# Arithmetic Aptitude 2

• Last Updated : 01 Sep, 2020

 Question 1
512 x 512 + 488 x 488 = ?
 512438 502568 500288 514318

Question 1-Explanation:
```Let X=500 & Y=12
Now, (X + Y)2 + (X – Y)2 = 2 ( X2 + Y2 )
= 2 ( 5002 + 122 )
= 2 ( 250000 + 144 )
= 2 * 250144
= 500288
```
 Question 2

There is bag of lots of integers from 1 to 10000, but you can only pick the numbers that are of 3-digit and also divisible by 3. What maximum sum of numbers you can pick.

 165150 1600843 168132420 165322501

Question 2-Explanation:
```All 3 digit numbers divisible by 3 are :
102, 105, 108, 111, ..., 999.

This is an A.P. with first element 'a' as
102 and difference  'd' as 3.

Let it contains n terms. Then,
102 + (n - 1) x 3 = 999
102 + 3n-3 = 999
3n = 900 or n = 300
Sum of AP = n/2 [2*a  + (n-1)*d]
Required sum = 300/2[2*102 + 299*3] = 165150. ```
 Question 3
Which of Following is not divisible from 4 ?
 546702 556824 367312 467536

Question 3-Explanation:
If last 2 digits are divisible by 4, then number is also divisible by 4.
```In case of 546702 last 2 digits are 02 (x)
In case of 556824 last 2 digits are 24 (/)
In case of 367312 last 2 digits are 12 (/)
In case of 467536 last 2 digits are 36 (/) ```
 Question 4
What should be the value of * in 985*865, if number is divisible by 9?
 6 5 4 0

Question 4-Explanation:
If a number is divisible by 9, the sum of digits is also divisible by 9
```9 + 8 + 5 + * + 8 + 6 + 5 = 9x
41 + * = 9x
Nearest value of 9x must be 45
41 + * = 45
* = 4```
 Question 5
The least perfect square, which is divisible by each of 15, 20 and 36 is:
 1200 800 1000 900

Question 5-Explanation:
```LCM of 15, 20 and 36 is 180

Now 180 = 3 x 3 x 2 x 2 x 5

To make it perfect square, it must
be multiplied from 5.

So required no. = 32 x 22 x 52 = 900```
 Question 6
What should be the value of x in equation (x / √216) = (√96 / x)
 12 13 9 11

Question 6-Explanation:
```Let (x / √216) = (√96 / x)

Then x2 = √(216 x 96)
= √(36 x 2 x 3 x 16 x 2 x 3)
= √(62 x 42 x 22 x 32)
= 6 x 4 x 2 x 3
= 144
Or x = 12
```
 Question 7

Sum of the age of 4 children born at interval of 4 years is 36. What is the age of youngest child?

 2 years 3 years 4 years 5 years

Question 7-Explanation:
```Let the ages of children be x, (x+4),
(x+8) and (x+12) years.

Then x + x + 4 + x + 8 + x +12 = 36
4x + 24 = 36
4x = 12
x = 3
Age of the youngest child = x = 3 years```
 Question 8
A is 5 years older than B who is thrice as old as C. If the total of ages of A, B and C is 40, then how old is C ?
 6 7 5 8

Question 8-Explanation:
```Let C’s age be x years then B’s age be 3x
years and A’s age be (3x+5) years

Therefore  x + 3x + (3x + 5) = 40
7x + 5 = 40
7x = 35
x = 5```
There are 8 questions to complete.