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A certain desk calendar shows the number of the day of the year and th 02 Nov 2023, 11:25
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A certain desk calendar shows the number of the day of the year and the number of days remaining in the year. If the calendar shows 1/364 for Sunday, January 1, on what day of the week does the calendar show 214/151?

A. Sunday
B. Monday
C. Tuesday
D. Wednesday
E. Thursday

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A certain desk calendar shows the number of the day of the year and th 02 Nov 2023, 12:43
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yrozenblum
A certain desk calendar shows the number of the day of the year and the number of days remaining in the year. If the calendar shows 1/364 for Sunday, January 1, on what day of the week does the calendar show 214/151?

A. Sunday
B. Monday
C. Tuesday
D. Wednesday
E. Thursday
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Given

January 01 → Sunday

The next Sunday is January 8, which the desk calendar shows as 8/357
The third Sunday is January 15, which the desk calendar shows as 15/350
.
.
Inference → Every Sunday has the numerator in the form of 7n+1

Hence, we can conclude that 7*(30) + 1 is a Sunday

211 → Sunday
212 → Monday
213 → Tuesday
214 → Wednesday

Option D
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A certain desk calendar shows the number of the day of the year and th 22 Apr 2024, 10:14
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214 MOD 7 = 4

SUN    MON    TUE    WED    THU    FRI    SAT
  1         2        3         4         5­        6       7­
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A certain desk calendar shows the number of the day of the year and th 22 Apr 2024, 17:29
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­A certain desk calendar shows the number of the day of the year and the number of days remaining in the year. If the calendar shows 1/364 for Sunday, January 1, on what day of the week does the calendar show 214/151?

Day 1 is a Sunday.

Day 214 is 213 days later.

Every 7 days later will be another Sunday.

210 is divisible by 7.

So, day 213 is 213 - 210 = 3 days after a Sunday.

Monday - 1

Tuesday - 2

Wednesday - 3

A. Sunday
B. Monday
C. Tuesday
D. Wednesday
E. Thursday

Correct answer: D
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A certain desk calendar shows the number of the day of the year and th 18 Jul 2025, 02:15
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For those that made the silly mistakes in counting which number the corresponding day of the week falls (dumbass who chose Thursday here), I find it helps to write out the sequence and the day next to it to visualise and avoid this confusion.
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A certain desk calendar shows the number of the day of the year and th 06 Aug 2025, 05:19
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1+7n will be Sunday, for every integer n.

n = 30 means 211 days will have 30 cycles complete.

212 = Monday
213 = Tuesday
214 = Wednesday - our answer.
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A certain desk calendar shows the number of the day of the year and th 29 Aug 2026, 11:47
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hi
can you elaborate a bit more on this ?


Rohanx9
1+7n will be Sunday, for every integer n.

n = 30 means 211 days will have 30 cycles complete.

212 = Monday
213 = Tuesday
214 = Wednesday - our answer.
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A certain desk calendar shows the number of the day of the year and th 01 Sep 2026, 11:34
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Hi laborumpossimus,

The posts above are all correct, but they jump fast, so let me walk the whole path slowly. There are really two small ideas hiding in this question.

Idea 1: What does "214/151" actually tell us?

The calendar shows day number / days remaining. On Jan 1 it reads 1/364, and notice that 1 + 364 = 365 - the whole year. So every display always adds up to 365.

Check the target: 214 + 151 = 365. It fits, so "214/151" simply means day number 214 of the year. That's all that display is - we can ignore the 151 from here on.

Idea 2: Which weekday is day 214?

Day 1 is a Sunday, and the weekdays repeat in a 7-day cycle. So every time we add 7 to the day number, we land on Sunday again:

- Day 1 - Sunday
- Day 8 - Sunday
- Day 15 - Sunday

That's the "7n + 1 is a Sunday" pattern the earlier posts used. The biggest Sunday at or below 214 is:

- 7 × 30 + 1 = 211 - Sunday

Now just step forward from there, one day at a time:

- 211 - Sunday
- 212 - Monday
- 213 - Tuesday
- 214 - Wednesday

So the answer is D, Wednesday.

The one spot people slip

The trap (this is why some pick Thursday) is counting the days between instead of landing on the right day. Day 214 is 213 days after day 1, not 214. Since 213 = 7 × 30 + 3, you move 3 days past Sunday - Monday, Tuesday, Wednesday. Writing the short list out, like above, kills that off-by-one error every time.

Answer: D

laborumpossimus
hi
can you elaborate a bit more on this ?



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