# Problems On Numbers Aptitude Question and Answer – Quantitative Aptitude

Problems On Numbers Aptitude Question and Answer – Formulas & Tricks

Problems On Numbers Formulas

• (A + B)(A – B) = (A2 – B2)
• (A + B)2 = (A2 + B2 + 2AB)
• (A – B)2 = (A2 + B2 – 2AB)
• (A + B + C)2= A2 + B2 + C2 + 2(AB + BC + CA)
• (A3 + B3) = (A + B)(A2 – AB + B2)
• (A3 – B3) = (A – B)(A2 + AB + B2)
• (A3 + B3 + C3 – 3ABC) = (A + B + C)(A2 + B2 + C2 – AB – BC – AC)
• When A + B + C = 0, then A3 + B3 + C3 = 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 n2
• 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 ExplanationQuantitative 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?
 A 11pm B 12pm C 1pm D 2pm
Question 1 Explanation:
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?
 A 57.5 degrees B 67.5 degrees C 77.5 degrees D 87.5 degrees
Question 2 Explanation:
Explanation: Question 3
How many times do the hands of a clock coincide in a day?
 A 20 B 21 C 22 D 24
Question 3 Explanation:
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?
 A 22 B 24 C 44 D 48
Question 4 Explanation:
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:
 A 80o B 75o C 60o D 105o
Question 5 Explanation:
Explanation: Therefore, Required Angle = (255 - 180)o = 75o
 Question 6
How many times in a day, are the hands of a clock in straight line but opposite in direction?
 A 20 B 22 C 24 D 48
Question 6 Explanation:
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:
 A 120o B 125o C 130o D 135o
Question 7 Explanation:
Explanation: Question 8
At what time between 5:30 and 6:00 will the hands of a clock be at right angles?
 A 44mins past 5 B 44(7/11)mins past 5 C 43(7/11)mins past 5 D 43mins past 5
Question 8 Explanation:
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)
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?
 A 154o B 180o C 170o D 160o
Question 9 Explanation:
Explanation:
We know that angle traced by hrs hand in 12hrs = 360o
From 7 to 1, there are 6 hrs
Angle traced by the hour hand in 6hrs = 6 * (360/ 12)= 180o
 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?
 A 10 : 27 : 41 AM B 8 : 51 : 04 AM C 9 : 45 : 15 PM D 10 : 23 : 20 PM
Question 10 Explanation: