24-09-2021 Answers

1. Find the value to replace question mark if 121^3 * 11 / (1331^2) = 11?

Answer: 1

Solution: 1331 = 121*11

So the expression becomes,

11^6 * 11/(11^6) = 11. Hence ?=1


2. Find the value of (5555+3600)/1831

Answer: 5

Solution: 5555 = 5*1111, 3600 = 5*720

As 1831 = 1111+720, the expression can be written as 5*(1111+720)/(1111+720) = 5


3. Find the value of 12.05 * 6.3/0.7

Answer: 108.45

Solution: 12.05 * 6.3/0.7 = 12.05 * 63/7

= 12.05 * 9 = 12.05 * (10-1) = 120.5 - 12.05 = 108.45


4. Find the value of (2 - 1/3) (1 - 1/4)(1 - 1/5) ....... (1 - 1/99)(1 - 1/100)

Answer: 0.05

Solution: (2 - 1/3) = 5/3

(1 - 1/4) = 3/4

(1 - 1/5) = 4/5

(1 - 1/100) = 99/100

So expression becomes 5/3 * 3/4 * 4/5 * ..... 98/99 * 99/100 = 5/100 = .05


5. If a/b = 1/3 and 9a + b = 48, then find the value of a.

Answer: 4

Solution: a/b = 1/3, So b=3a.

using the other equation, 9a+3a = 48, a=48/12=4


6.


Answer: 9/11

Solution: Dividing by B, the expression becomes

(A/B - 1)/(A/B + 1) = (10-1)/(10+1) = 9/11


7. What is the value of 512/5 + 211/5 + 461/5 + 157/5 ?

Answer: 268.2

Solution: Dividing by 5 is nothing but multiplying by 2/10.

Hence the above expression becomes (512+211+461+157)*2/10 = (1341)*2/10 = 268.2


8. What is the value of the below expression?


Answer: 5997

Solution: The expression becomes 999*6 + (1/7 + 2/7 + ... + 6/7)

= 5994 + 21/7 = 5997


9. Find the value to replace question mark so that (7/15 + 2/5) * ? = 1/20

Answer: 3/52

Solution: As 15 is the LCM of denominators, 7/15 + 2/5 = 13/15

So 13/15 * ? = 1/20

? = 15/(13*20) = 3/52


10. Find the value of 3219/25 + 1121378/25 + 99129/25

Answer: 48949.04

Solution: 25 is nothing but 100/4

Hence the expression is (3219+1121378+99129)*4/100 = 4894904/100 = 48949.04


11. Find the value of (0.76 × 0.76 × 0.76 - 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04)

Answer: 0.56

Solution: Here a=0.76 and b=0.2

The expression can be written as (a^3 - b^3)/(a^2 +ab + b^2) = a-b = 0.76-0.2 = 0.56


12. If  a-b = 3 and a^2 + b^2 = 29, find the value of ab.

Answer: 10

Solution: (a-b)^2 = a^2 + b^2 -2ab

9 = 29 - 2ab, ab = (29-9)/2 = 10


13. Find the value of the expression below.


Answer: 200 and 172/315

Solution: To simplify, first consider the whole number part alone.

44 + 66 + 88 = 198

Now consider the fractions.

4/5 + 6/7 + 8/9 =  (252+270+280)/315 = 802/315

So answer is 198 +  802/315 = 200 + 172/315 = 200 and 172/315


14. If a+b=5 and 3a+2b=20, then 3a+b is

Answer: 25

Solution: a+b=5, So 2a+2b=10.

As 3a+2b=20, a=10 and b=-5. So 3a+b = 30-5 = 25


15.


Answer: 4/3

Solution: Dividing by B, the expression becomes

(A/B + 1)/(A/B - 1) = (7+1)/(7-1) = 8/6 = 4/3


16. What is the value of the below expression?

143/11 + 1023/33 + 165/11

Answer: 59

Solution: Using the formula a^2 - b^2 = (a+b)(a-b), the expression can be written as

(12+1)(12-1)/(12-1) + (32+1)(32-1)/(32+1) + (13+2)(13-2)/(13-2)

= 13 + 31 + 15 = 59


17. Find the value of 9983 * 984 + 9983 * 6

Answer: 9883170

Solution: Given expression can be written as 9983 * (1000 - 16) + 9983 * 6

= 9983000 - 9983*16 + 9983 * 6 = 9983000 - 99830 = 9883170


18. If 1/3 + 1/2 + 1/x = 4, then what is the value of x?

Answer: 6/19

Solution: 1/x = 4 - (1/3 + 1/2)

= 4 - 5/6 = 19/6, So x = 6/19


19. Find the value of the below expression.


Answer: 1739832

Solution: 9999 1/29 = (10000 - 28/29) = (290000-28)/29 =

so expression becomes (289972/29) * 174 = 289972 * 6 = 1739832


20. What is the value when 8/13 is divided by 192/559 ?

Answer: 43/24

Solution: 8/13/192/559 = (8/13) * (559/192) = 43/24

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