a PS from Gmat

[diebeatsthegmat]

A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

(A) 36 grams
(B) 40 grams
(C) 42 grams
(D) 48 grams
(E) 50 grams

[rijul007]

Vol of first coin = (pi)(15/2)^2 * 2 = [(pi)(15)^2]/2 = v/2

vol of Aluminium = vol of Silver = v/4
2* wt of Aluminium (a) = wt of silver(s) = 2s
s = 2a

2a + a = 30
a for v/4 = 10gm


vol of sec coin = (pi)(30/2)^2 * 1 = v
a for v/4 ==> 10gm
a for v ==> 40 gm

Option B

[neelgandham]

Volume of the cylinder = pi*r*r*h (where r = radius of the cylinder and h = height of the cylinder)

Volume of cylinder UNO = pi *15*0.5*15*0.5*2
Volume of Silver in cylinder UNO = pi *15*0.5*15*0.5
Volume of Aluminium in cylinder UNO = pi *15*0.5*15*0.5

Let Ds, Da be the densities of Silver and Aluminium respectively and Ds = 2*Da(silver is twice heavier than aluminium), So

Weight of Silver in cylinder UNO = pi *15*0.5*15*0.5*Ds = pi *15*0.5*15*0.5*2*Da (Weight = Volume * Density)
Weight of Aluminium in cylinder UNO = pi *15*0.5*15*0.5*Da
Total Weight of of the cylinder UNO = pi *15*0.5*15*0.5*Da + pi *15*0.5*15*0.5*2*Da = 30

pi *15*0.5*15*0.5*3*Da = 30

Volume of cylinder DOS = pi *15*15*1
Volume of Silver in cylinder DOS = 0
Volume of Aluminium in cylinder DOS = pi *15*15*1


Weight of Silver in cylinder DOS = 0
Weight of Aluminium in cylinder DOS = pi *15*15*Da
Total Weight of of the cylinder DOS = pi *15*15*Da = ?

pi *15*0.5*15*0.5*3*Da = 30
pi *15*15*Da = 30/(0.5*0.5*3) = 40

IMO Answer B

[anu009]

i didnt quite get why did you divide v/2 and then later V/4, volume of alloy