How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together ?

Correct Answer: 9944

Explanation:

The largest 4 digit number is = 9999
After dividing 9999 with 88, we get 55 as remainder
so largest 4 digit number divisible by 88 = 9999-55 = 9944.

Correct Answer: 42437

Explanation:

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

Correct Answer: 222

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: 12/35

Explanation:

Let a and b are the numbers.Then a+b is 12 and ab is 35.

 

a+b/ab = 12/35

 

1/b + 1/a = 12/35

Correct Answer: 2

Explanation:

6)4456(742
42
--------
25
24
-------
16
12
-----
4
------
Required number = (6-4) = 2.

Correct Answer: 4

Explanation:

132 = 4 x 3 x 11, So if the number is divisible by all three numbers 4,3 and 11,then the number is divisible by 132 also.
264   => 4,3,11(/)
396   => 4,3,11(/)
462   => 11,3
792   => 4,3,11(/)
968   => 11,4
2178 => 11,3
5184 => 3,4
6336 => 4,3,11(/)
Required number of numbers=4.

Correct Answer: 2

Explanation:

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = ( 22 + x ), which must be divisible by 3.

When x=2. [(22 + 2) = 24 is divisible by 3]

So, the answer is 2

Correct Answer: 9

Explanation:

The maximum number of bows will be 4 yards (= 4 x 36 inches) divided by 15 inches.

This gives 9.6. But as a fraction of a bow is no use, we can only make 9 bows.