Simplifications

1.

Find the value of 1/(3+1/(3+1/(3-1/3))) 

   A.) 3/10
   B.) 10/3
   C.) 27/89
   D.) 89/27

Answer: Option 'C'

1/[3 + (1/(3+1/(3 - 1/3)))] 
=> 1/[3 + 1/(3 + 1/(8/3))] 
=> 1/[3 + 1/(3 + 3/8)] 
=> 1/[3 + 8/27] 
=> 1/(89/27) 
=> 27/89

2.

Find the value of

   A.) 3½ 99;
   B.) 34/99
   C.) 2.131313
   D.) 3.141414

Answer: Option 'D'


6/9 + 7/9 + 9/9 + 69/99 
2/3 + 7/9 + 1 + 69/99 
(66 + 77 + 99 + 69)/99 
311/99 => 3.141414

3.

Find the value of
((0.1)3 + (0.6)3 + (0.7)3 − (0.3)(0.6)(0.7))/((0.1)2 + (0.6)2 + (0.7)2 − 0.006 − 0.42 − 0.07)

   A.) 14/10
   B.) 1.35
   C.) 13/10
   D.) 0

Answer: Option 'A'

((0.1)3 + (0.6)3 + (0.7)3 − (0.3)(0.6)(0.7))/((0.1)2 + (0.6)2 + (0.7)2 − 0.006 − 0.42 − 0.07)
=> (0.1 + 0.6 + 0.7)3/(0.1 + 0.6 + 0.7)2
=> 0.1 + 0.6 + 0.7 => 1.4 = 14/10

4.

Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04) 

   A.) 0.56
   B.) 0.65
   C.) 0.54
   D.) 0.45

Answer: Option 'A'

0.56

5.

Find the value of × in the following 
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7) 

   A.) 4
   B.) 3
   C.) 3.6
   D.) 3.06

Answer: Option 'C'

3.6

6.

Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100) 

   A.) 1/50
   B.) 1/25
   C.) 1/20
   D.) 1/40

Answer: Option 'C'

(2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20

7.

Find the value of (875 233/899) × 899 

   A.) 786588
   B.) 786858
   C.) 786885
   D.) 786885

Answer: Option 'B'

(875 233/899) × 899 
(786625 + 233)/899 × 899 
786858/899 × 899 
786858

8.

Find the value of 3/11 × [(1 + 1/3) (1 + 1/4) …………. (1 + 1/120)] is 

   A.) 121
   B.) 11
   C.) 10.6
   D.) 7.82

Answer: Option 'B'

3/11 × [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)] 
3/11 × [4/3 + 5/4 × ........ 121/120] 
3/11 × 4/3 × 5/4 × .... 121/120 
121/11 = 11.

9.

If 13 + 23 + 33 +......+ 103 = 516 then the value of 23 + 43 + 63 + ..... + 203 is

   A.) 1013
   B.) 1032
   C.) 516
   D.) 900

Answer: Option 'B'

2(13 + 23 + 33 + ---------- + 103)
2 × 516 = 1032

10.

If 13 + 23 + ..... + 93 = 1025 then the value of (0.07)3 + (0.14)3 + (0.21)3 + ..... +(0.63)3 Is close to

   A.) 0.351575
   B.) 0.251575
   C.) 2.515575
   D.) 3.51575

Answer: Option 'A'

0.351575

11.

If X = 2 + 1/(1+1/(1-1/2))then the value of 4x+7/3 

   A.) 11
   B.) 34/3
   C.) 11 2/3
   D.) 5

Answer: Option 'C'

X = 2 + 1/(1+1/(1-1/2)) 
= 2 + 1/(1+2) 
= 2 + 1/3 
X = 7/3 ==> 4X + 7/3 => 4(7/3) + 7/3 
==> 28/3 + 7/3 
==> 35/3 
==> 11 2/3.

12.

(121)1/6 is equal to

   A.) 1
   B.) √11
   C.) 11
   D.) ∛11

Answer: Option 'D'

(121)1/6
=>(112)1/6
=> 11 2/6
=> 111/3
=> ∛11

13.

Find the value of (27/343)−2/3

   A.) -(9/49)
   B.) 49/3
   C.) 5 4/9
   D.) 49

Answer: Option 'C'

(27/343)−2/3
(3/7)−2
(7/3)2
49/9
5 4/9.

14.

Find the value of (√1.21)/(√0.81) + (√1.44)/(√0.49) is

   A.) 181/63
   B.) 185/61
   C.) 185/63
   D.) 181/61

Answer: Option 'C'

(√1.21)/(√0.81) + (√1.44)/(√0.49)
11/9 + 12/7 => (77 + 108)/63 => 185/63

15.

Find the value of [2 − 3(2 − 3)−1]−1

   A.) 0.02
   B.) 0.2
   C.) 0.25
   D.) 0

Answer: Option 'B'

0.2

16.

Find the value of 302 − 117 = 24.52 + ?

   A.) 127.70
   B.) 127.65
   C.) 182.75
   D.) 172.05

Answer: Option 'C'

182.75

17.

Find the value of 2/7 of 105 = ? × 90

   A.) 1/2
   B.) 2/5
   C.) 1/3
   D.) 1/4

Answer: Option 'C'

1/3

18.

0.8 × 42 − 36 × 0.7 = ?

   A.) 18.4
   B.) 28.4
   C.) 8.4
   D.) None of these

Answer: Option 'C'

8.4

19.

√(4.9 − 0.49) = ?

   A.) 10.42
   B.) 5.84
   C.) 12.84
   D.) None of these

Answer: Option 'D'

None of these

20.

(139 × 13?)/1312 = 13

   A.) 5
   B.) 4
   C.) 7
   D.) 1

Answer: Option 'B'

4


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