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
A-Addition
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

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Answer: 2.

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

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Answer: 3

3. 497÷7×91÷13+√38.44+³√9.261 =?

1)500.3

2) 505.3

3) 675.3

4) 513.3

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Answer: 2(use BODMAS rule)

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

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Answer: 4

5.Find the value of     

Untitled

1) 320

2)230

3)430

4) None of these

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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

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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

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Answer: 4

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

2) 8950

3) 8935

4) 8975

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Answer: 3

9. (15.01)² × 730 = ?

1) 6125

2) 6225

3) 6200

4) 6075

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Answer: 4

10. 42% of ? = 4116

1) 9400

2) 9600

3) 9800

4) 10200

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Answer: 3

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