Numbers problems

Correct Answer: 945

Explanation:

Required numbers are 10,15,20,25,...,95
This is an A.P. in which a=10,d=5 and l=95.
Let the number of terms in it be n.Then t=95
So a+(n-1)d=95.
10+(n-1)*5=95,then n=18.
Required sum=n/2(a+l)=18/2(10+95)=945.

Correct Answer: 10

Explanation:

(2272-875) = 1397, is exactly divisible by N.

Now , 1397 = 11 x 127

The required 3-digit number is 127,the sum of digits is 10.

Correct Answer: 8

Explanation:

Let the two consecutive odd integers be (2x + 1) and (2x + 3)

Then,

(2x + 3)² - (2x + 1)²

= (2x + 3 + 2x + 1) (2x + 3 - 2x - 1)

= (4x + 4)(2)
= 8 (x + 1), which is always divisible by 8

Correct Answer: 75

Explanation:

Let Divisor be x. We know that Dividend = Remainder+Divisor×Quotient So Divisor = (Dividend - Remainder)/Quotient ⇒ x = (4150 - 25)/55 ⇒ x = 4125/55 ⇒ x = 75 Hence Divisor is 75.

Correct Answer: 5

Explanation:

The pattern is -45, -35, -25, -15

The next number = 20-15= 5

Correct Answer: ⁴⁄₅

Explanation:

Let the required fraction be x. Then	1	- x =	9
	x		20

∴	1 - x2	=	9
	x		20

  ⟹   20 - 20x² = 9x

  ⟹   20x² + 9x - 20 = 0

  ⟹   20x² + 25x - 16x - 20 = 0

  ⟹   5x(4x + 5) - 4(4x + 5) = 0

  ⟹   (4x + 5)(5x - 4) = 0

x =	4
	5

Correct Answer: 100

Explanation:

Let the number be x.Then

 

60% of 3 5of x=36.

 

=>  60 100 * 3 5 * x = 36

 

=>  9 x 25 = 36 => x= 25 * 36 9 = 100

 

Required number is 100.

Correct Answer: 4964

Explanation:

The pattern is  1 2 2 2 , 3 2 4 2 , 5 2 6 2, 

?The next number= 7 2 8 2= 4964

Correct Answer: 8 and 5

Explanation:

Let the number  be 476ab0 

 

476ab0 is divisible by 3 

=> 4 + 7 + 6 + a + b + 0 is divisible by 3

=> 17 + a + b is divisible by 3 ------------------------(i)

 

476ab0 is divisible by 11

[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11

=> [3 + (b - a)] is 0 or divisible by 11  --------------(ii)

 

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.

 

if a=6 and b=2, 

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

 

if a=8 and b=2, 

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer

 

if a=6 and b=5, 

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

 

 

if a=8 and b=5, 

17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1

[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2

Since these values satisfies both equation 1 and equation 2, this is the answer

Correct Answer: 42437

Explanation:

The square of a natural number never ends in 7.
42437 is not the square of a natural number