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[Reasoning] Calendar Questions: Finding day or date, concepts, shortcuts
explained
1. Introduction
2. Concept: 7 Day cycle
1. SSC-CGL 2000 Question on 7-Day cycle
3. Concept: Day Gain Day loss
1. What is Leap year?
2. SSC Investigator 2010 (Anniversary)
3. SSC CGL 2011 (Anniversary)
4. CAT-2001 Question on calendar5. Question 1988 to 1989
6. Speed Techniquetip#1
7. Speed Technique tip#2
4. Concept: Date Without reference Day
1. Table#1: The odd days
2. Tablet #2: Number-Day
3. What day of week was on15th ugust,1947?
4. Speed increase tip#1:
5. Find the day on 10th May, 1857?6. Speed Technique #3
5. Mock questions
Introduction
Articleprepared with help of Mr. Deepak Singh.
There are two main types of questions from Calendar
when youre given a reference day when youre given no
reference Day
What day of week was it on 5th November, 1989
if it wasMonday on 4th April, 1988 ?
a. Monday
b. Tuesday
c. Saturday
d. Sunday
What wasthe day on 15th
august 1947?
a. Sunday
b. Monday
c. Tuesday
d. Friday
Here question tells us that 4thApril 88 was
Monday, so we have a reference day.
Here question doesnt give
us any reference day.
can be solved with just two concepts
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1. 7 day cycle
2. day gain-Day loss concept
need to just mugup 2 table,
and few steps.
Although calendar question is not asked every year in every exam. But If and
when calendar question is asked, just follow the given procedure and youll get
the accurate answer= one mark is guaranteed=in that sense, cost: benefit is
great.
Concept: 7 Day cycle
Name of the day will repeat after seven
days.
1stAugust 2013= Thursday. Therefore 1st
August + 7 =8thAugust also has to beThursday.
Then what day will be 10thAugust 2013?
1stAugust =Thursday => 1+7=8 August is
also Thursday
And 8 August + 2 =10 August will be
Thursday + 2 days =>Saturday.
lets try a simple question from SSC
SSC-CGL 2000 Question on 7-Day cycle
If 9thof the month falls on the day preceding Sunday, then on what day will 1st
of the month fall?
a. Friday
b. Saturday
c. Sunday
d. Monday
As per the question 9thof the Month=Saturday. (day preceding Sunday)
Day name repeats after 7 days.
Therefore 9 minus 7=2ndof the given month is also Saturday.
Then 1stof the given month= Saturday Minus one day = Friday, Ans A
Concept: Day Gain Day loss
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Tuesday on 30thSeptember 2003 Ans A.
Now, How about a CAT level question:
CAT-2001 Question on calendar
Dec 9, 2001 is Sunday then what was the day on Dec 9, 1971?
A. Thursday
B. Wednesday
C. Saturday
D. Sunday
Same day gain, Day loss
1971 to 2001=how many jumps?
2001-1971=Total 30 years jump
Out of those 30 years, how many leap years?
72, 76,.,00 (multiples of of 4 and 2000 is also leap year because It is multiple
of 400)
but no need to manually count leap years.
if you observe
18 x 4 =(19)72
25x 4 =(20)00
so from 18 to 25 = total 8 leap years. (plz note: 25-18=7 years, but weve to
include both years as welltherefore.. in such counting, itll be 25-18+1=8 leap
years)
back to the start: 30 years jump and out of them 8 were leap years.
Meaning 22 normal years + 8 leap years = total 30 years
22 normal years (+1 day gain) 22 x 1 =22 days
8 leap years (+2 days gain) 8 x 2= 16 days
total gain 22+16=38 days
38/7=(75)+3 remainder
Meaning whatever was the day on Dec 9, 1971, itll move to +3 days on dec 92001
Reverse is also true: Whatever was the day on Dec 2001, itll be three days less
on Dec 9 1971:
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Since Dec 2001 was Sunday therefore,
Sunday Minus 3 days= (just count in your head): SaturdayFridayThursday.
Final answer is A: Thursday
Question 1988 to 1989
What day of week was it on 5th November,1989 if it was Monday on 4th April,
1988 ?
1. Monday
2. Tuesday
3. Saturday
4. Sunday
Recall our Day gain Day loss principle
For Non-Leap year, When we proceed forward by one year, then 1 day is gained
and vice-versa.
If 4th April, 1988 = Monday, then 4th April, 1989 = Tuesday (Because 1989 is a
non-leap year)
Remaining days until 5thNov.89
Month DaysApril (4 to 30) 26
May 31
June 30
July 31
Aug 31
Sep 30
Oct 31
Nov 5
total 215
=Tuesday + 215
Divide 215 with 7 to find the remainder
215=(30*7)+5 Hence five is the remainder
Back to the problem
= Tuesday + [5 days]
What is the 5thday after Tuesday? Count on your fingertip: Wed, Thurs., Fri,
Sat., Sunday
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=Sunday (Final answer D)
Speed Technique tip#1
in above problem, if you dont want to waste time in adding the days like
26+31+30. then use following approach
30 days=(7*4)+2=> 2 remainder
31 days=(7*4)+3=> 3 remainder.
Month Days Remainder with 7
April (4 to 30) 2 6 5 (because 26=7*3+5)
May 31 3
June 30 2
July 31 3
Aug 31 3Sep 30 2
Oct 31 3
Nov 5 5
total dont need 26
Divide this by 7 and find remainder: 26=(7*3)+5 so remainder is 5
=Tuesday + 5
= Tuesday + 5 days
=Sunday
Speed Technique tip#2
in speed tech #1, if you dont want to waste time in adding the remainders of
seven: 5+3+2. then do following
pickup remainders that add upto 7 and cancel them.
for example 5+2=7. So Ill cancel each such pair in the table. Observe
Month Days Remainder with 7after cancelling numbers that add upto
7 (e.g. 5+2)
April (4 to
30) 26 5
May 31 3
June 30 2July 31 3
Aug 31 3
Sep 30 2
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Oct 31 3
Nov 5 5
total dont
need 12
After cancelling the two pairs of (5+2), Im left with four 3s= 12 (because 4 x
3=12)
=Tuesday + 12
now divide 12 with 7 find remainder: 12=7*1 +5
= Tuesday + 5 days
=Sunday
Concept: Date Without reference Day
Example: What was the day on 15 thAugust 1947?
To solve this type of questions, youve to first mug up these two tables:
Table#1: The odd days
100 5
200 3
300 1
400, 800, 1200, 1600 etcmultiples of 400 0
^ok but what is the use of above table? It tells us the number of odd days in
that given year. I dont want to bore you with the theory so just mug up those
values.
Tablet #2: Number-Day0, 7 Sunday
1 Monday
2 Tuesday
3 Wednesday
4 Thursday
5 Friday
6 Saturday
Just remember that 1 to 6 is Monday to Saturday and 0 or 7=Sunday.
^ok but what is the use of above table? just hang on for a few more paragraphs
and youll know! Now lets try a sum
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What day of week was on 15th ugust,1947?
Step 1:
Subtract the given year by 1.
1947 -1 = 1946
Step 2:
Break into relevant years as in table #1.
100 5
200 3
300 1
400, 800, 1200, 1600 etc (multiples of 400) 0
Therefore,
1946 = 1600 + 300 + ( 46 )
Step 3:
Now write corresponding values from the table: 1600=0 and 300=1
1946=>0+1+(46)
Step 4:
Now for the number in bracket (46), divide it by 4 and add quotient in same
line.
in this case 46=(11x4)+2 therefore, 11 is quotient and 2 is remainder. Were
concerned with number and quotient here
1946=0+1+(46+11)
Step5:
Now add all these numbers and divide by 7
0+1+(46+11)
=58
And when you divide 58 by 7, you get 58= (7*8)+2. Therefore remainder is 2.
we got the number 2 = well call this our 31Dec Number
Observe second table
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0, 7 Sunday
1 Monday
2 Tuesday
3 Wednesday
4 Thursday
5 Friday
6 Saturday
From this table we can see that 2=>Tuesday
It means 31stDecember 1946 was Tuesday. Now we apply our 7day cycle
concept to find out the day on 15thAugust 1947 using the following formula
Given day= (our 31Dec Number 2)+ *how many days till we reach 15 th
August?*
Step 6
from 1stJan 1947 till we reach 15thAugust 1947 days in given month
Jan 31
feb (not leap year) 28
march 31
april 30
may 31
june 30july 31
august (upto 15thAug) 15
total 227 days
back to the bold part
(Our 31Dec Number)+ *how many days till we reach 15thAugust?*
=2 + 227
=229
Step 7
Divide this number (229) by 7 and whatever remainder you get= that is our day
from table #2
229/7=(32*7)+5
so 5 is the remainder and as per table#2
0, 7 Sunday
1 Monday
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2 Tuesday
3 Wednesday
4 Thursday
5 Friday
6 Saturday
5=>Friday.
That means 15thAugust 1947 was Friday.
Speed increase tip#1:
in above 15thAugust example, Back to the step6
31Dec Number+ *how many days till we reach 15thAugust?*
after that, we did following:
from 1stJan 1947 till we reach 15thAugust 1947 days in given month
Jan 31
feb (not leap year) 28
march 31
april 30
may 31
june 30july 31
august (upto 15thAug) 15
total 227 days
^as you see we had to sum of 31+28+31.=lot of time taken in doing the
addition (+).
So, it is better to just add remainders for each month with 7
30=(7*4)+2=> 2 remainder
31=(7*4)+3=> 3 remainder.
Now observe again
from 1stJan 1947till we reach 15thAugust
1947
days in given
month
remainder with
7
Jan 31 3
feb (not leap year) 28 0march 31 3
april 30 2
may 31 3
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june 30 2
july 31 3
august (upto 15thAug) 15 1 (because
14+1)
total 227 days 17
now instead of 227 we can simply write 17
Our 31Dec Number+ *how many days till we reach 15thAugust?*
=2+17
=19
Therefore 19/7 = its remainder will tell us the final day
19=(7*2) + 5=therefore remainder is 5 and as per table#2, 5 means Friday.
Find the day on 10th May, 1857?
Subtract 1 from the given year
1857-1=1856
Now breakup 1856 as per our table #1
100 5200 3
300 1
400, 800, 1200, 1600 etc (multiples of 400) 0
1856
=1600+200+(56)
write corresponding values from table#1
=0+3+(56)
Divide the bracket number by 4 and write quotient along with number
56=14*4 + 0 therefore quotient is 14
1856
=0+3+(56+14)
add these numbers and divide by 7 find remainder
=73/7
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=remainder 3
Speed Technique #3
after doing the division with 4 to find quotient step, you got following
=0+3+(56+14)
Whenever you see the multiple of 7, just scratch that number (because itll give
remainder zero anyways)
for example
=0+3+(56+14)
Here both 56 and 14 are multiples of 7 so even if you divide them by 7, youre
going to get zero as remainder.
=0+3+0+0=3 is 31Dec Number
as per table#2: 3 means Wednesday. Meaning 31stDecember 1856 was
Wednesday
now our 31Dec Number+ how many days till 10th May, 1857?
from 1stJan 1857till we reach 31th
May 1857
days in given
month remainder with 7
Jan 31 3
feb (not leap year in 1857) 28 0
march 31 3
april 30 2
may 10 3, Because 10=(7 x
1)+3
total *not needed* 11
back to our problem
our 31Dec Number+ how many days till 10th May, 1857?
=3 + 11
=14
when 14 is divided by 7 we get zero as remainder.
as per table#2
0, 7 Sunday
1 Monday
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2 Tuesday
3 Wednesday
4 Thursday
5 Friday
6 Saturday
Zero means Sunday. so final answer 10thMay 1857 was Sunday.
Extra facts:
1. The 1st day of a century must be Tuesday, Thursday, or Saturday.
2. The last day of a century cannot be Tuesday, Thursday, or Saturday.
Mock questions
1. In 2013, Gandhis birth-anniversary is on Wednesday. In which nearest
future year, will his birth-anniversary be on Monday?
2. If 29thApril 2013 is Monday then what is the day on 30thNovember 2013?
3. If June 11, 2013 is Monday, what was the day on July 11, 2000
4. What was the day on 9/11 attacks in 2001
5. What was the day on 26/11 attacks in 2008
Answers
1. 2017
2. 30/nov/13=Saturday3. 11/jul/00=Monday
4. 11/09/01=Tuesday
5. 26/11/08=Wednesday
For more articles on aptitude, visit Mrunal.org/aptitude
URL to article: http://mrunal.org/2013/08/reasoning-calendar-questions-finding-
day-or-date-concepts-shortcuts-explained.html
Posted By Mrunal On 09/08/2013 @ 22:58 In the category Aptitude
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