**Problems On Numbers Aptitude Question and Answer – Formulas & Tricks**

**Problems On Numbers Formulas**

- (A + B)(A – B) = (A
^{2}– B^{2}) - (A + B)
^{2}= (A^{2}+ B^{2}+ 2AB) - (A – B)
^{2}= (A^{2}+ B^{2}– 2AB) - (A + B + C)2= A
^{2}+ B^{2}+ C^{2}+ 2(AB + BC + CA) - (A
^{3}+ B^{3}) = (A + B)(A^{2}– AB + B^{2}) - (A
^{3}– B^{3}) = (A – B)(A^{2}+ AB + B^{2}) - (A
^{3}+ B^{3}+ C^{3}– 3ABC) = (A + B + C)(A^{2}+ B^{2}+ C^{2}– AB – BC – AC) - When A + B + C = 0, then A
^{3}+ B^{3}+ C^{3}= 3ABC

**Problems On Numbers** **Points to Remember**

- Products of Two Numbers = ((Sum + Difference) * (Sum – Difference) / 4)
- Two Numbers x and y can be found as
- X = ((Sum + Difference) / 2
- Y = ((Sum – Difference) / 2

- Sum of the digits of a two-digit number is given. If the digit are reversed, the number is decreased by d, in this case, this number = 5[Sum of digits + (Decrease / 9)] + (1/2)[Sum of digits – (Decrease / 9)]
- If the difference between a two digit number and the number obtained by interchanging the digits is given, the difference of two digits is given by = (Difference in normal and interchanged number / 9)
- Sum of first n odd numbers is n
^{2} - Sum of first n even numbers is n(n + 1)
- Sum of squares of first n natural numbers is n(n + 1)(2n + 1) /6
- Sum of Cubes of first n natural numbers is [n(n+1) / 2]
^{2}

Problems On Numbers Aptitude Question and Answer **With Detailed Explanation** – Quantitative Aptitude

## Clocks

Question 1 |

A Clock is set right at 5a.m. The clock loses 16mins in 24hrs. What will be the true time when the clock indicates 10p.m on 4th day?

11pm | |

12pm | |

1pm | |

2pm |

Question 1 Explanation:

**Answer: Option A**

__Explanation:__

Time from 5am. on a day to 10pm, on 4th day = 89hrs.

Now 23hrs 44min of this clock = 24hrs of correct clock.

356/15 hrs of this clock = 24hrs of correct clock

89hrs of this clock = (24 * 31556 * 89)hrs of correct clock.

= 90hrs of correct clock.

So, the correct time is 11p.m.

Question 2 |

At what angle the hands of a clock are inclined at 15mins past 5?

57.5 degrees | |

67.5 degrees | |

77.5 degrees | |

87.5 degrees |

Question 2 Explanation:

**Answer: Option B**

__Explanation:__

Question 3 |

How many times do the hands of a clock coincide in a day?

20 | |

21 | |

22 | |

24 |

Question 3 Explanation:

**Answer: Option C**

__Explanation:__

The hands of a clock coincide 11 times in every 12hrs (Since between 11 and 1, they coincide only once, i.e. at 12 o'clock).

**AM**

12:00

1:05

2:11

3:16

4:22

5:27

6:33

7:38

8:44

9:49

10:55

**PM**

12:00

1:05

2:11

3:16

4:22

5:27

6:33

7:38

8:44

9:49

10:55

The hands overlap about every 65mins, not every 60mins.

Therefore, The hands coincide 22 times in a day.

Question 4 |

How many times are the hands of a clock at right angle in a day?

22 | |

24 | |

44 | |

48 |

Question 4 Explanation:

**Answer: Option C**

__Explanation:__

In 12hrs, they are at right angels 22 times.

Therefore, In 24hrs, they are at right angles 44times.

Question 5 |

The angel between the minute hand and the hour hand of a clock when the time is 8:30, is:

80 ^{o} | |

75 ^{o} | |

60 ^{o} | |

105 ^{o} |

Question 5 Explanation:

**Answer: Option B**

__Explanation:__

Therefore, Required Angle = (255 - 180)

^{o}= 75

^{o}

Question 6 |

How many times in a day, are the hands of a clock in straight line but opposite in direction?

20 | |

22 | |

24 | |

48 |

Question 6 Explanation:

**Answer: Option B**

__Explanation:__

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12hrs. (Because between 5 and 7 they point in opposite directions at 6o'clock only).

So, in a day, the hands point in the opposite direction 22 times.

Question 7 |

At 3:40, the hour hand and the minutes hand of a clock form an angle of:

120 ^{o} | |

125 ^{o} | |

130 ^{o} | |

135 ^{o} |

Question 7 Explanation:

**Answer: Option C**

__Explanation:__

Question 8 |

At what time between 5:30 and 6:00 will the hands of a clock be at right angles?

44mins past 5 | |

44(7/11)mins past 5 | |

43(7/11)mins past 5 | |

43mins past 5 |

Question 8 Explanation:

**Answer: Option C**

__Explanation:__

Given: H = 5 and A = 90, Since 5 and 6 lies in the first half, a positive sign is considered.

T = (2/11)[H * 30 ± A]

T = (2/11)[5 * 30 + 90]

T = (2/11)[240]

T = 480/11

**T = 43(7 / 11)**

Question 9 |

An Accurate clock shows 7am. Through how many degrees will the hour hand rotate when the clock shows 1pm?

154 ^{o} | |

180 ^{o} | |

170 ^{o} | |

160 ^{o} |

Question 9 Explanation:

**Answer: Option B**

__Explanation:__

We know that angle traced by hrs hand in 12hrs = 360

^{o}

From 7 to 1, there are 6 hrs

Angle traced by the hour hand in 6hrs = 6 * (360/ 12)= 180

^{o}

Question 10 |

A watch gains 5 secs in 3 mins and was set right at 8AM. What time will it show at 10PM on the same day?

10 : 27 : 41 AM | |

8 : 51 : 04 AM | |

9 : 45 : 15 PM | |

10 : 23 : 20 PM |

Question 10 Explanation:

**Answer: Option D**

__Explanation:__

The watch gains 5secs in 3mins = 100secs in 1hrs

From 8AM to 10PM on the same day, time passed is 14hrs

In 14hrs, the watch would have gained 1400secs or 23mins 20secs

So, When the correct time is 10PM, the watch would show 10 : 23 : 20PM

There are 10 questions to complete.