A) 28 | B) 29 |

C) 31 | D) 35 |

Explanation:

Clearly, we have :

A = B - 3 ...(i)

D + 5 = E ...(ii)

A+C = 2E ...(iii)

B + D = A+C = 2E ...(iv)

A+B + C + D + E=150 ...(v)

From (iii), (iv) and (v), we get: 5E = 150 or E = 30.

Putting E = 30 in (ii), we get: D = 25.

Putting E = 30 and D = 25 in (iv), we get: B = 35.

Putting B = 35 in (i), we get: A = 32.

Putting A = 32 and E = 30 in (iii), we get: C = 28.

A) 13 | B) 26 |

C) 39 | D) 52 |

Explanation:

The total cards in the deck are** 52**. These 52 cards are divided into 4 suits of 13 cards in each suit. Two Red suits and Two black suits.

**Red suits ::** Heart suit and Diamond suit **= 26**

**Black suits ::** Spade suit and Club suit **= 26.**

A) 20 | B) 30 |

C) 18 | D) 24 |

Explanation:

6 choose 3 means number of possible unordered combinations when 3 items are selected from 6 available items i.e, nothing but **6C3.**

Now **6C3 = 6 x 5 x 4/3 x 2 x 1 = 120/6 = 20.**

A) 0 | B) 19 |

C) 29 | D) 91 |

Explanation:

Here in the given numbers 91 is a Composite number. Since it has factors of 7 and 13 other than 1 and itself.

**Composite Numbers :**

A composite number is a positive integer which is not prime (i.e., which has factors other than 1 and itself).

Examples :: 4, 6, 8, 12, 14, 15, 18, 20, ...

A) B and C together are sufficient | B) Any one pair of A and B, B and C or C and A is sufficient |

C) C and A together are sufficient | D) A and B together are sufficient |

Explanation:

From the given data,

Let the two gits of a number be x & y

A) x + y = 15

B) ${x}^{2}-{y}^{2}=45$

(x+y) (x - y) = 45

C) x - y = 3

From any 2 of the given 3 statements, we can find that 2 digit number as

2x = 18 => x = 9

=> y = 6

Hence, 2 digit number is 96.

Any one pair of A and B, B and C or C and A is sufficient to find.

A) -ve | B) +ve |

C) 0 | D) Can't be determined |

Explanation:

We know the Mathematical rules that

$\frac{\mathbf{+}}{\mathbf{+}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{+}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{\mathbf{+}}{\mathbf{-}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{\mathbf{-}}{\mathbf{+}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{\mathbf{-}}{\mathbf{-}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{+}$

A) TRUE | B) FALSE |

Explanation:

We know that,

**Alternate Exterior Angles Theorem::**

The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent .

**Converse of the Alternate Exterior Angles Theorem ::**

Converse of the Alternate Exterior Angles Theorem states that, If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.

A) 4 | B) 3 |

C) 2 | D) 1 |