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Metro City street cleaning occurs according to the following schedule: 19 Feb 2024, 23:06
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X: Central Street Y: First Street
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

65% (02:08) correct 35% (02:17) wrong based on 2194 sessions

History

Date
Time
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Not Attempted Yet
­Metro City street cleaning occurs according to the following schedule:

• First Street: every Thursday

• Second Street: every fourth Tuesday

• Third Street: every Monday

• Central Street: every third Wednesday

• Grand Street: every fourth Saturday

• Main Street: every second Friday

Select for X and for Y two streets such that every cleaning of the street chosen for X must be followed on the next day by a cleaning of the street chosen for Y, consistent with the given information. Make only two selections, one in each column.­

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X Y
First Street
Second Street
Third Street
Central Street
Grand Street
Main Street
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Metro City street cleaning occurs according to the following schedule: 21 Feb 2024, 00:32
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chetan2u
every cleaning of the street chosen for X must be followed on the next day by a cleaning of the street chosen for Y,

This means we take a street which is less often cleaned as X and more frequently cleaned as Y.

So Y should be checked for the ones cleaned every week. Every Monday and every Thursday.
Look for X as some street that is cleaned on a day prior that is Sunday or Wednesday. We have Central street being cleaned every third Wednesday.

Thus the two options that fit in are
X: Central street - every third Wednesday
Y: First street - every Thursday
Show more
­Hi chetan2u
Consider the situation, every second friday main street cleaning happens which is followed by the cleaning in first street in thursday. Hence, X can be main street and Y can be first street.
What is wrong here ?
Thanks
Anish­
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Metro City street cleaning occurs according to the following schedule: 21 Feb 2024, 00:57
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anish777

chetan2u
every cleaning of the street chosen for X must be followed on the next day by a cleaning of the street chosen for Y,

This means we take a street which is less often cleaned as X and more frequently cleaned as Y.

So Y should be checked for the ones cleaned every week. Every Monday and every Thursday.
Look for X as some street that is cleaned on a day prior that is Sunday or Wednesday. We have Central street being cleaned every third Wednesday.

Thus the two options that fit in are
X: Central street - every third Wednesday
Y: First street - every Thursday
­Hi chetan2u
Consider the situation, every second friday main street cleaning happens which is followed by the cleaning in first street in thursday. Hence, X can be main street and Y can be first street.
What is wrong here ?
Thanks
Anish­
Show more
­Hi Anish

Every cleaning on a given day in X should be followed by cleaning on next day on Y.
If you take X as the main street. X gets cleaned every second Friday, so Y should get cleaned at least on every second Saturday. But first street gets cleaned on every Thursday.

Thus, in your example, Y happens first and X happens on the next day. Actually, it has to be the other way.
 
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Metro City street cleaning occurs according to the following schedule: 17 Mar 2024, 19:57
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chetan2u
every cleaning of the street chosen for X must be followed on the next day by a cleaning of the street chosen for Y,

This means we take a street which is less often cleaned as X and more frequently cleaned as Y.

So Y should be checked for the ones cleaned every week. Every Monday and every Thursday.
Look for X as some street that is cleaned on a day prior that is Sunday or Wednesday. We have Central street being cleaned every third Wednesday.

Thus the two options that fit in are
X: Central street - every third Wednesday
Y: First street - every Thursday
Show more
­
how did we come to this?? whats the logic? please can you explain
"This means we take a street which is less often cleaned as X and more frequently cleaned as Y"
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Metro City street cleaning occurs according to the following schedule: 05 Oct 2024, 15:14
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the question wants a day (x) where we will have a consequent day (y) that will be cleaned. so if X is cleaned, then Y is cleaned the day after. I tried using options for X an pair them with Y. For example: if X is is • First Street: every Thursday, then we need a Y that is cleaned every Friday, and there is no such street cleaned every Friday, so X could not be First Street, then X: Second Street: every fourth Tuesday, then we will need a Y that is cleaned every Wednesday, and there is no such Y for example if x is Second Street and Y is Central Street: every third Wednesday, they could coincide or not, so X could not be Second street.But if X is Central Street: every third Wednesday, we will have a Y that will ALWAYS be cleaned after X, y will be First Street: every Thursday. we don not. care if X is all Wednesdays cleaned, we only care that if X is cleaned, as it says even 3 Wednesdays, we for sure will have the next day Y First Street: every Thursday cleaned. for example

monday:
Tuesday
Wednesday: X Central Street: every third Wednesday
Thursday: Y First Street: every Thursday
friday
Saturday

monday:
Tuesday
Wednesday: here there will no be cleaning since it is every 3 Wednesday
Thursday: Y First Street: every Thursday
friday
Saturday

monday:
Tuesday
Wednesday: here there will no be cleaning since it is every 3 Wednesday
Thursday: Y First Street: every Thursday
friday
Saturday

NOW THE SEQUENCE REPETS AGAIN

monday:
Tuesday
Wednesday: X Central Street: every third Wednesday
Thursday: Y First Street: every Thursday
friday
Saturday

anish777
chetan2u
every cleaning of the street chosen for X must be followed on the next day by a cleaning of the street chosen for Y,

This means we take a street which is less often cleaned as X and more frequently cleaned as Y.

So Y should be checked for the ones cleaned every week. Every Monday and every Thursday.
Look for X as some street that is cleaned on a day prior that is Sunday or Wednesday. We have Central street being cleaned every third Wednesday.

Thus the two options that fit in are
X: Central street - every third Wednesday
Y: First street - every Thursday
­Hi chetan2u
Consider the situation, every second friday main street cleaning happens which is followed by the cleaning in first street in thursday. Hence, X can be main street and Y can be first street.
What is wrong here ?
Thanks
Anish­
Show more
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Metro City street cleaning occurs according to the following schedule: 06 Oct 2024, 02:17
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A quick way would be logical way to tackle it but the solution in the video would surely be a safer way to get to the answer.

Logical way: every cleaning of the street chosen for X must be followed on the next day by a cleaning of the street chosen for Y,

This means we take a street which is less often cleaned as X and more frequently cleaned as Y.

So Y should be checked for the ones cleaned every week. Every Monday and every Thursday.
Look for X as some street that is cleaned on a day prior that is Sunday or Wednesday. We have Central street being cleaned every third Wednesday.

Thus the two options that fit in are
X: Central street - every third Wednesday
Y: First street - every Thursday

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Metro City street cleaning occurs according to the following schedule: 14 Jan 2025, 07:19
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Even though I got this question wrong in the mock, it's actually quite simple.

The question basically asks: "Which street will ALWAYS be cleaned the next day if you choose street X first?"

There is only 1 solution: every time you choose Central street, always the next day First street has to be cleaned.
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Metro City street cleaning occurs according to the following schedule: 27 Dec 2025, 10:33
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This took me 2 mins but this is how I solved. We need pairs ok
Mon Tues
Tues, wed
wed, thurs
thurs, frid
Frid, Satu

Now it cannot happen that a cleaning happens say on first day and not on second day....let's start elimination

Mon Tues - every monday will not have tues cleaning - out
Tues, wed - Can be a tuesday without wed cleaning - out
wed, thurs - yes every wed cleaning (even if it happens in 3rd week) will have thurs
thurs, frid - No
Frid, Satu - Nopes - don't get confused here - there can be a friday without Saturday cleaning.

This still took 2 mins :(
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Metro City street cleaning occurs according to the following schedule: 09 Jan 2026, 14:07
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This question is definitely easier to answer with a table. I made a table showing column headings:

M-Tu-W-Th-Fr-S

With rows for:

- Street Name
- Street Frequency

And the answer jumps out at you pretty quickly in that format.
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Metro City street cleaning occurs according to the following schedule: 27 Jun 2026, 07:56
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X = Central Street
Y = First Street

Quick 750-level check:

Third Street → every Monday → next day is Tuesday, but Second Street is cleaned only every fourth Tuesday, so NOT guaranteed.

Central Street → every third Wednesday → next day is Thursday, and First Street is cleaned every Thursday, so this MUST happen every time.

First Street → every Thursday → next day is Friday, but Main Street is cleaned only every second Friday, so NOT guaranteed.

Main Street → every second Friday → next day is Saturday, but Grand Street is cleaned only every fourth Saturday, so NOT guaranteed.

Therefore, the only pair that always works is:

Final Answer:
X = Central Street
Y = First Street.


The key insight is:
"Must be followed on the next day" means Y must occur EVERY time X occurs.
So immediately eliminate all streets that do not happen every week, because their next-day partner cannot be guaranteed.
Schedule:
  • First Street: every Thursday (weekly)
  • Second Street: every fourth Tuesday (not weekly)
  • Third Street: every Monday (weekly)
  • Central Street: every third Wednesday (not weekly)
  • Grand Street: every fourth Saturday (not weekly)
  • Main Street: every second Friday (not weekly)
Now think only in terms of weekdays:
Monday → Tuesday ❌ (Tuesday is not every week)
Wednesday → Thursday ✅ (Thursday is every week)
Thursday → Friday ❌ (Friday is not every week)
Friday → Saturday ❌ (Saturday is not every week)
Saturday → Sunday ❌ (no street)
Tuesday → Wednesday ❌ (Wednesday is not every week)
Only one chain survives:
Central Street (every third Wednesday) → First Street (every Thursday)
Why does this work?
The fact that Central Street occurs only every third Wednesday does not matter. Whenever it does occur, the next day is always Thursday, and First Street is always cleaned on Thursday. So the condition "must be followed on the next day" is satisfied every single time.
750-Level Mental Process (under 20 seconds):
  1. Mark weekly streets: Monday, Thursday.
  2. For a guaranteed next-day relationship, Y must be weekly.
  3. Check predecessors of weekly streets:
    • Monday needs Sunday → none.
    • Thursday needs Wednesday → Central Street.
  4. Answer: Central → First.
Pattern to memorize:
For "must always happen after" questions:
  • Start from the destination (Y).
  • Y must occur at least as frequently as X.
  • Weekly beats biweekly, monthly, or every nth week.
  • Then check only the day-of-week adjacency.
This avoids testing every possible pair one by one.
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