Discussion Room : Quant

• @vinaycat2017

120 rupees is the original price
25 rupees down payment means 95 rupees is what we are "Borrowing" from the shop.
Amount paid in instalments = 25 * 4 = 100
So 100 - 95 = 5 is the interest
Now this interest gained (Rs 5) is through the interest gained in the available amount month by month.
5 = 95R/(12 * 100) + 70R/(12 * 100) + 45R/(12 * 100) + 20R/(12 * 100)
5 = 230R/(12 * 100)
R = 6000/230 = 26.09%

• Working together B and C take 50% more number of days than A, B and C together take and A and B working together, take 8/3 more number of days than A, B and C take together. If A, B and C all have worked together till the completion of the work and B has received Rs. 120 out of total earnings of Rs, 450, then in how many days did A, B and C together complete the whole work?

• @vinaycat2017 Answer is 30 square units

• In how many ways can distinct words of 5 letters each be made using the English alphabet?

• @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?

• @zabeer • 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

• • SOLVE
(X^4+X^2+1)/(X^2-4X-5) < 0

SOLVE
(X^2+6X-7)/(X^2 + 1)

• N = 2³ * 5³ * 7², how many sets of two factors of N are co-prime

• @vinaycat2017 45:72:80
197--78800
72-28800

• 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.

• two

• 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=?

• 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 + 71/211s

Now 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 = 0

4 equations in 4 unknowns. Solve.

• Find sum of
√{5+√[11+√【19+√(29..........To infinity

7

8

3

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