Latest Elitmus Aptitude Question SOLUTION: data sufficiency :two spheres are melted to form a combined sphere x. Find the diameter of x. St 1)the radius of 2nd sphere was given St2) the weight of sphere 1 is 8 kg and spher

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Data Sufficiency

Elitmus Question Papers:

(#M40157784) ELITMUS Numerical Ability question Keep an EYE

data sufficiency :two spheres are melted to form a combined sphere x. Find the diameter of x.
St 1)the radius of 2nd sphere was given
St2) the weight of sphere 1 is 8 kg and sphere 2 is 10 kg and they are made of same material

Asked In Elitmus Sniper (7 years ago)

Unsolved Read Solution (2)

Is this Puzzle helpful?   (1)   (2) Submit Your Solution Data Sufficiency

Read Solution (2) :

abdullah imran  (7 years ago)

General Info:
4*pi*r1 ^3 /3 + 4*pi*r2 ^3 /3 =4*pi*rc ^3 /3.................................(1)

s1) 4 pi (r2) ^3 /3 =m/d (density = mass/volume) ........(2)
here we need value of m and d to get the value of r2 ..But these values are not available so not possible to find r2.. Thus we can not find x as at least two variable values are required to solve equation of three variable ...(1) alone not possible

s2)m1/d + m2/d = mc/d ----> 8/d + 10/d = mc/d -------> mc=18 ........(3)

also for combined sphere:
4*pi*rc ^3 /3 = mc/d...... here we need value of d to find rc so alone not possible

Now s1 + s2:
for 2nd sphere ----> 4*pi*r2^3 /3 = m/d ----> 4*pi*r2^3 /3 = 10/d.....(4) now r2 value is given so find d.

fOR COMBINED SPHERE:
4*pi*rc^3 /3 = m/d------>4*pi*rc^3 /3 = 18/d----> putting the value of d from equation (4) rc value can be calculated.

Is this solution Helpfull? Yes (2) | No (1)  

Ankit  (2 years ago)

As we know the resultant sphere was made by mixing of the two spheres.So the volume of sphere x is sum of the volume of the both sphere.
i.e r1^3+r2^3=x^3 ------------------------------------------(1)
now according to the statement one:
its given the radius of the 2nd sphere but i dont know the value of r1.so from eq 1 i get different value of x as i change the value of r1
so statement 1 is insufficient
i know the weight will be same after mixing both the spheres because both the sphere are of the same material
so the weight of x=18=4/3(pir^3) from here i can find the value of r and also the diameter.thus it gives a unique value for the diameter,
so statement 2 alone is sufficent.

Is this solution Helpfull? Yes (1) | No   

Please Login to Read Solution.