CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions

schander2020

Hi implex..would u plz explain in detail about how to find D(x). i am not much clear about the explanation u gave..

Aarav

Quote:

Originally Posted by schander2020

Hi implex..would u plz explain in detail about how to find D(x). i am not much clear about the explanation u gave..

Here is the full solution to the problem.

Solution:
X^16 + x^8 + x^6 + x^4 + x^2 + 1 = d(x).(x^3 - 1) + R(x), where R(x) has degree lesser than that of the quotient. Thus if we put x^3 = 1 in both LHS and RHS we get, x + x^2 + 1 + x + x^2 + 1 = 2(x^2 + x + 1) = R(x)

For D(x), as we know that a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca) x^6 + 4x^3 + 8 has a quadratic factor D(x) as x^2 - 2x + 2 as we can put a = x^2, b = -2x and c = 2. Want to try factorizing x^6 + 5x^3 + 8?

medulla

Hi,

I don't know why no one is replying today. Can you give some hint as to how to factorize?

Quote:

Originally Posted by Aarav

Here is the full solution to the problem.

Solution:
X^16 + x^8 + x^6 + x^4 + x^2 + 1 = d(x).(x^3 - 1) + R(x), where R(x) has degree lesser than that of the quotient. Thus if we put x^3 = 1 in both LHS and RHS we get, x + x^2 + 1 + x + x^2 + 1 = 2(x^2 + x + 1) = R(x)

For D(x), as we know that a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca) x^6 + 4x^3 + 8 has a quadratic factor D(x) as x^2 - 2x + 2 as we can put a = x^2, b = -2x and c = 2. Want to try factorizing x^6 + 5x^3 + 8?

medulla

Hi schinnar,

There is a typo error in the R(x)

medulla

Quote:

Originally Posted by schinnar

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Quantitative Question # 017
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Let R(x) be the remainder when x^16 + x^8 + x^6 + x^4 + x^2 + 1 is divided by x^3 - 1. Let D(x) be the divisor (less than degree 4) of x^6 + 4x^3 + 8. Then which among the following is true?

(1) The sum of the coefficients of R(x) and D(x) is equal

(2) The sum of the absolute value of coefficients of R(x) and D(x) is equal
(3) R(x) > D(x) for all non-positive x

(4) at least 2 of the above

(5) none of the above

Ans:

The remainder when x^16 + x^8 + x^6 + x^4 + x^2 + 1 is divided by X^3-1 is 2x^2+2 +1 ---> 1

R(x)=2x^2+2+1

x^2+2 divides x^6+4X^3+8 which is degree < 4

D(x)=x^2+2

option 1 is not true

option 2 I am bit confused i assume absolute value of coefficient is constant term then this is false

option 3 is clearly false
take the value of -1 R(x) = 1 D(x) = 3
if my assumption is correct then ans is 5

amit_adobe

Thanks PG for starting Quant a day again. I will try to be regular here. I must make a mention that Quant a day helped me immensely to score 99.9+ in quant in CAT, but my Verbal skills didn't impress IIM's. PG - any plans of coming with VA a day?

srikar2097

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Quantitative Question # 018
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Two spherical balls lie on the ground touching. If one of the balls has a radius of 8 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball?
(1) 18 cm (2) 40/3 cm (3) 25/2 cm (4) 13 cm (5) none of the these
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srikar2097

The point of contact of the 2 spheres is 10 cm above the ground. This point has to be the radius of one of the spheres.
It's given tha the radius of one of the spheres is 8cm. So that means that the second sphere has a radius greater than 8. In fact the radius of the second sphere is 10cm.

So the answer is (5) None of these.

rajeev_hts

Quote:

Originally Posted by srikar2097

The point of contact of the 2 spheres is 10 cm above the ground. This point has to be the radius of one of the spheres.
It's given tha the radius of one of the spheres is 8cm. So that means that the second sphere has a radius greater than 8. In fact the radius of the second sphere is 10cm.

So the answer is (5) None of these.

Point of contact doesn't necessarily need to be radius of any of circle.
check it by making to circles of different radii, touching each other.

slam

Quote:

Originally Posted by srikar2097

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Quantitative Question # 018
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Two spherical balls lie on the ground touching. If one of the balls has a radius of 8 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball?
(1) 18 cm (2) 40/3 cm (3) 25/2 cm (4) 13 cm (5) none of the these
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using similar triangles, we get:
( 10-8 )/8 = ( R-8 )/( R+ 8 ), where R is the radius of the larger ball.
(I'll have to draw a figure to explain this better, and will try to come up with it, but as of now i'm just posting this part)

which gives us R = 40/3,=> option(2)

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slam.

pavanpadekal · 07:39 AM

From similar triangles we get r/(r-10)=8/2=4
=>r=40/3
Correct option is (2) 40/3 cm