Tricks to Solve Simplification - Addition and Subtraction

# Series/Addition/Subtraction

Q1 Find 8 + 888 + 8888 + 88888 ?


a) 97760 b) 98572 c) 98672 d) 97672 e) None of the above

Q2. Find 9.4 + 99.44 + 999.444 + 9999.4444 ?

a) 11207.728 b) 11107.728 c) 11106.728 d) 11111.728 e) None of these

Q3. ( 2.3 + 3.3 ) [ ( 2.3)² - 2.3✘3.3 + (3.3)² ] = ?

a) 48.104 b) 47.104 c) 47.204 d) 48.204 e) None of these

Q4. (3-2) [(3)⁴+((3)³✘2)+(3)²✘(2)²+(3✘2³)+2⁴] = ?

a) 311 b) 211 c) 201 c) 221 d) 301 e) None of these

Q5. (125.824+124.654)² + (125.824-124.54)² / ((125.824)²+(124.54)²)

a) 1.166 b) 1 b) 2 c) 625 d) 250.478 e) None of these

Q6. Evaluate 1 +  ¹/_1*3 + ¹/_1*3*9 + ¹/_1*3*9*27 + ¹/_1*3*9*27*81 up to three places of decimals ? 

a)1.367 b) 1.370 c) 1.361 d) 1.267 e) None of these

Q7. 2 ÷ [2+ 2÷{2+2 ÷ 4)}]= x / 19. Find x.

a) 3 b) 4 c) 5 d) 6 e) None of these

a) 0.67 b) 0.77 c) 0.87 d) 0.97 e) None of these

Q9) Find the sum of all even natural numbers less than 75.

a) 1416 b) 1426 c) 1396 d) 1406 e) None of these

Solution:

(1)
Sol : Option (c)
8*(12345) - 88 = 98672

(2)
Sol: Option (b)
9✘(1234) = 11106
 4✘(4321) = 17284
=1.7284
=11106+1.7284=11107.7284

(3)
Sol: Option (a)
(a³ + b³)=(a+b) (a²-ab+b²)
a = 2.3, b = 3.3;
(a)³ = 12.167, (b)³ = 35.937 (a³+b³)=48.104

(4)
Sol: option (b)
(a⁵-b⁵)=(a-b) [a⁴+a³b+a²b²+ab³+b⁴] = ?
a = 3, b = 2; (3)5=243, (2)5 =32;
(a⁵-b⁵) = 243-32= 211

(5)
Sol: Option (b)
(a+b)² + (a-b)²=2((a)²+(b)²) Hence Answer is 2

(6)
Sol: Option (a)
1+0.33+0.0370 ... hence (a) is the answer no further addition is required.

(7)
Sol: option (e)
Using VODMAS method
Step 1. [ 2+ 2/4 ] = 5/2.
Step 2. ( 2 + 2 ÷5/2) = 2÷ 2✘2/5 =14/5
Step 3. [2+2÷14/5]=2+2*5/14=19/7
Step 4. L.H.S = 2÷19/7=14/19 = x/19 Hence x=19

(8)
Sol: Option (c)
= -4 + 0.45 + 2 + ^927-9/₉₉₀ +6/9
= -4 + 0.45 + 2 + ⁹¹⁸/990 +3/2
= (- 4 + 2) + (0.45+1.5) + (⁵¹/55)
= -2 + 1.95 + 0.92  = 0.87

(9)
Sol: Option (d)
sum= 2 + 4 + 6 + ...+74 a=2 , d=(4-2)=2,l=74 n=37; sum= n/2 (a+l) 37/2✘(2+74)=(37✘38) =37✘(40-2) =(37✘40)-(37✘2) =(1480-74)=1406

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