Quantitative Aptitude - Arithmetic Ability Questions

For solving this problem first we would break the whole range in 5 sections

1) From 1 to 9
Total number of zero in this range = 0

2) From 10 to 99
Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer)

3) From 100 to 999 - three type of numbers are there in this range
a) x00 b) x0x c) xx0 (here x represents a non zero number)
Total possibilities
for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18
for x0x = 9*1*9 = 81, hence total zeros = 81
similarly for xx0 = 81
total zeros in three digit numbers = 18 + 81 +81 = 180

4) From 1000 to 9999 - seven type of numbers are there in this range
a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx
Total possibilities
for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27
for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162
for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162
for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162
for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729
for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729
for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729
total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700
thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)
= 2893

We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 x 30 x 8)/ 150 = (35 x D2 x 6) / 200
D2 = (60 x 30 x 8 x 200) / (150 x 35 x 6) => D2 = 91.42 days =~ 91.5 days.

16200 = 23×34×52

A perfect cube has a property of having the indices of all its prime factors divisible by 3.

Required number = 32×5 = 9x5 = 45.

Given the ratio of the circumference of front wheel  is 40 inches and back wheel is 70 inches. 

Distance covered = Circumference of the wheel × No. of Revolutions made by the wheel

If n is the number of revolutions made by back wheel, the number of revolutions made by front wheel is n+15

Distance covered by both the wheels is the same

i.e, 40*(n+15)=70n

 n=20 

                Front wheel      :      Back Wheel 

 Circumference       40      :      70 

 Revolutions           35      :      20

Distance covered  :  40×35 = 70×20 = 1400 inches.

Since level of water increased in cylinder by height 4. 

This is because of the rectangular block .

Therefore , area of rectangular block immersed in water is 

= 227×6×6×4  

Thats why portion of block immersed in water is 

= (22/7 * 36 * 4) / total vol. of rectangle 

= (22/7 * 36 * 4)/ (7*5*6) 

= (22/7 * 24)/ 35.

A = P(1 + rt/100)

So, A= 3P (it becomes triples)

3P = P(1 + 8r/100)→r = 25%

Now, when t = 20

⇒A = P(1 + 25*20/100)

⇒A = P(1+ 5)⇒A = 6P

So, it becomes 6 times.

NOTE: For an century year,it is divided by 400,when leaves a remainder 0 then it is a leap year.

So, 1600