Explanation needed for a few questions please.

[ravjitg]

Question 1:

During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiemnt?

(1) For each tank, 30% of the volume of the water that was in the tank at the beginning of the experiment was removed during the experiment.

(2) The average (arithmetic mean) volume of the water in the tanks at the end of the experiment was 63 gallons.

Answer? - I think the answer for this questions is (A) because if 30% of the volume of the water was removed from each tank then the std. deviation would also change by 30%? Correct? Please advise?

Question 2:

In the xy-plane, at what two points does the graph of y=(x+a)(x+b) intersect the x-axis?

(1) a+b = -1
(2) The graph intersects the y-axis at (0,-6).

I couldn't figure this one out. Any thoughts?

Question 3:

At least 100 students at a certain high school study Japanese? If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?

(1) 16 students at the school study both French and Japanese.
(2) 10% of the students at the school who study Japanese also study French.

Answer - Please help. Any thoughts?

[kvcpk]

Question 1:

In the xy-plane, at what two points does the graph of y=(x+a)(x+b) intersect the x-axis?

(1) a+b = -1
(2) The graph intersects the y-axis at (0,-6).

y=(x+a)(x+b)
A line intersects x-axis when y=0
So (x+a)(x+b)=0
Hence the line intersects x-axis at either x=-a and x=-b

a+b = -1
We do not know the values of a and b, they can be anything.
INSUFF

The graph intersects the y-axis at (0,-6).
on y-axis, x=0
therefore, y=ab
hence ab=-6
Again, we do not know each of a or b. hence INSUFF

Combining:
a+b=-1
ab=-6
We will get a and b values.
hence SUFFICIENT.

pick C

Hope this helps!!

[kvcpk]

Question 3:

At least 100 students at a certain high school study Japanese? If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?

(1) 16 students at the school study both French and Japanese.
(2) 10% of the students at the school who study Japanese also study French.

Answer - Please help. Any thoughts?

J>100
Let the number of students who study french be F.
.04F study both F and J
Question is F>J??

16 students at the school study both French and Japanese.
0.04F = 16
F=400

But we will not get if F>J or J>f
INSUFF

10% of the students at the school who study Japanese also study French.
0.1J=0.04F
J=0.4F
Hence J<F

SUFFICIENT.

pick B

I didnt make use of j>100. I am still thinking why its given...