# Quantitative Aptitude Quiz – 22 (Simplifications)

Hi readers, While we are practicing simplification, we should have knowledge about some basic formulas, some previously defined results and the Rule for BODMAS. Here we are providing those basics with some problems.

BASIC FORMULAE

1. (a + b)² = a² + b² + 2ab
2. (a – b)² = a² + b² – 2ab
3. (a + b)² – (a – b)² = 4ab
4. (a + b)² + (a – b)² = 2 (a² + b²)
5. (a² – b²) = (a + b) (a – b)
6. (a + b + c)²= a² + b² + c² + 2 (ab + bc + ca)
7. (a³ + b³) = (a +b) (a² – ab + b²)
8. (a³ – b³) = (a – b) (a²+ ab + b²)
9. (a³ + b³ + c³ -3abc) = (a + b + c) (a² + b² + c² – ab – bc – ca)
10. If a + b + c = 0, then a³ + b³ + c³ = 3abc.

SOME IMPORTANT RESULTS

(i) (1 + 2 + 3 +…. + n) =n(n+1)/2
(ii) (1² + 2² + 3² + … + n²) = n (n+1)(2n+1)/6
(iii) (1³ + 2³ + 3³ + … + n³) =n²(n+1)²

BODMAS

This rule is used to execute the operations in the correct sequence,then only we can find the correct answer for the given expression.

B-Brackets
O-Of
D-Division
M-Multiplication
S-Subtraction

#### Problems

1. 95% of 75% of 4860 – 45% of 55%of 5550=?

1)1890.135

2) 2089.125

3) 1889.135

4) 2910.235

StepI :95/100 * 75/100 *4860 – 45/100* 55/100* 5550

Step II := 27702-10989/8

Step III :=16713/8=125

2. 937+23.124-32.768-38.439=?

1)1.874

2)1.934

3)1.854

4) 1.826

3. 497÷7×91÷13+√38.44+³√9.261 =?

1)500.3

2) 505.3

3) 675.3

4) 513.3

Step I: 497/7 * 91/13 + 6.3 +4.2

Step II: 505.3

4. 3640÷14×16+340=?

1)0.70

2)3525

3)9600

4) None of these

5.Find the value of

1) 320

2)230

3)430

4) None of these

Answer: 2 (use the formula No.8:(a³ – b³) = (a – b) (a²+ ab + b²)) Step I: Our given equation in the form of (a³ – b³)/(a²+ ab + b²) = (a – b) Step II: the value of a=343 and b=113 then (a-b)= 343-113=230

6. Find the value of (1- 1/3 ) (1- 1/4 ) (1- 1/5 )….. (1- 1/100 )

1) 1/25

2) 1/100

3) 1/50

4) None of these

Answer: 3 Step I: simplifying the given equation we get sequence as 2/3 * 3/4 * 4/5 *…. 99/100 Step II: after solving we get 2/100=1/50

7. 32.05% of 259.99 = ?
1) 92

2) 88

3) 78

4) 83

8. 25.05 × 123.95 + 388.999 × 15.001 = ?
1) 900

2) 8950

3) 8935

4) 8975

9. (15.01)² × 730 = ?

1) 6125

2) 6225

3) 6200

4) 6075