Aptitude and Reasoning Questions

Absolute value of a number :

It means that the distance of a number from 0 on a number line. 

Here absolute value of 9 is that on a number line 9 is 9 units away from 0. Hence its absolute value is 9. Similarly, absolute value of -9 means -9 is also 9 units away from the 0 on number line. Hence, absolute value of -9 is also 9.

Hence, the absolute value of 9 is 9.

Given equation  5x-17 = -x+7

Add 1x to each side of the equation

5x-17+x = -x+7+x

6x=24

x=4

We know that zero can't be in hundreds place. But let's assume that our number could start with zero.

The formula to find sum of all numbers in a permutation is

111 x no of ways numbers can be formed for a number at given position x sum of all given digits

No of 1 s depends on number of digits

So,the answer us

111 x 20 x (0+1+2+3+4+5) = 33300

We got 20 as follows. If we have 0 in units place we can form a number in 4*5 ways. This is for all numbers. So we have substituted 20 in formula.

Now, this is not the final answer because we have included 0 in hundreds place. so we have to remove the sum of all numbers that starts with 0.

This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5. Because 0 at first place makes it a 2 digit number.

So the sum for this is 11 x 4 x (1+2+3+4+5).
=660

Hope u understood why we use 4. Each number can be formed in 4x1 ways

So, the final answer is 33300-660 = 32640

A:B = 200 : 169
A:C = 200 : 182
 CB = CA×AB 

182200×200169

=> 182:169

When C covers 182 m , B Covers 169 m
When C covers 350 m , B Covers 169182×350
=> 325 m

So C beats B by (350 - 325) = 25 m.

Clearly, People cannot be deprived of enjoying the festival for lack of arrangements. Also, it becomes necessary to deploy police to regulate big crowds and avert any mishap in public gatherings. Further, it costs nothing but might prove useful to put hospitals on alert to be ready to provide quick medical aid to patients in case of any eventuality. So, both b and c follow.