of the students in class X and class Y combined is \[\dfrac{10(120)+20(129)}{30}\,=126\,cm\] and the ratio of the averages of the individual classes is \[\dfrac{120}{129}\] ; not sufficient.
Hence, the both statements (1) and (2) are not sufficient.
So, the correct option is “option D”.
So, the correct answer is “Option D”.

Note: Keep in mind that both statements (1) and (2) provide information; therefore, combining (1) and (2) is no more helpful than either (1) or (2) taken independently, because the identical examples are used to demonstrate that statement (2) is insufficient by including the information from statement (1). One more thing you have to note is that the ratio will be the same then we can say that statement is true. As we can see in the second part of the question even after taking different sets of values of class X and Y average height of combined is same but ratio is different hence, it is not sufficient. So, this we have to remember while solving such types of problems.