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# How many times does Mary get paid in a certain year X ?

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Math Expert
Joined: 02 Sep 2009
Posts: 59561
How many times does Mary get paid in a certain year X ?  [#permalink]

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20 Feb 2018, 09:12
00:00

Difficulty:

35% (medium)

Question Stats:

58% (00:48) correct 42% (00:44) wrong based on 41 sessions

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How many times does Mary get paid in a certain year X ?

(1) Mary is paid every Friday.

(2) The year X is a leap year.
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Joined: 22 Aug 2013
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Location: India
Re: How many times does Mary get paid in a certain year X ?  [#permalink]

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20 Feb 2018, 09:30
Bunuel wrote:
How many times does Mary get paid in a certain year X ?

(1) Mary is paid every Friday.

(2) The year X is a leap year.

Every leap year has 366 days. Now, if we divide 366 by 7, and write it in the form 'Dividend = Divisor*Quotient + Remainder' then we get:

366 = 7*52 + 2

This means all 7 days (Monday to Sunday) appear at least 52 times in a leap year, but there are 2 days which will appear one more time. These two days will obviously be the first two days of the year. So if a leap year has started with Monday (meaning if 1st January is Monday), then the first two days (Monday and Tuesday) will appear 53 times in that year, rest five days (Wednesday to Sunday) will appear 52 times.

Statement 1

Mary is paid every Friday, but we dont know how many Fridays are there in that year, we dont know whether its a normal year or a leap year. Not sufficient.

Statement 2
No information about how often Mary gets paid. Not sufficient.

Combining the two statements, Mary is paid every Friday, and this is a leap year. Now, if this year starts with Thursday or Friday, then Friday will appear 53 times this year (first two days will be 53 times, as explained above). But if this year starts with any other day then Friday will appear 52 times only.
so Mary is paid either 52 or 53 times, not sufficient.

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Re: How many times does Mary get paid in a certain year X ?  [#permalink]

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20 Feb 2018, 10:04
IMO E.

A. In general we can infer that she gets paid 52 times but if it is a leap year then we cannot claim this with certainty unless we know: starting day of the year & type of the year. Insufficient.

B. No information about how many times she gets paid. Insufficient.

A & B together: Still we have no idea about the starting day of the year. Hence, she might have been paid 52 times or 53 times. Thus, Insufficient.
Re: How many times does Mary get paid in a certain year X ?   [#permalink] 20 Feb 2018, 10:04
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