A) 7 | B) 23 |

C) 9 | D) 21 |

Explanation:

Let the greater and smaller number be p and q respectively.

4q = p + 5 ------ (I)

p = 3q+2 ------- (II)

From equation (I) and (II)

q = 7

p = 23

A) 91 | B) 71 |

C) 41 | D) 31 |

Explanation:

**Prime Numbers ::** Numbers which are divisible by only 1 and itself are Prime Numbers.

It's answer will be 91.

Because 91 can be divisible by 7,13,91,1.

It is quite clear that prime number should be divisible only by itself and by 1.

A) 29 | B) 27 |

C) 31 | D) 33 |

Explanation:

Let the five consecutive odd numbers be x-4, x-2, x, x+2, x+4

According to the question,

Difference between square of the average of first two odd number and the of the average last

two odd numbers is 396

i.e, x+3 and x-3

$\mathbf{\Rightarrow}{\left(\mathbf{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{3}\right)}^{\mathbf{2}}\mathbf{}\mathbf{-}\mathbf{}{\left(\mathbf{x}\mathbf{}\mathbf{-}\mathbf{}\mathbf{3}\right)}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{396}\phantom{\rule{0ex}{0ex}}\mathbf{\Rightarrow}\mathbf{}{\mathbf{x}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{9}\mathbf{}\mathbf{+}\mathbf{}\mathbf{6}\mathbf{x}\mathbf{}\mathbf{-}\mathbf{}{\mathbf{x}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{6}\mathbf{x}\mathbf{}\mathbf{-}\mathbf{}\mathbf{9}\mathbf{}\mathbf{=}\mathbf{}\mathbf{396}\phantom{\rule{0ex}{0ex}}\mathbf{\Rightarrow}\mathbf{}\mathbf{12}\mathbf{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{396}\phantom{\rule{0ex}{0ex}}\mathbf{\Rightarrow}\mathbf{}\mathbf{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{33}$

Hence, the smallest odd number is **33 - 4 = 29.**

A) 12, 34, 42 | B) 12, 18, 36, |

C) 6, 4, 14 | D) 4, 8, 16 |

Explanation:

The Multiples of 6 are **6, 12, 18, 24, 30, 36, 42, 48, 54, 60.**

The Multiples of 4 are **4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.**

The Common Multiples of 4 & 6 upto 60 numbers are given as **12, 24, 36, 48, 60.**

A) 7, 5 | B) 9, 3 |

C) 8, 4 | D) 6, 6 |

Explanation:

Let the number of girls = x

=> x + x + 4 = 12

=> 2x = 8

=> x = 4

=> Number of girls = 4

=> Number of boys = 4 + 4 = 8

A) 1 | B) 2 |

C) 3 | D) 0 |

Explanation:

A number is divisible by 9 only if the sum of the digits of the number is divisible by 9.

Here 86236 = 8 + 6 + 2 + 3 + 6 = 25

We must add 2 to 25 to become 27 which is divisible by 9.

A) 18 | B) 20 |

C) 19 | D) 17 |

A) 57 | B) 75 |

C) 48 | D) 39 |

Explanation:

Let the two-digit number be 10a + b

a + b = 12 --- (1)

If a>b, a - b = 6

If b>a, b - a = 6

If a - b = 6, adding it to equation (1), we get

2a = 18 => a =9

so b = 12 - a = 3

Number would be 93.

if b - a = 6, adding it to the equation (1), we get

2b = 18 => b = 9

a = 12 - b = 3.

Number would be 39.

There fore, Number would be 39 or 93.

A) 1020 | B) 1040 |

C) 1060 | D) 1022 |

Explanation:

Lowest 4-digit number is 1000.

LCM of 3, 4 and 5 is 60.

Dividing 1000 by 60, we get the remainder 40. Thus, the lowest 4-digit number that exactly divisible by 3, 4 and 5 is 1000 + (60 - 40) = 1020.

Now, add the remainder 2 that's required. Thus, the answer is 1022.