# Simplification and Approximation

• Last Updated : 27 Sep, 2023

 Question 1
(1015)2 = ? 1040125 1030225 1050125 1025125

Question 1-Explanation:
```10152 = (1000+15)2
= 10002 + 152 +2 x 1000 x 15
=1000000 + 225 + 30000
=1030225```
 Question 2
103 x 103 + 97 x 97 = ? 21348 20018 19648 21428

Question 2-Explanation:
```103 x 103 + 97 x 97
= (100+3)2 + (100-3)2
= 2 (1002 + 32 )
[ (X +Y)2 + ( X – Y)2 = 2 ( X2 + Y2 ) ]
= 2 (10000 + 9 )
= 2 x 10009
= 20018```
 Question 3
9848 x 125 = ? 1232000 1242000 1231000 1233000

Question 3-Explanation:
```9848 x 125 = 9848 x (250 / 2)
= 4924 x (500 / 2)
= 2462 x (1000 / 2)
= 1231 x (1000)
= 1231000```
 Question 4
512 x 512 + 488 x 488 = ? 512438 502568 500288 514318

Question 4-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 5
What should be the value of x in equation (x / √216) = (√96 / x) 12 13 9 11

Question 5-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 6
7 + 72 + 73...........76 =? 140136 142156 133256 137256

Question 6-Explanation:
```Given series is a G. P. with a = 7, r = 7 and n = 6

∴ Sn = a(rn-1) / (r-1)

∴ Sn = 7(76-1) / 6

Sn = = 137256```
 Question 7
What could be the maximum value of Y in the following equation given that neither of X, Y, Z is zero? 5X8 + 3Y4 + 2Z1 = 1103 0 7 8 9

Question 7-Explanation:
```  1 1    <- CARRY

5 X 8
+ 3 Y 4
+ 2 Z 1
--------
11 0 3
--------
```
Clearly, X + Y + Z + 1 = 10 => X + Y + Z = 9 Now, since neither of X, Y, Z can be zero, the value of Y will be maximum when X = Z = 1. => Max Y = 7
 Question 8
What is the unit's digit in the product (267)153 x (66666)72 ? 7 6 1 2

Question 8-Explanation:
We have to find the unit digit only.
```In 267 unit digit is 7 and cyclicity of 7 is 4.
So, (267)153 can be written as (267)Rem(153)/4 = (267)1
Unit digit of (267)1 = 7.
similarly for 66666 unit digit is 6 and cyclicity for 6 is 1.
Unit digit for (66666)72 = 6.

Therefore , Unit digit of the resultant is 7 * 6 = 2```
 Question 9
√7321 x 35.999 = ? 3060 3204 3410 2930

Question 9-Explanation:
85*9*100/25=765*4=3060
 Question 10
5432.91 ÷ 2324.65 × 210.05 =? 471 431 491 501

Question 10-Explanation:
Approx: 2.3*210 = 483
There are 23 questions to complete.