Discussion Room : Quant

@zabeer
A sphere passes through the midpoints of the twelve edges of a cube that has edges of length 6 inches. What is the surface area of the sphere, in square inches? Express your answer in terms of pi.

What is the remainder when 13^66 – 23 is divided by 183?


Usain is an athlete. While running, the number of calories burnt by him is directly proportional to the square root of his speed. If he runs 10 km at a constant speed of 25 km/hr, the total number of calories burnt is equal to 2400. On a particular day he ran at a constant speed of 36 km/hr and burnt 1800 calories. What was the distance run by him on that day? (Assume that calories burned are directly proportional to the distance travelled)
Can anybody help.

@deepalis727
Given : No. of calories ∝ dist × √ (Speed)
so we can say that No. of calories burnt = K×dist×√ (Speed)
2400=K×10×5, Here k comes out to be "48".
Now, 1800=Dist×48×6
Dist=6.25 Km

Please explain.

SOLVE
(X^4+X^2+1)/(X^24X5) < 0SOLVE
(X^2+6X7)/(X^2 + 1)

N = 2³ * 5³ * 7², how many sets of two factors of N are coprime

@vinaycat2017 45:72:80
19778800
7228800

If F(x) = x^4  360x^2 + 400 (for any integral value of x) and if F(x) is a prime number, then what is the sum of all possible values of F(x)? Cold anyone help [email protected] sir please help.


find the maximum value of n such that
42×57×92×91×52×62×63×64×65×66×67 is perfectly divisible by 42*n

@swanandk12 I think it is infinity. As x increases the value of F(x) will keep on increasing. So possible values of F(x) are infinite. Hence the sum of possible values F(x) is infinity. Thoughts?

If 76/(4+√7+√11)=p+q√7+r√11+s√77 then p+q+r+s=?

@rohitchopra01 said in Discussion Room : Quant:
If 76/(4+√7+√11)=p+q√7+r√11+s√77 then p+q+r+s=?
Multiply both sides by (4 + 71/2 + 111/2)
76 = (4 + 71/2 + 111/2)p + 71/2(4 + 71/2 + 111/2)q + 111/2(4 + 71/2 + 111/2)r + 771/2(4 + 71/2 + 111/2)s
Expand out:
76 = 4p + 71/2p + 111/2p + 71/24q + 7q + 771/2q + 111/24r + 771/2r + 11r + 771/24s + 111/27s + 71/211sNow get everything together:
76 = (4p+7q+11r) + 71/2(p+4q+11s) + 111/2(p+4r+7s) + 771/2(q+r+4s)Rewrite the LHS:
76 + 0 * 71/2 + 0 * 111/2 + 0 * 771/2 = (4p+7q+11r) + 71/2(p+4q+11s) + 111/2(p+4r+7s) + 771/2(q+r+4s)So we have the following system of equations:
4p + 7q + 11r = 76
p + 4q + 11s = 0
p + 4r + 7s = 0
q + r + 4s = 04 equations in 4 unknowns. Solve.