Quantitative Aptitude - Arithmetic Ability Questions

$$\begin{gathered} 68 x ? - 3421 = 591 \\ ? = 4012/68 \\ ? = 59 x 59 \\ ? = 3481 \end{gathered}$$

3 letters can be choosen out of 9 letters in 9C3 ways.

More than one vowels ( 2 vowels + 1 consonant  or  3 vowels ) can be choosen in (4C2*5C1)+4C3 ways

Hence,required probability = 4C2*5C1+4C39C3 = 17/42

You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines.

AB , AC

BA , BC

CA , CB

There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB.

The lines are: AB, BC and AC ; 3 lines only.

So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important.

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. 

Area of each tile = 41×41cm2  

Required number of tiles  = 1517×90241×41= 814

Area = (13.86 x 10000) sq.m = 138600 sq.m

πR2=138600⇒R2=138600×722⇒R=210m 

Circumference = 2πR2=2×227×210=1320m 

Cost of fencing = Rs. (1320 x 4.40) = Rs. 5808.

Water in 60 gm mixture=60 x 75/100 = 45 gm. and Milk = 15 gm.

After adding 15 gm. of water in mixture, total water = 45 + 15 = 60 gm and weight of a mixture = 60 + 15 = 75 gm.

So % of water = 100 x 60/75 = 80%.