Number System-Test 3

Answer: Option D

Explanation

Let the ten's digit be 'x' and unit's digit be 'y'

Then, two digit number =10x+y

According to the question

⇒ x+y=8  ---Eq(1)

Again,

⇒ 10x+y=18(10y+x)

⇒ 10x+y-10y-x=18

⇒ 10x-x+y-10y=18

⇒ 9x-9y=18

⇒ x-y=2   ---Eq(2)

Substitute Eq(1) from Eq(2) we get 

⇒ -2y=-6

⇒ y=3

Substitute 'y' value in Eq(1)

⇒ x+3=8

⇒ x=5

∴ The number is ⇒ 10x+y

⇒ 10×5+3

⇒ 53.

Hence, Option D is correct.

Answer: Option C

Explanation

Let the ten's digit be 'x'

Then, unit's digit= x+2

= 10x+(x+2)=11x+2

Sum of digits =x+(x+2)=2x+2

= (11x+2)(2x+2)=144

= 22x²+22x-140=0

= 11x²+13x-70=0

= (x-2)(11x+35)=0

= x=2

∴The required number  = 11x+2=24

Hence, Option C is correct.

Answer: Option A

Explanation

Let the ten's digit be 'x' and unit's digit be 'y'

Then, (10x+y)-(10y+x)=36

⇒ 9(x-y)=36

⇒ x-y=4

Hence, Option A is correct.

Answer: Option D

Explanation

Let the ten's digit be 'x' and unit's digit be 'y'

Then, (10x+y)-(10y+x)=45

⇒ 9(x-y)=45

⇒ x-y=5

Given data is inadequate

Hence, Option D is correct.

Answer: Option D

Explanation

Let the Four consecutive odd integers is 2n-3,2n-1,2n+1,2+3

And thier average= 42

and thier sum is = 42×4= 168

⇒  (2n-3)(2n-1)+(2n+1)+(2+3)=168

⇒  8n=168

⇒  n=21

∴ The numbers are J=39, K=41, L=43, M=45

The product of K and M is 41×45=1845.

Hence, Option D is correct.