25-09-2021 Answers

 1. Find the sum of following numbers.

54 + 108 + 216 + 432 + 864 + 1728 + 3456

Answer: 6858

Solution: The ratio of multiplication is 2 (A term is twice the previous term). There are 7 terms in the series.

Hence  using the speed math trick, sum = (2^7 - 1)*54/(2-1) = (127*54) =  6858

2. Find the sum of following numbers.

25 + 75 + 225 + 675 + 2025 + 6075 + 24300 + 97200 + 388800 + 1555200

Answer: 2074600

Solution: There are two series.

First let us find sum of 25 + 75 + 225 + 675 + 2025 + 6075.

Sum using the speed maths trick is =  (3^6 -1)*25/(3-1) = 9100 [Each number is thrice the previous term]

Next for the series 24300 + 97200 + 388800 + 1555200,

Sum using the speed maths trick is =  (4^4 -1)*24300/(4-1) = 2065500. [Each number is four times the previous term]. Total = 9100 + 2065500 = 2074600

3. What is the value of 52 * 5.5 + 64*22 + 82 * 11?

Answer: 2596

Solution: This problem is based on speed maths trick to multiply a number with 11.

The expression can be written as

26*11 + 128*11 + 82*11.

The trick is when multiplying a number with 11, write a space between unit digit and the remaining digits. The sum of the digits should be inserted in the blank. Carry forward should happen if the sum is more than 9.

So 26*11 = 2(2+6)6 = 286,

128*11 = 12(12+8)8 = 12(20)8 = (12+2)08 = 1408  (Carry forward 2)

Similarly 82*11 = 902. So required value = 286+1408+902 = 2596

4. What is the value of the below expression?

5000.4 * 5000.6

Answer: 25005000.24

Solution: The above can be written in fraction form as 5000(4/10) * 5000(6/10)

The shortcut is (Multiply the common whole number with one more than itself. Then append the product of the fractional part).

5000*5001(4*6/(10*10) = 25005000(24/100) = 25005000.24

5. What is the value of the below expression?

1999.2 * 1999.8

Answer: 3998000.16

Solution: The above can be written in fraction form as 1999(2/10) * 1999(8/10)

The shortcut is (Multiply the common whole number with one more than itself. Then append the product of the fractional part).

1999*2000(2*8/(10*10) = 3998000(16/100) = 3998000.16

6. What is the value of 160% of 12.5 + 180% of 20 + 90% of 25 ?

Answer: 78.5

Solution: This question is based on the speed maths trick that we can flip the percentage.

Hence the above expression is

12.5% of 160 + 20% of 180 + 25% of 90

= 160/8 + 180/5 + 90/4 = 20+36+22.5 = 78.5

7. Find the digit to replace question mark in the below expression.

985412368745621 * 587214695 = 578648?23562187368100595

Answer: 6

Solution: We can use digital sum technique to solve these type of problems.

Sum of digits in 985412368745621 = 71 = 7+1 = 8

Sum of digits in 587214695 = 47 = 4+7 = 11 = 1+1 = 2

Multiplying digital sums = 8*2 = 16 = 1+6 = 7

Hence the digital sum of the product should also be 7.

Sum of digits in 578648?23562187368100595 = 109+? = 10+? = 1+?

So 1+? = 7, Hence ? =6

8. What is the hundredth digit in 91838478398468179123455912 * 11 ?

Answer: None of these

Solution: 11 = 10+1,

91838478398468179123455912 * (10+1)

= 918384783984681791234559120 +  91838478398468179123455912

Just adding till hundredth digit it is ....032

9. Find the value of 29*9 + 42*9 + 11*99 + 240*27 + 21*3 + 152*9

Answer: 9639

Solution: All these terms have 9 as a multiplier.

So the expression becomes, (29+42+121+720+7+152)*9 = (1071)*9 = 9639

10. What is the value of 32 * 125 + 50 * 4080?

Answer: 208000

Solution: 32 x 125  = 16 * 250 = 8 * 500 = 4 * 1000 = 4000. 

50 * 4080 = 100 * 2040 = 204000, Sum = 208000

11. Find the square root of 123904.

Answer: None of these

Solution: Express the larger number as a product of smaller squares.

123904 is divisible by 123904.

So 123904 = 4 * 30976

= 4 * 4 * 7744 = 4*4*4*1936 = 4*4*4*4*484 = 4*4*4*4*4*121

Now taking square root the value is = 2*2*2*2*2*11 = 352

12. Find the sum of following expression.

12*16 + 32*36 + 42*38 + 18*22

Answer: 3336

Solution: The shortcut to find product of two numbers differing by four is ,

Hence 12*16 = 14^2 - 4 = 196-4 = 192. So the overall sum is = 192+1152+1596+396 = 3336

13. Find the sum of following numbers.

1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192

Answer: 127/192

Solution: The common ratio multiplier is 1/2 and there are 7 terms in the series.

Sum using the speed maths trick is =  (1/(2^7) - 1)* 1/3/(1/2-1)

= -127/128 * -2/3 = 127/192

14. Find the value of M if  5287987 * M  = 28983456747

Answer: 5481

Solution: We can use digital sum technique to solve these type of problems.

Sum of digits in 5287987 = 46 = 4+6 = 10 =1+0 =1

Sum of digits in 28983456747 = 63 = 6+3 = 9

Hence the digital sum of the digits in the option should be 9 so that 9*1 = 9.

Verifying each option only 5481 gives digital sum as 9.

15. What is the value of the below expression?

12378916 * 25 * 64

Answer: 19806265600

Solution: 25*4 = 100.

So the expression becomes 12378916 * 16 * 100, 16 is 10+6.

So the expression can be simplified as (12378916*10 + 12378916*6)*100 = 19806265600

16. Find the sum of following numbers.

2026 + 2027 + 2028 + 2029 + 2030 + 2031 + 2032 + 2033 + 2034

Answer: 18270

Solution: The speed math trick is as below.

When numbers are in sequence add the smallest and largest number. So 2026+2034 = 4060.

There are 9 numbers. So multiply it by 9. So 4060*9 =  36540.

Now divide the value by 2. So 36540/2 = 18270.

17. 26 × 12 ÷ 8 + ? = 76

Answer: 37

18. Find the sum of following expression.

11*14 + 15*18 + 19*22 + 21*24

Answer: The shortcut to find product of two numbers differing by three is (Square of one more than smaller number + One less than smaller number).

Hence 11*14 = 12^2 + (11 -1) = 154

Similarly 15*18 = 16^2 + (15-1) = 270

Hence the sum is 154+270+418+504 = 1346

19. What is the value of 32 * 525 + 50 * 6842?

Answer: 35890032 x 525  = 8 * 2100 = 16800

50 * 6842 = 100 * 3421 = 342100, Sum = 358900

20. What is the value of 120% of 50 + 31% of 200 + 90% of 50 ?

Answer: 167

Solution: This question is based on the speed maths trick that we can flip the percentage.

Hence the above expression is

50% of 120 + 200% of 31 + 50% of 90 = 60+62+45 = 167