Data Sufficiency

Q2:
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.

Fab wrote:Q2:
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.

E.
1) you don't have the average height of Y, so (1) is insufficient
2) you don't know X or Y, insufficient

Together) it gives you the average of both, but you still don't have the exact number of students per class. (2) is not average of "avg x" and "avg y". So depending on the size of the classroom, the average will vary.

So I would say E. What's the correct answer?

the OA is E

Here is a good takeaway. I read it from one of Ian's posts. Just want to share with others.

For these kinds of problems, if you have any three of the four points below, it is sufficient to answer.

Say you have 2 groups (X and Y).
1. Avg of X
2. Avg of Y
3. Combined Avg of X and Y
4. Ratio of X and Y


Applying this takeaway to this prob,
Qn: Ratio of X and Y?

(1) You have Avg (X) [Point #1]. Still need other 2 points (Avg of Y and Combined Avg of X and Y)
(2) You have Combined Average [Point #3]. Still need other 2 points (Avg of X and Avg of Y)

Combined,
You are still missing a key info --> point #2 (Avg of Y). Hence insufficient.


If you remember this takeaway, you could solve this prob in 10-15 seconds. A very handy takeaway. Special thanks to Ian!!

hhmmm but if you know the average of x=120 is it not true that (120 + y)/2 = 126? therefore giving you Y which is the missing point we need to know if we can find the ratio? i chose D... but apparently it's wrong. Can someone explain why i'm wrong?

money9111 wrote:hhmmm but if you know the average of x=120 is it not true that (120 + y)/2 = 126? therefore giving you Y which is the missing point we need to know if we can find the ratio? i chose D... but apparently it's wrong. Can someone explain why i'm wrong?

I thought it was "C". But then realized, shouldn't both averages be divided by the number of students in x + y to get an average of 126? Please correct me if I am wrong. Thanks.

mah927 wrote:

money9111 wrote:hhmmm but if you know the average of x=120 is it not true that (120 + y)/2 = 126? therefore giving you Y which is the missing point we need to know if we can find the ratio? i chose D... but apparently it's wrong. Can someone explain why i'm wrong?

I thought it was "C". But then realized, shouldn't both averages be divided by the number of students in x + y to get an average of 126? Please correct me if I am wrong. Thanks.

Ok.Let me clarify this doubt of yours.
THe question says:-
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.

Now,we don't know if the no. of students in both the classes are same or not.
Had they been same,we could have added their averages but since that data is not given it would be incorrect to apply the formula:-(120 + y)/2 = 126

Let me give you an example:-
suppose in class A heights are 120,140,150=average = 136.67
in class B heights are 180,190 =average =185
total average of A and B = 156
but avg. of 136.67 and 185 = 160.835
I hope you get my point.