# Splification - Quantitative Aptitude

Q21. In an objective examination of 90 questions, 5 marks are alloted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the questions, a student got a total of 387 marks. The number of questions attempted wrong were

(a) 5

(b) 9

(c) 12

(d) 16

**Answer:** (b) 9

Let the no. of wrong answer be x

∴ No. of correct answer = 90 - x

∴ 5(90-x) - 2x = 387

∴ 7x = 450 - 387

∴ x = 63/7 = 9

Q22. If P/Q = 5 then (P+Q)/(P-Q) = ?

(a) 1/2

(b) 3/2

(c) 3/5

(d) 5/7

**Answer:** (b) 3/2

P + Q | = | P/Q + 1 | = | 5 + 1 | = | 6 | = | 3 |

P - Q | P/Q - 1 | 5 - 1 | 4 | 2 |

Q23. If a = (1-x), b = (3x+1) and a = b then x = ?

(a) 0

(b) 3

(c) 5

(d) 6

**Answer:** (a) 0

a = b

⇒ 1 - x = 3x + 1

⇒ 4x = 0

⇒ x = 0/4 = 0

Q24. Each boy contributed rupees equal to the number of girls and each girl contributed rupees equal to the number of boys in a class of 60 students. If the total contribution thus collected is Rs. 1600, how many boys are there in the class ?

(a) 25

(b) 29

(c) 33

(d) Data inadequate

**Answer:** (d) Data inadequate

Let, the No. of boys be x

∴ No. of girls be (60-x)

A/Q x(60-x) + (60-x)x = 1600

⇒ 2x(60-x) = 1600

⇒ 60x - x^{2} = 800

⇒ x^{2} - 60x + 800 = 0

⇒ x^{2} - 40x - 20x + 800 = 0

⇒ x(x-40) - 20(x-40) = 0

⇒ (x-40)(x-20) = 0

∴ x - 40 = 0 or x - 20 = 0

⇒ x = 40 ⇒ x = 20

Hence the data is inadequate

Q25. Two fifth of 60 is how much more than one third of 45 ?

(a) 5

(b) 9

(c) 11

(d) 14

**Answer:** (b) 9

Required Number = (2/5) X 60 - (1/3) X 45 = 24 - 15 = 9

Q26.

a^{2} - (b-c)^{2} |
+ | b^{2} - (a-c)^{2} |
+ | c^{2} - (a-b)^{2} |
= ? |

(a+c)^{2} - b^{2} |
(a+b)^{2} - c^{2} |
(b+c)^{2} - a^{2} |

(a) 1

(b) 3

(c) 7

(d) 9

**Answer:** (a) 1

(a+b-c)(a-b+c) | + | (b+a-c)(b-a+c) | + | (c+a-b)(c-a+b) |

(a+c+b)(a+c-b) | (a+b+c)(a+b-c) | (b+c+a)(b+c-a) |

= | a+b-c | + | b+c-a | + | c+a-b |

a+b+c | a+b+c | a+b+c |

= | a+b-c+b+c-a+c+a-b |

a+b+c |

= | a+b+c |

a+b+c |

= 1

Q27. Some students planned a picnic. The budget for food was Rs. 500. But 5 of them failed to go and thus cost of food for each member increased by Rs. 5. How many students attended the picnic ?

(a) 16

(b) 17

(c) 20

(d) 23

**Answer:** (c) 20

Let, the no. of students who planned the picnic be x

A/Q | 500 | - | 500 | = 5 |

x - 5 | x |

⇒ | 1 | - | 1 | = | 5 |

x - 5 | x | 500 |

⇒ | x - (x-5) | = | 1 |

x(x - 5) | 100 |

⇒ | 5 | = | 1 |

x(x - 5) | 100 |

⇒ x(x - 5) = 500

⇒ x^{2} - 5x - 500 = 0

⇒ x^{2} - 25x + 20x - 500 = 0

⇒ x(x-25) + 20(x-25) = 0

⇒ (x-25)(x+20) = 0

∴ x = 25

Required no. of student = 25 - 5 = 20

Q28.

5(9/14) | = ? |

5 + 3/(3 + (1/3)/5) |

(a) 1

(b) 4

(c) 5

(d) 8

**Answer:** (a) 1

5(9/14) |

5 + 3/(3 + (1/3)/5) |

= | 79/14 |

5 + 3/(3 + 5/3) |

= | 79/14 |

5 + 3/(14/3) |

= | 79/14 |

5 + 9/14 |

= | 79/14 |

79/14 |

= 1

Q29. A class starts at 10 am and lasts till 1.27 pm. Four periods are held during this interval. After every period, 5 minutes are given free to the students . The exact duration of each period is

(a) 35 min

(b) 39 min

(c) 43 min

(d) 48 min

**Answer:** (d) 48 min

Let, the required time be x min

∴ Total duration of class = 13h 27min - 10h = 3h 27min = 207min

Now 3(x+5) + x = 207

⇒ 3x + 15 + x = 207

⇒ 4x = 192

⇒ x = 48 min

Q30.

2 | X | 3 | = ? |

3 | 5/6 ÷ 2/3 of 1¼ |

(a) 2

(b) 3

(c) 5

(d) 7

**Answer:** (a) 2

2 | X | 3 |

3 | 5/6 ÷ (2/3 X 5/4) |

= | 2 | X | 3 |

3 | 5/6 ÷ 5/6 |

= | 2 | X | 3 |

3 | 5/6 X 6/5 |

= | 2 | X 3 |

3 |

= 2

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