CAT 2019 – Slot 1 – Quantitative Ability – A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper

Q. 1: A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is 1.8464π 2.928π 3.1026(1 + π) 4.1044(4 + π)

As cylinders have the same volume and each of these has radius 3 cm. So volume of each cylinder will be equal to HCF of (405, 783 and 351) which is 27.

So volume of each cylinder = 27

No of cylinders = [ 405/27 ] + [783/27] + [351/27] = 15 + 29 + 13 =57

Using V = πr^2 h

27 = 22/7 *9 *h

So h = 3/ π cm

total surface area of all these cylinders = 57*(Surface area of one cylinder ) = 57*2* πr(h+r)=57*2π*3 (3/π+3)=1026(1+π)

Q. 2: Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is 1. 10 2. 8√2 3. 6√2 4. 5

Maximum possible value of AP occurs when a = b, so a= b=10 root 2

On solving, we get AP = 10 units

Q. 3: The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is 1.8√3 2.10√2 3.12 4.5√5

As we know that the square pyramid of edge length a has height

h=1/2 sqrt(2)* a,

So, h = ½ * root 2* 20 = 10 root 2

Q. 4: Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals