GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Feb 2019, 01:05

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

Find the probability that a randomly selected year has 53 Sundays.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
User avatar
G
Joined: 11 Dec 2013
Posts: 114
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
GMAT ToolKit User
Find the probability that a randomly selected year has 53 Sundays.  [#permalink]

Show Tags

New post 30 Jan 2019, 21:23
2
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

27% (02:06) correct 73% (01:17) wrong based on 22 sessions

HideShow timer Statistics

Find the probability that a randomly selected year has 53 Sundays.
A) \(\frac{1}{7}\)
B) \(\frac{2}{7}\)
C) \(\frac{3}{7}\)
D) \(\frac{3}{28}\)
E) \(\frac{5}{28}\)

_________________

KUDOS will increase your score

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: Find the probability that a randomly selected year has 53 Sundays.  [#permalink]

Show Tags

New post 31 Jan 2019, 07:00
4d wrote:
Find the probability that a randomly selected year has 53 Sundays.
A) \(\frac{1}{7}\)
B) \(\frac{2}{7}\)
C) \(\frac{3}{7}\)
D) \(\frac{3}{28}\)
E) \(\frac{5}{28}\)



The question involves knowing leap year and number of days in a year..

So, let us talk of this question in two different cases..
(1) A normal year
It has 365 days which is 52 weeks and 1 day. So any of the 7 days from Sunday to Saturday that the year starts with will be 53 and rest 6 will be 52. Probability of Sunday will be as any of other seven so \(\frac{1}{7}\).
(2) A Leap year
It has 366 days which is 52 weeks and 2 days. So any 2 of the 7 days from Sunday to Saturday that the year starts with will be 53 and rest 5 will be 52. Probability of Sunday will be as any of other seven so \(2*\frac{1}{7}=\frac{2}{7}\). Multiplication by 2 is because we have 2 days that can be 53.

Now we have to check the probability of a normal year and a leap year.
Here, we will take a standard case that every 4th year is leap year and will not consider the 1000th year as non-leap
so Probability of normal year is 3/4 and that of leap year is 1/4.

Answer \(\frac{3}{4}*\frac{1}{7}+\frac{1}{4}*\frac{2}{7}=\frac{5}{28}\)

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

SVP
SVP
User avatar
G
Joined: 18 Aug 2017
Posts: 1926
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: Find the probability that a randomly selected year has 53 Sundays.  [#permalink]

Show Tags

New post 31 Jan 2019, 08:25
4d wrote:
Find the probability that a randomly selected year has 53 Sundays.
A) \(\frac{1}{7}\)
B) \(\frac{2}{7}\)
C) \(\frac{3}{7}\)
D) \(\frac{3}{28}\)
E) \(\frac{5}{28}\)


Total days in year = 365 or say 52 weeks and 1 day
Total days in leap year = 366 days or say 52 weeks and 2 days

so P of sunday in non leap year = 1/7
and P of sunday in leap year = 2*1/7 ; reason why since we have a day extra in a leap year so chances are that sunday can be on that extra day

P of a leap year is 1/4 and non leap year is 3/4
so for sunday
1/4*2/7 + 3/4*1/7
2+3/28 ; 5/28
IMO E
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Senior Manager
Senior Manager
avatar
G
Joined: 02 Apr 2014
Posts: 476
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Find the probability that a randomly selected year has 53 Sundays.  [#permalink]

Show Tags

New post 11 Feb 2019, 19:24
Non leap year case: (365 % 7) = 1, (every day in a week, repeats 52 times), now for 53 sundays, the remaining last day has to be sunday, then Jan 1 of that year must be sunday.

probability of 53 sundays = (3/4)(probability of non-leap year) * (1/7) ( probability of jan1 of that year to be sunday) = 3/28

Leap year case: (366 % 7) = 2, (every day in a week, repeats 52 times), now two days remaining, for 53 sundays, either of last two days must be sunday, then Jan 1 of that year has to be either saturday or sunday.

probability of 53 sundays = (1/4) (probability of leap year) * (2/7) (probability of jan 1 of that year to be either sunday or saturday) = 2/28

so total probability (leap year case + non leap year case) = (3/28) + (2/28) = 5/28
GMAT Club Bot
Find the probability that a randomly selected year has 53 Sundays.   [#permalink] 11 Feb 2019, 19:24
Display posts from previous: Sort by

Find the probability that a randomly selected year has 53 Sundays.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.