## Saturday, June 28, 2014

### calendar ( Quantitative Aptitude ) Practice Questions

Odd Days:
We are supposed to find the day of the week on a given date.
For this, we use the concept of 'odd days'.
In a given period, the number of days more than the complete weeks are called odd days.
·  Leap Year:
(i). Every year divisible by 4 is a leap year, if it is not a century.
(ii). Every 4th century is a leap year and no other century is a leap year.
Note: A leap year has 366 days.
Examples:
1. Each of the years 1948, 2004, 1676 etc. is a leap year.
2. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
3. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.
·  Ordinary Year:
The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.
·  Counting of Odd Days:
1. 1 ordinary year = 365 days = (52 weeks + 1 day.)
1 ordinary year has 1 odd day.
1. 1 leap year = 366 days = (52 weeks + 2 days)
1 leap year has 2 odd days.
1. 100 years = 76 ordinary years + 24 leap years
= (76 x 1 + 24 x 2) odd days = 124 odd days.
= (17 weeks + days) 5 odd days.
Number of odd days in 100 years = 5.
Number of odd days in 200 years = (5 x 2) 3 odd days.
Number of odd days in 300 years = (5 x 3) 1 odd day.
Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.
Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.
·  Day of the Week Related to Odd Days:
 No. of days: 0 1 2 3 4 5 6 Day: Sun. Mon. Tues. Wed. Thurs. Fri. Sat.

SOLVED EXAMPLES
1.     What was the day of the week on, 16th July, 1776 ( Tuesday)
2.     What was the day of the week on 16th August, 1947? (Saturday)
3.     What was the day of the week on 16th April, 2000? (Sunday )
4.     On what dates of Jull.2004 did Monday fall? (5th , 12th , 19th and 26th )
5.     Prove that the calendar for the year 2008 will serve for the year 2014.
6.     Prove that any date in March of a year is the same day of the week corresponding date in November that year.
EXERCISE
1.     January 1, 2004 was Thursday. What day of the week lies on Jan. 1, 2005?
2.     On 8th March, 2005 Wednesday falls. What day of the week was it on 8th March, 2004?
3.     The calendar for the year 2005 is the same as for the year:
i.      2010     ii. 2011   iii. 2012   iv. 2013
4.     On what dates of April, 2001 did Sunday fall?
A.        1st , 8th , 15th , 22nd , 29th              B. 2nd , 9th , 16th , 23rd , 30th
C.        4th , 11th , 18th , 25th                      D. 3rd , 10th , 17th , 24th
5.     What will be the day of the week on 1st January, 2010?
6.     What was the day of the week on 17th June, 1998?
7.     What was the day of the week on 28th May, 2003?
8.     Today is Friday. After 62 days, it will be:
9.     The last day of a century cannot be:
i.      Monday    ii. Wednesday   iii. Friday   iv. Tuesday
10.                        The first Republic Day of India was celebrated on 26th January, 1950. It was:

### clocks ( Quantitative Aptitude ) Practice Questions

IMPORTANT FACTS
The Face or dial of a watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.
A clock has two hands. The smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.
i) In 60 minutes, the minute hand gains 55 minutes on the hour hand.
ii) In every hour, both the hands coincide once.
iii) The hands are in the same straight line when they are coincident or opposite to each other.
iv) When the two hands are at right angles, they are 15 minute spaces apart.
v)When the hand's are in opposite directions, they are 30 minute spaces apart.
vi)Angle traced by hour hand in 12 hrs = 360°.
vii)Angle traced by minute hand in 60 min. = 360°.

Too fast and too slow: If a watch or a clock indicates 8.15, when the correct time, 8 is said to be 15 minutes too fast.
On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

SOLVED EXAMPLES
1.     Find the angle between the hour hand and the minute hand of a clock when 3.25.(47 ½ )
2.     At what time between 2 and 3 o'clock will the hands of a clock be together?(10 10/11 minutes pas 2)
3.     At what time between 4 and 5 o'clock will the hands of a clock be at right angle? (5 5/11 minutes past 4  or 38 2/11 minutes past 4)
4.     Find at what time between 8 and 9 o'clock will the hands of a clock being the same straight line but not together. (10 10/11 minutes past 8)
5.     At what time between 5 and 6 o'clock are the hands of a clock 3 min apart? (24 minutes past 5 or 31 5/11 minutes past 5)
6.     The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose? ( 10 10/43 minutes in 24 hours)
7.     A watch which gains uniformly is 6 min. slow at 8 o'clock in the morning Sunday and it is 6 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct? (20min past 7pm on Wednesday)
8.     A clock is set right at 6 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day? (11 pm)

9.     A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day? (48 minutes past 12)

EXERCISE
1.     A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:(155)
2.     An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? (180)
3.     At 3.40, the hour hand and the minute hand of a clock form an angle of: (135)
4.     The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: (75)
5.     The angle between the minute hand and the hour hand of a clock when the time is 8.30, is: (10)
6.     At what angle the hands of a clock are inclined at 15 minutes past 5?  (67 ½ )
7.     The reflex angle between the hands of a clock at 10.25 is: (197 ½ )
8.     How many times do the hands of a clock coincide in a day?  (22)
9.     How many times in a day, the hands of a clock are straight? (44)
10.                        How many times are the hands of a clock at right angle in a day? (44)
11.                        How many times in a day, are the hands of a clock in straight line but opposite in direction? (22)
12.                        How much does a watch lose per day, if its hands coincide every 64 minutes? (32 8/11)
13.                        At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other? (16 4/11)
14.                        At what time between 9 and 10 o'clock will the hands of a watch be together? (49 1/11 minutes past 9)
15.                        At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? (5 5/11 minutes past 7)
16.                        At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions? (54 6/11 minutes past 4)
17.                        At what time between 5.30 and 6 will the hands of a clock be at right angles? (43 7/11 minutes past 5)
18.                        A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?        (2 pm on Wednesday)
19.                        A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is: (4 pm)

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