How many days per calendar year is the month a factor of the day?

1 Jan 31 31/1=31
2 Feb 28 28/2=14
3 Mar 31 31/3=10
4 Apr 30 30/4=7
5 May 31 31/5=6
6 Jun 30 30/6=5
7 Jul 31 31/7=4
8 Aug 31 31/8=3
9 Sep 30 30/9=3
10 Oct 31 31/10=3
11 Nov 30 30/11=2
12 Dec 31 31/12=2
Total=90
Thus D

D.

Months will be 1,2,3 till 12.

Calculated manually with 28 for feb and 30/31 for rest months to come to addition of all the no of days for.
Eg: jan is 1. It's s factor of all 31 days. So, 31.
Feb is 2. Factor of all even nos till 28. So, 14.
And likewise

Posted from GMAT ToolKit
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30 + 15 + 30/3 + floor (30/4) + ......+ffloor (30/12)
=90

VERITAS PREP OFFICIAL SOLUTION:

Solution: 90

All 31 days in January, because 1 is a factor of all integers

14 of the 28 days in February (because every other day is divisible by 2)

10 of the 31 days in March (the multiples of 3 between 3 and 30)

7 days in April (the multiples of 4 between 4 and 28)

6 days in May (the multiples of 5 between 5 and 30)

5 days in June (the multiples of 6 between 6 and 30)

4 days in July (the multiples of 7 between 7 and 28)

3 days in August (the multiples of 8 between 8 and 24… so, so close if only the month were 32 days long!)

3 days in September (9th, 18th, 27th)

3 days in October (10th, 20th,30th)

2 days in November (11th, 22nd)

2 days in December (12th, 24th)

And there you have it! As you can see, as you move through the months, your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights… This is a very valuable skill to remember on test day!
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Are we required in GMAT to know how many days each month has ?
(30-31 )

Even if not for GMAT, ideally one should know the number of days in each of the months.
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January = 1st month = factor of all 31 days = 31

February = 2nd month = factor of all even days = 14

March = 3rd month = factor of all 'multiple of 3' days = 10

April = 4th month = factor of all 'multiple of 4' days = 7

May = 5th month = factor of all 'multiple of 5' days = 6

June = 6th month = factor of all 'multiple of 6' days = 5

July = 7th month = factor of all 'multiple of 7' days = 4

August = 8th month = factor of all 'multiple of 8' days = 3

September = 9th month = factor of all 'multiple of 9' days = 3

October = 10th month = factor of all 'multiple of 10' days = 3

November = 11th month = factor of all 'multiple of 11' days = 2

December = 12th month = factor of all 'multiple of 12' days = 2


Total: 31 + 14 + 10 + 7 + 6 + 5 + 4 + 3 + 3 + 3 + 2 + 2 = 90.

Answer D
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