official practice test questions

[sonikamadala]

What is the greatest possible area of a triangle region with one vertex at the center of a circle with radius one and the other two vertices on the circle?
A)(3^0.5)/4
B) 0.5
C)pie/4
D)1
E)(2^0.5)
OA B

[/quote]

Becoz greatest possible area of a triangle region with one vertex at the center of a circle and the other two vertices on the circle happens, only when the angle b/w the legs of the triangle is 90 w.r.t center of the triangle.

So the area of triangle T = (1/2)*base *height
T= 1/2

So C wins

[sonikamadala]

A certain car averages 25 miles per gallon when driven in the city, and 40 miles per gallon when driven on the highway. According to these rates, which of the following is the closest to the number of miles per gallon that the car averages when driven 10 miles in the city and 50 miles on the highway?
A)28 B)30 C)33 D)36 E)38
OA D[/quote]


No.of gallons required to drive 10 miles in city = 10/25 = 2/5 gallons
No.of gallons required to drive 50 miles on highway = 50/40 = 5/4 g
Avg. number of miles per gallon = 10+50/ (2/5 + 5/4)
=60*20/33 = 1.8*20 = approx 36
So D wins

[ss1]

i don't understand the last line for question 2. why did you divide 60 by (2/5+5/4)?

i rechecked the answer for the first one, its definitely B.
i realized from your hint (that greatest triangle is when angel is 90) that the area of such a triangle would be 1/2 x base x height
where base is 1 (the radius), and height is also 1(the other radius), so 1/2 x bx h= 1/2
the error you have made by assuming that the area of triangle is 1/4 the area of the circle includes that circular region as well, and is the area of the sector (with an angle 90) rather than the area of the triangle. that would be smaller than the area of the sector.

[sonikamadala]

i rechecked the answer for the first one, its definitely B.
i realized from your hint (that greatest triangle is when angel is 90) that the area of such a triangle would be 1/2 x base x height
where base is 1 (the radius), and height is also 1(the other radius), so 1/2 x bx h= 1/2
the error you have made by assuming that the area of triangle is 1/4 the area of the circle includes that circular region as well, and is the area of the sector (with an angle 90) rather than the area of the triangle. that would be smaller than the area of the sector.[/quote]

Yes. u r right. Sorry, I mis read the question. I have modified my post.
Thank u buddy.

[sonikamadala]

[quote=ss1;842814]i don't understand the last line for question 2. why did you divide 60 by (2/5+5/4)?


Becoz, question was asking us to find the avg number of mile per gallon.

number of miles n = 60
gallons used g = 2/5+5/4
the avg number of mile per gallon A = n/g

On avg the milage is 36