Explanation
ANALYTICAL REASONING
Questions 1–4
A workshop that restores used pieces of furniture operates according to the following schedule:
A piece of furniture is examined three calendar days after it is received in the workshop. (Thus, if it is received on the first day of the month, it is examined on the fourth.) On the next Monday following the examination, the piece of furniture is delivered to the restoration room.
Restoration work may be finished one, two, or three calendar days after a piece of furniture is delivered to the restoration room. On the next Wednesday following the completion of the restoration work, a piece of furniture is varnished. Two calendar days later, the varnish is dry, and a piece of furniture may be shipped. All restored pieces of furniture are shipped at the close of business on the 15th or the 30th day of the month.
This year, the first day of the month of January is a Friday.
1. If the workshop receives a steady supply of used pieces of furniture, on how many days during January will piece of furniture varnishing take place?
A) Two
B) Three
C) Four
D) Five
E) Six
Varnish only happens on Wednesdays.
January Wednesdays = 6, 13, 20, 27 → that’s 4.
And because steady supply ensures that there’s always some piece ready, varnishing happens every Wednesday.
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2. If a used piece of furniture is received at the workshop on Tuesday, January 5th, its restoration work will be completed no later than:
A) Monday the 11th
B) Wednesday the 13th
C) Thursday the 14th
D) Friday the 15th
E) Wednesday the 20th
Receive = Jan 5 (Tue).
Exam = Jan 8 (Fri).
Next Monday = Jan 11 → delivery.
Restoration completes 1–3 days later → at the latest = Jan 14 (Thu).
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3. To be certain that a restored piece of furniture will be shipped from the workshop on January 30th, what is the latest date by which it may be received at the workshop?
A) Thursday the 14th
B) Friday the 15th
C) Saturday the 16th
D) Monday the 18th
E) Tuesday the 19th
Work backwards:
To be shipped Jan 30, varnish must be dry by Jan 30.
Dry = varnish + 2 days. So latest varnish = Jan 28.
But varnish must be a Wednesday, so the latest is Jan 27.
For varnish on Jan 27, completion must be by Jan 26.
Completion = delivery + ≤3 days → latest delivery = Jan 23. But deliveries only occur Mondays → must be Jan 18 (Monday).
Delivery = next Monday after exam. For delivery Jan 18, exam must fall Jan 12–17.
Exam = receive + 3. So receive must be no later than Jan 14 (exam on 17 → delivery 18).
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4. The longest delay in shipping a restored piece of furniture will involve a piece of furniture whose cover varnish dries on:
A) January 1st
B) January 8th
C) January 15th
D) January 22nd
E) January 29th
We want the case where varnish dries just after a shipping date, so the item must wait the longest before the next shipping date.
If dry Jan 1 → next ship Jan 15 → 14-day wait.
If dry Jan 8 → next ship Jan 15 → 7-day wait.
If dry Jan 15 → can ship immediately that same day → 0-day wait.
If dry Jan 22 → next ship Jan 30 → 8-day wait.
If dry Jan 29 → next ship Jan 30 → 1-day wait.
The longest wait = drying on Jan 1 → wait until Jan 15 (14 days).
