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Q. Find the common factors of
(a) 8, 20 \: (b)\: 9, 15

a)  8=2×2×2
     20=2×2×5
    common factor =2×2=4

b)  3×3=9,

    3×5=15
   3 is the common  factor of 9 and 15 

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Posted by

Satyajeet Kumar

Q10. Find the values of the letters in each of the following and give reasons for the steps involved.

The addition of A and B is giving a number whose ones digit is 9. The sum can only be 9 not 10 as a sum of two single digits cannot exceed 18. hence there will not be any carry for the next step 

2 + A = 0 

implies A = 8 

2 + 8 = 10 and 1 is the carry for next step.

1 + 1 + 6 = A = 8 

it satisfies hence A = 8 and B = 1 is the correct answer.

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Posted by

Pankaj Sanodiya

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Q9. Find the values of the letters in each of the following and give reasons for the steps involved.

The additiion of B and 1 is 8  is giving a number whose ones digit is 8. this means digit B is 7 . 

B + 1 = 8 and no carry for next step.

next step :

Now, A + B = 1 => A + 7

which implies A = 4 

A  + B = 11 and 1 is carry for next step 

1 + 2 + A  = B

1 + 2 + 4 = 7 

Hence A = 4 and B = 7 is correct answer.

 

 

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Posted by

Pankaj Sanodiya

Q8. Find the values of the letters in each of the following and give reasons for the steps involved.

The addition of 1 and B gives a number whose ones digit is 0. this is possible when digit B = 9 . 

1 + B  = 10  and 1 is the Carry for the next step 

Now, A + 1 + 1 = B => 9

Implies  A = 7.

Hence A = 7 and B = 9 is Correct answer

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Posted by

Pankaj Sanodiya

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Q7. Find the values of the letters in each of the following and give reasons for the steps involved.

The product of 6 & B gives a number whose unit digit is B again.

possible value of B = 0. 2 , 4, 6 or 8 

If B = o then our product will be zero. hence this value of B is not possible.

If B = 2, then B x 6 = 12 . Carry for next step = 1.

6A + 1 = BB = 22

implies A = 21/6 = not any integer value hence this case is also not possible.

If B = 6  then B *6 = 36 and 3 will be carry for next step.

6A + 3 = BB = 66

implies A = 63/6 = not an integer value hence this case is also not possible.

If B = 8 then B * 6 = 48 and 4 will be carry for next step.

6A + 4 = BB = 88 

implies A = 14 however A is a single digit number hence this case is also not possible.

If B = 4 then B*6 = 24 and 2 will be carry for next step.

6A + 2 = BB = 22 

implies A = 7 .

Hence A = 7 and B = 4 is the correct answer.

 

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Posted by

Pankaj Sanodiya

Q6.Find the values of the letters in each of the following and give reasons for the steps involved.

Here , multiplication of B and 5 gives a number whose ones digit is B. this is possible when B = 0 or 5

let B = 5 

B * 5 = 5 * 5 = 25

Carry = 2

5*A + 2 = CA  , This os possible only when A = 2 or 7

when A = 2 ,

5*2 + 2 = 12 which implies C = 1

when A = 7 

5*7 + 2 = 37 which implies C = 3

 

now  B = 0 

B*5 = 0*5 = 0 

Carry = 0 so 

5 * A = CA which is possible when A = 0 or 5 Howerver A cannot equal to 0 since AB is a two digit number

so A = 5

5*5 = 25 which implies C = 2

hence possible values of A B and C are

A = 5, 2, 7 , B = 0, 5, 5 and C = 2, 1, 3

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Posted by

Pankaj Sanodiya

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Q5.Find the values of the letters in each of the following and give reasons for the steps involved. .

Here multiplication of 3 and B gives  a number whose unit place digit is B .

Possible value of B = 0 and 5

let B = 5 

3 * A  + 1 = CA

this is not possible for any value of A. 

Hence B = 0

now  A * 3 = CA ( a number whose unit place digit is A itself when multiplied by 3) hence 

possible value of A = 5 and 0 

since AB is a two digit number A can not equal to 0.

hence A = 5 

A * 3 + 1 = CA

5 * 3 + 1 = 15

hence C = 1

A = 5, B = 5 and C = 1.

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Posted by

Pankaj Sanodiya

Q4.Find the values of the letters in each of the following and give reasons for the steps involved

There can be two cases

1. when the addition of unit place digit doesn't  produce Carry

A + 3 = 6

A = 3

However, to get 3 in unit place of our answer our B has to be 6 and that would produce carry hence this case is not possible.

2. when the addition of unit place digit produces Carry

A + 3 +1 = 6

A = 2

for getting 2 in unit place of answer we need the sum of unit digit of numbers = 12

B + 7 = 12

B = 5

Hence A = 2 and B = 5

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Posted by

Pankaj Sanodiya

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Q3. Find the values of the letters in each of the following and give reasons for the steps involved.

Here

first clue :

we have A = a number which when multiplied by itself gives the same number in the unit digit. 

possible numbers = 1 and 6 

Second Clue:

number when multiplied with 1 and added with the reminder of previous multiplication( A*A) = 9 

both first and second clue implies that A = 6.

 

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Posted by

Pankaj Sanodiya

Q2. Find the values of the letters in each of the following and give reasons for the steps involved.

Here

answer's unit place = 3 , possible addition of unit places digit = 13 

A + 8 = 13   

A = 13 - 8 = 5

remainder = 1

Ten's place of answer  = 4 + 9 + 1 =  14 

B = 4 

remainder = 1 

100's place = C = 1

 

Hence value of  A = 5 , B = 4 and C = 1.

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Posted by

Pankaj Sanodiya

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