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# Suppose July of year N has five Mondays. Which of the following must

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Math Expert
Joined: 02 Sep 2009
Posts: 62289
Suppose July of year N has five Mondays. Which of the following must  [#permalink]

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18 Mar 2019, 23:11
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Difficulty:

55% (hard)

Question Stats:

53% (02:24) correct 47% (01:47) wrong based on 19 sessions

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Suppose July of year N has five Mondays. Which of the following must occurs five times in the August of year N? (Note: Both months have \$31\$ days.)

(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday

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Posts: 3334
Re: Suppose July of year N has five Mondays. Which of the following must  [#permalink]

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18 Mar 2019, 23:40

Solution

Given:
• The month July of year N has five Mondays.

To find:
• Among the given options, which day must occur five times in the August of year N

Approach and Working:
If July has five Mondays, then those Mondays can be any one of 1 – 8 – 15 – 22 – 29th July OR 2 – 9 – 16 – 23 – 30th July OR 3 – 10 – 17 – 24 – 31st July.

Case 1: 1 – 8 – 15 – 22 – 29th July are Mondays
In such case,
• 1st August: Thursday
• 2nd August: Friday
• 3rd August: Saturday

Hence, Thursday or Friday or Saturday can occur 3 times on August.

Case 2: 2 – 9 – 16 – 23 – 30th July are Mondays
In such case,
• 1st August: Wednesday
• 2nd August: Thursday
• 3rd August: Friday

Hence, Wednesday or Thursday or Friday can occur 3 times on August.

Case 3: 3 – 10 – 17 – 24 – 31st July are Mondays
In such case,
• 1st August: Tuesday
• 2nd August: Wednesday
• 3rd August: Thursday

Hence, Tuesday or Wednesday or Thursday can occur 3 times on August.

Now, combining all 3 cases, we can definitely say that Thursday will occur 3 times in August.

Hence, the correct answer is option D.

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Re: Suppose July of year N has five Mondays. Which of the following must   [#permalink] 18 Mar 2019, 23:40
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