SOLVED MATHS QUESTIONS

1:What least number must be added to 7986 to make it exactly divisible by 74?

Answer: When 7986 is diveded by 74,we get 68 as remainder

ie:7986÷74=107+68(Where 68 is Remainder)

Then The Number to be added =74₋68=6

2:The number which when multiplied by 17 increases by 640, is ..........

Answer:Let the number be 𝒳 ,

Then 17𝒳= 𝒳 +640

⇒16 𝒳=640

ie 𝒳 =640÷16=40

3:How many numbers upto 100 are  divisible by 3?

Answer:The quotient obtained on dividing 100 by 3 is the required number of numbers.

ie 100=33×3+1

So There are 33 numbers. 

4:The greatest number,by which the product of three consecutive multiples of 3 is always divisible is ..?

A)54

B)81

C)162

D)243

Answer:Let 3a,3b,&3c be the three consecutive multiples of 3 ,where a,b&c are three consecutive numbers.In any three consecutive numbers,at least one of them will be a multiple of 2 and another of them , a multiple 3, or one of them will be both ⇒a×b×c=3×2×𝒳  where 𝒳 is another number 

So 3a×3b×3c ⇒27(abc)=27×6𝒳=162𝒳

5:The H.C.F  of three numbers is 12 .if they are in the ratio 1:2:3,the numbers are

A)12,24,36

B)10,20,30

C)6,12,8

D)24,48,72

Answer:Let the numbers be 1𝒳,2𝒳 &3𝒳. Their HCF =𝒳=12.

So The numbers are 1×12=12

                                 2×12=24

                                       &

                                 3×12=36

ie The Numbers are 12,24,36

6:The L.C.M of two numbers is 1920 and their  H.C.F is 16.If one of the numbers is 128,then the other number is ..?

A)204

B)240

C)260

D)320

Answer:Product of two number =product of their H.C.F & L.C.M

ie 128×Second number=16×1920

⇒16×1920÷128=240

7:When a number is divided by 56,the remainder obtained is 29, what will be the remainder when the number is divided by 8?

A)4

B)5

C)3

D)7

Answer: If  𝒳  is the quotient  obtained when the number is divided by 56,

Number:56 𝒳 +29=8×7𝒳+8×3+5

ie The number is multiple of 8+5⇒The remainder when it is divided by 8 is 5.