bhavin422 Says1 only...2 and 3 may not be true...
care to explain a bit..
Neo
care to explain a bit..
Neo
care to explain a bit..
Neo
let us assume 5 house each with price 150 k
150,150,150,150,150
if median is 130k atleast one of the entry in this case would be 170k
hence 1 is always correct 2 and third may be wrong
snip sorry
a) How to solve ( sqrt(9 + sqrt(80)) + sqrt(9 - sqrt(80)) ) ^2?
b) What is the maximum possible area for a triangle one of whose vertices is in the center of the circle with radius 1 and the other two vertices lie on the circle?
Last month 15 homes were sold in town x. The avg sale price of homes was 150,000 Rs and the median sale price was 130,000 rs . Which of following are true?
1.Atleast one of the homes was sold for more than 165,000 rs
2.Atleast one of the homes was sold for more than 130,000 and less than 150,000
3. Atleast one of the homes was sold for less than 130,000
a. 1 only
b. 2 only
c. 3 only
d. 1 and 2
e. 1 and 3
Neo
care to explain a bit..
Neo
here is my approach..
median is 130000 implies 7 values are lesser than or equal to 130000 and 7 values are greater than or equal to 130000
and also avg of 15 is 150000..
consider st 1 : if all 8 homes equal 130000, prices of remaining 7 homes have to be such that it needs to compensate the difference of (150000 - 130000) * 8 to maintain an average of 150000...in simple terms middle value is 130000, for every value below 130000 there needs to be a value of 170000 plus to keep the average..hence there has to be atleast 1 value above 165000..
consider st 2: this may not be necessary..
consider 1 of the possibilities...
let all the lower 8 values be 130000, and let all the upper values be equal..
by using similar logic as above, we can safely say each equal value is 170000 plus..
if we want to know exact value...it goes this way (2250000-1040000)/7
consider st 3:
not necessary again...all the lower 7 values can be equal to 130000 and still the median can be 130000...so not necessary to have a value less than 130000..
hope this helps...
a) How to solve ( sqrt(9 + sqrt(80)) + sqrt(9 - sqrt(80)) ) ^2?
b) What is the maximum possible area for a triangle one of whose vertices is in the center of the circle with radius 1 and the other two vertices lie on the circle?
For a) take eqn as (a + b) ^ 2 where a = sqrt(9 + sqrt (80)) and b = sqrt (9 - sqrt(80))
so (a + b) ^ 2 => a^2 + 2*a*b + b^2 => 9 + sqrt(80) + 2(sqrt( 9*9 - sqrt(80)*sqrt*(80)) + 9 - sqrt(80)
This reduces the above line to 9 + 2 + 9 = 20
So answer is 20 for this one
For Q b)
in a given circle a triangle area can be decsribes as (r^2 * sin( Angle between the radius)/2 .. max value of sin of any angle is 1 so ..this means max value of any triangle here would be r^2/2 ===> 1*1/2 = 0.5 is the ans
For a) take eqn as (a + b) ^ 2 where a = sqrt(9 + sqrt (80)) and b = sqrt (9 - sqrt(80))
so (a + b) ^ 2 => a^2 + 2*a*b + b^2 => 9 + sqrt(80) + 2(sqrt( 9*9 - sqrt(80)*sqrt*(80)) + 9 - sqrt(80)
This reduces the above line to 9 + 2 + 9 = 20
So answer is 20 for this one
For Q b)
in a given circle a triangle area can be decsribes as (r^2 * sin( Angle between the radius)/2 .. max value of sin of any angle is 1 so ..this means max value of any triangle here would be r^2/2 ===> 1*1/2 = 0.5 is the ans
yup...even am getting ans as 20 and 0.5...have solved it in similar way..
bhavin422 Saysyup...even am getting ans as 20 and 0.5...have solved it in similar way..
hi Rohan and Bhavin,
Thank you for your response.For question 1,although I knew that I had to use (a+b)^2 formula,
I didnot know how to compute the product of the form, sqrt(a+ sqrt(b)) x sqrt(a - sqrt(b))
I'm still unclear how 2ab part became 2(sqrt( 9*9 - sqrt(80)*sqrt*(80)) .
Thanks,
Raj
hi Rohan and Bhavin,
Thank you for your response.For question 1,although I knew that I had to use (a+b)^2 formula,
I didnot know how to compute the product of the form, sqrt(a+ sqrt(b)) x sqrt(a - sqrt(b))
I'm still unclear how 2ab part became 2(sqrt( 9*9 - sqrt(80)*sqrt*(80)) .
Thanks,
Raj
Here is the reason to that .. sqrt(a * b) = sqrt(a)*sqrt(b)..when things appear in products they are distributive in nature..
hi Rohan and Bhavin,
Thank you for your response.For question 1,although I knew that I had to use (a+b)^2 formula,
I didnot know how to compute the product of the form, sqrt(a+ sqrt(b)) x sqrt(a - sqrt(b))
I'm still unclear how 2ab part became 2(sqrt( 9*9 - sqrt(80)*sqrt*(80)) .
Thanks,
Raj
Also can u tell me where I can find formulas like r^2. sin(angle)/2?
Is there a list of such formalae that I can use?
Thanks,
Raj
Also can u tell me where I can find formulas like r^2. sin(angle)/2?
Is there a list of such formalae that I can use?
Thanks,
Raj
Well such formulaes are all there in 12th or 10th std math..am not sure of the exact book names though... but in trigonometry such formulae are kinda mentioned as basic ones .
hi Rohan and Bhavin,
Thank you for your response.For question 1,although I knew that I had to use (a+b)^2 formula,
I didnot know how to compute the product of the form, sqrt(a+ sqrt(b)) x sqrt(a - sqrt(b))
I'm still unclear how 2ab part became 2(sqrt( 9*9 - sqrt(80)*sqrt*(80)) .
Thanks,
Raj
hi Raj,
(a+b)(a-b) = a^2-b^2...2roota*rootb= 2 root (ab)..
let the root sign remain...and perform a^2-b^2 within the square root sign and simplify...in this case it simplifies to root 1 i.e 1..
hope this clears your doubt..
Also can u tell me where I can find formulas like r^2. sin(angle)/2?
Is there a list of such formalae that I can use?
Thanks,
Raj
hi raj...let me explain how we derive this formula..
Now , area of triangle is 1/2*product of any 2 sides * sine of included angle..
Hence, u have 1/2*base * height since included angle between base and height is 90 and sin 90 is 1..
Now, in the above sum, 1 of the vertices is the centre of circle and other 2 vertices lie on the circumference, implies 2 of the sides of the triangle is radius of circle..
Hence, area of circle becomes 1/2*radius*radius *sine of angle between radii..
i.e A= 1/2*r^2*sine(angle between radii)...
Hence, area of triangle resembles sinusoidal relation with angle between radii..i.e area increases between angle 0 to 90 and again reduces from 90 to 0 and is max when angle is 90...
max A is when angle is 90...
hope this helps...no need to remember formulae as such..
a) How to solve ( sqrt(9 + sqrt(80)) + sqrt(9 - sqrt(80)) ) ^2?
b) What is the maximum possible area for a triangle one of whose vertices is in the center of the circle with radius 1 and the other two vertices lie on the circle?
Prob 1) A shortcut
We need to find the square root of the surds.
There's a method we learn in our high school here.
say you want to find sq.rt( 9 + sq.rt(80) ) where sq.rt is the square root
Follow the below steps to arrive at answer
a. we should always try to extract 2 out of the inner sq. rt . i.e sq.rt(80) = sq.rt(4*20) = 2 * sq.rt(20)
b. Now you should check if the number left in the inside sq.rt after extraction of 2...i.e 20 here has two factors whose sum is equal to the remaining number in the outer square root. i.e 9 here. Usually this is done by trivial observation
what i mean is 20 = 4* 5 and 4+ 5 = 9 (the isolated number in sq.rt)
c. after that observation you can simply write the result as sq.rt(5) + sq.rt(4) = sq.rt(5) + 2
sq.rt( 9 + sq.rt(80) ) = sq.rt(5) + 2
similarly sq.rt( 9 - sq.rt(80) ) = sq.rt(5) - 2 (simply inserting - sign between a large and small number)
Hence given problem reduces to (2 sq.rt(5) ) ^2 = 4*5 = 20
20 is the answer.
Believe me, By a little practice you can solve such qns by simple observations !! No pen or pencil on paper.. I could just write the square root by seeing the surd. You can too :)
Prob 2
I think others have already explained. 1/2 will be the answer
Neo
Prob 1) A shortcut
We need to find the square root of the surds.
There's a method we learn in our high school here.
say you want to find sq.rt( 9 + sq.rt(80) ) where sq.rt is the square root
Follow the below steps to arrive at answer
a. we should always try to extract 2 out of the inner sq. rt . i.e sq.rt(80) = sq.rt(4*20) = 2 * sq.rt(20)
b. Now you should check if the number left in the inside sq.rt after extraction of 2...i.e 20 here has two factors whose sum is equal to the remaining number in the outer square root. i.e 9 here. Usually this is done by trivial observation
what i mean is 20 = 4* 5 and 4+ 5 = 9 (the isolated number in sq.rt)
c. after that observation you can simply write the result as sq.rt(5) + sq.rt(4) = sq.rt(5) + 2
sq.rt( 9 + sq.rt(80) ) = sq.rt(5) + 2
similarly sq.rt( 9 - sq.rt(80) ) = sq.rt(5) - 2 (simply inserting - sign between a large and small number)
Hence given problem reduces to (2 sq.rt(5) ) ^2 = 4*5 = 20
20 is the answer.
Believe me, By a little practice you can solve such qns by simple observations !! No pen or pencil on paper.. I could just write the square root by seeing the surd. You can too :)
Prob 2
I think others have already explained. 1/2 will be the answer
Neo
Thanks Bhavin .I think I get it now. This problem isn't really a tough one. The ugly square roots deceived me :-)
Neo,
That was a magical short cut.I'm surprised that there could be such amazing shortcuts.But I guess it'll be little late to appy these for my GMAt that is 20 days away.But thank you anyways.
One question from GMAT Prep test. I am not able to solve it, Can any one help me in find ing the answer?
If XY=1 then what would be the value of 2 (x+y)^2 / 2 (x-y)^2
Ans:
A 2
B 4
C 8
D 16
E 32
The answer it showing as D (16) . I didn't understand the answer!
With the given information (i.e., XY=1) how can we solve the given equation?.
Regards,
Mahesh
One question from GMAT Prep test. I am not able to solve it, Can any one help me in find ing the answer?
If XY=1 then what would be the value of 2 (x+y)^2 / 2 (x-y)^2
Ans:
A 2
B 4
C 8
D 16
E 32
The answer it showing as D (16) . I didn't understand the answer!
With the given information (i.e., XY=1) how can we solve the given equation?.
Regards,
Mahesh
whether X or Y could be integer , even this info is not given?
One question from GMAT Prep test. I am not able to solve it, Can any one help me in find ing the answer?
If XY=1 then what would be the value of 2 (x+y)^2 / 2 (x-y)^2
Ans:
A 2
B 4
C 8
D 16
E 32
The answer it showing as D (16) . I didn't understand the answer!
With the given information (i.e., XY=1) how can we solve the given equation?.
Regards,
Mahesh
dear mahesh,
if question is exactly as mentioned then it is wrong. and x,y cannot be both integers because then only possible soln. is x=y=1 which is not possible here. but there some ques in which x/y is given and if u substitute say t=x/y entire eqn. comes in form of t only . although in gmat u need not worry about substitution just plug in 2 sets of values of x and y and check for answer,
One question from GMAT Prep test. I am not able to solve it, Can any one help me in find ing the answer?
If XY=1 then what would be the value of 2 (x+y)^2 / 2 (x-y)^2
Ans:
A 2
B 4
C 8
D 16
E 32
The answer it showing as D (16) . I didn't understand the answer!
With the given information (i.e., XY=1) how can we solve the given equation?.
Regards,
Mahesh
Mahesh the question in indeed wrong in GMATPrep.
it should be read as 2^(x+y)^2 / 2^(x-y)^2
Regards,
HG
Hey guys ,
Can someone help with the following problems:
1) The residents of town x participated in a survey to determine no.of. hrs per week each resident spent watchin tv. The distribution of results of survey had a mean of 21 hrs and a std deviation of 6 hrs. the no. of hrs that Pat a resident of town x watch tv last week was between 1 & 2 std deviation bvelow mean. Which of the foll could be a no. of hrs that Pat saw TV last week.
30 20 18 12 6
2) In the xy plane, line k has positive slope and x intercept is 4. If the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k?
1) -6
2) -4
3) -3
4) 3
5) 6
3) Which of the following is equal to (2^12 2^6) / (2^6 2^3)?
A. 2^6 + 2^3
B. 2^6 2^3
C. 2^9
D. 2^3
E. 2
Also, need to know if there is a specific way to solve the problems on graphs i.e findind the x or y intercept of a line equation.
Thanx!
Can someone help with the following problems:
1) The residents of town x participated in a survey to determine no.of. hrs per week each resident spent watchin tv. The distribution of results of survey had a mean of 21 hrs and a std deviation of 6 hrs. the no. of hrs that Pat a resident of town x watch tv last week was between 1 & 2 std deviation bvelow mean. Which of the foll could be a no. of hrs that Pat saw TV last week.
30 20 18 12 6
2) In the xy plane, line k has positive slope and x intercept is 4. If the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k?
1) -6
2) -4
3) -3
4) 3
5) 6
3) Which of the following is equal to (2^12 2^6) / (2^6 2^3)?
A. 2^6 + 2^3
B. 2^6 2^3
C. 2^9
D. 2^3
E. 2
Also, need to know if there is a specific way to solve the problems on graphs i.e findind the x or y intercept of a line equation.
Thanx!