Clocks & Calendars – MBA CET questions with solutions

Approach: Calendar — count odd days between two dates of the same month.

Solution:
Rohit's birthday: 1 May = Sunday.
Shekhar's birthday: 20 May → 20 − 1 = 19 days later.
19 ÷ 7 = 2 weeks + 5 odd days.
Sunday + 5 days = Friday (Mon 1, Tue 2, Wed 3, Thu 4, Fri 5).

Why the other options are wrong:
B: Tuesday is Sunday + 2 — a counting slip.
A, C, D: Sunday + 1, 3 or 4.

Cetking shortcut: Same weekday repeats every 7 days: 1, 8, 15 May are Sundays → 15 + 5 = 20 is Friday.

Answer: E

Approach: Date range intersection.

Solution:
Charu: after 24, before 29 → 25, 26, 27, 28.
Sister: after 27, before 31 → 28, 29, 30.
Common dates: 28 only.
Brother: even date — 28 is even ✓.
Birthday = 28 May.

Why the other options are wrong:
A: 30 is outside Charu's range.
C, E: 26 and 24 are outside the sister's range (24 is outside Charu's too).
D: 29 is excluded by Charu and is odd.

Cetking shortcut: 'After 24' and 'before 29' are exclusive limits — list only the dates strictly between.

Answer: B

Approach: Faulty clock: real time / clock time = 24 h / (24 h − loss).

Solution:
Clock loses 16 min per 24 h → in 24 real hours it shows 23 h 44 min = 1424 min.
From 5:00 a.m. (day 1) to 10:00 p.m. (day 4) on the clock = 3 days + 17 h = 89 h.
Real time elapsed = 89 × 1440/1424 = 89 × 90/89 = 90 h.
5:00 a.m. + 90 h = 5:00 a.m. + 3 days 18 h = 11:00 p.m. on day 4.

Cetking shortcut: 1424/1440 = 89/90 — so 89 clock-hours = 90 real hours; the clock is exactly 1 hour slow.

Answer: B

Approach: Angle = |30H − 5.5M|.

Solution:
H = 2, M = 30.
Angle = |30 × 2 − 5.5 × 30| = |60 − 165| = 105°.

Cetking shortcut: At 2:30 the minute hand is at 180°, hour hand at 60° + 15° = 75° → 105°.

Answer: A

Approach: Odd days: an ordinary year shifts the weekday by 1.

Solution:
Jan 12, 1979 to Jan 12, 1980 contains no 29 February (1979 is not a leap year; 29 Feb 1980 comes after 12 Jan) → 365 days = 1 odd day.
Going back one year: Saturday − 1 = Friday.

Cetking shortcut: Check for Feb 29 inside the span — none here, so shift by 1.

Answer: A

Approach: Actual departure = arrival − travel time; usual departure = actual departure + 15 min.

Solution:
Reached the stop at 8.40 am; travel takes 10 min → left home today at 8.30 am.
Today he left 15 min earlier than usual → usual departure = 8.30 + 0.15 = 8.45 am.

Why the other options are wrong:
A 8.30: that is today's departure, not the usual one.
C 8.55: adds 15 min to the arrival time.
D 8.15: subtracts 15 min instead of adding.
E 8.50: adds only 10 min to the arrival.

Answer: B

Approach: Odd days: each ordinary year adds 1 day, each leap year 2.

Solution:
From 1 Jan 2010 to 1 Jan 2017 = years 2010–2016 = 7 years.
Leap years in between: 2012 and 2016 → 2 leap years, 5 ordinary.
Odd days = 5 × 1 + 2 × 2 = 9 → 9 mod 7 = 2.
Friday + 2 = Sunday.

Cetking shortcut: Odd days = number of years + number of leap years = 7 + 2 = 9 → 2.

Answer: D

Approach: Count days between the dates and use odd days.

Solution:
15 Aug 1947 → 15 Aug 1948 = 366 days (includes 29 Feb 1948).
15 Aug 1948 → 15 Aug 1949 = 365 days.
15 Aug 1949 → 26 Jan 1950 = 16 (Aug) + 30 + 31 + 30 + 31 + 26 = 164 days.
Total = 366 + 365 + 164 = 895 days.
895 = 7 × 127 + 6 → 6 odd days.
26 Jan 1950 is Thursday, so 15 Aug 1947 is 6 days earlier: Thursday − 6 = Friday.

Cetking shortcut: Going back 6 days = going forward 1 day: Thursday + 1 = Friday.

Answer: B

Approach: The hands coincide 11 times in every 12 hours, once every 65 5/11 min.

Solution:
From 1 o'clock up to 12 o'clock the hands coincide at about 1:05, 2:11, 3:16, 4:22, 5:27, 6:33, 7:38, 8:44, 9:49, 10:54 — that is 10 times — and again at 12:00.
Total = 10 + 1 = 11 times.

Why the other options are wrong:

• A (9), C (13), E (14): not consistent with one coincidence every 65 5/11 min.
• D (10): leaves out the 12:00 coincidence.
• 12 would assume one coincidence per hour, which is wrong because the hands do not meet between 11 and 1 o'clock except at 12.

Cetking shortcut: In 12 hours → 11 times; in 24 hours → 22 times. Between 11 and 1 o'clock the hands meet only once (at 12).

Answer: B

Approach: Calendars repeat when total odd days ≡ 0 (mod 7) and leap-year status matches.

Solution:
2010 is an ordinary year (1 odd day).
Odd days from 2010 to 2020: 11 years with 3 leap years (2012, 2016, 2020) → 11 + 3 = 14 ≡ 0 (mod 7).
So 1 Jan 2021 is the same weekday as 1 Jan 2010, and 2021 is also an ordinary year → same calendar.

Why the other options are wrong:

• A (2012), E (2020): leap years — cannot match an ordinary year's calendar.
• B (2014): 2010–2013 give 1 + 1 + 2 + 1 = 5 odd days.
• D (2017): 2010–2016 give 9 ≡ 2 odd days.

Cetking shortcut: Ordinary years: the 1st year after a leap year repeats after 6 years; the 2nd and 3rd years after a leap year repeat after 11 years. 2010 is the 2nd year after 2008 → 2010 + 11 = 2021.

Answer: C

Approach: First symbol = hour hand position, second symbol = minute hand position (number × 5 minutes).

Solution:
Codes: P=5, Q=8, R=12, $=10, #=3, &=7.
Check: P& → hour 5, minute hand at 7 → 35 min → 5:35 ✓
Alarm P# → hour 5, minute hand at 3 → 15 min → 5:15 AM.
Train Q$ → hour 8, minute hand at 10 → 50 min → 8:50 AM.
Time needed = 8:50 – 5:15 = 3 hr 35 min.
(The printed example '#R = 4:00' should read 3:00 by the same rule; it does not affect the answer.)

Answer: E

Approach: In 12 hours the hands are at right angles 22 times (not 24); double it for a day.

Solution:
In 12 hours the minute hand gains 11 full rounds on the hour hand.
Each round produces 2 right angles → 22 right angles in 12 hours.
In 24 hours: 22 × 2 = 44.
Overlaps and straight-line positions are separate events and are not counted anyway.

Why the other options are wrong:

• E (48): assumes 2 per hour × 24 — ignores that the hands gain only 22 rounds in a day.
• A, B, D: miscounts.

Cetking shortcut: Right angles = 44, straight (opposite) = 22, coincide = 22 in a day — memorise this triplet.

Answer: C

Approach: Count odd days from 26 January to 14 November (2026 is not a leap year).

Solution:
Odd days after 26 Jan: Jan 5, Feb 0, Mar 3, Apr 2, May 3, Jun 2, Jul 3, Aug 3, Sep 2, Oct 3, Nov 14 → 0.
Total = 5 + 0 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 0 = 26 → 26 mod 7 = 5.
(Check: 292 days = 41 weeks + 5 days.)
Monday + 5 = Saturday.

Cetking shortcut: Month codes: 26 Jan Monday → 14 Nov is 292 days later; 292 = 287 + 5 → Monday + 5 = Saturday.

Answer: C

Approach: Time calculation — add the durations in order; stop at the asked event.

Solution:
20 minutes to seven = 6:40 AM.
Travel 25 min → reaches Hemant's house at 7:05 AM.
Breakfast 15 min → they leave Hemant's house at 7:20 AM.
(The 35-minute office trip is after the asked event — not needed.)

Why the other options are wrong:
B 7:55: adds the 35-minute office journey to 7:20 (that is the arrival at office, not the departure).
A 8:05: an arithmetic slip.
C 7:50, E 7:45: misread '20 minutes to seven' or the durations.

Cetking shortcut: Read exactly which moment is asked — departure from Hemant's, not arrival at office.

Answer: D

Approach: The hour hand moves 30° per hour (0.5° per minute).

Solution:
From 7:00 to 11:30 = 4.5 hours
Rotation = 4.5 × 30° = 135°

Cetking shortcut: Hour hand: 0.5° per minute → 270 min × 0.5 = 135°.

Answer: C

Approach: Odd-days method: count odd days from a known reference (multiple of 400 years = 0 odd days).

Solution:
Years 1–2000 complete → 0 odd days (2000 is a multiple of 400)
2001–2009: 9 years incl. 2 leap years (2004, 2008) → 9 + 2 = 11 → 4 odd days
2010 up to 15 Aug: Jan 3, Feb 0, Mar 3, Apr 2, May 3, Jun 2, Jul 3, Aug (15) 1 → 17 → 3 odd days
Total = 0 + 4 + 3 = 7 → 0 odd days → Sunday

Cetking shortcut: Anchor on Independence Day: 15 Aug 1947 was a Friday; 63 years later with 16 leap days (1948–2008) → 79 → 2 odd days → Friday + 2 = Sunday.

Answer: A

Approach: Count odd days between the two dates and move backward from the known day.

Solution:
26 Jan 1998 → 26 Jan 2012 = 14 years with 3 leap days (Feb 2000, 2004, 2008) → 14 + 3 = 17 → 3 odd days
26 Jan 2012 → 15 Aug 2012: Jan 5, Feb 29 (leap) 1, Mar 3, Apr 2, May 3, Jun 2, Jul 3, Aug 15 → 1 → total 20 → 6 odd days
Total = 3 + 6 = 9 → 2 odd days
15 Aug 2012 is 2 days ahead of 26 Jan 1998 → Wednesday − 2 = Monday

Cetking shortcut: Move back 2 weekdays from Wednesday → Monday.

Answer: B

Approach: Hour hand moves 30° per hour.

Solution:
3 pm to 9 pm = 6 hours
Rotation = 6 × 30° = 180°

Answer: C

Approach: Angle = |30H − 5.5M|.

Solution:
At 8:00: H = 8, M = 0 → 30 × 8 = 240°
Smaller angle = 360° − 240° = 120°

Cetking shortcut: Minute hand at 12, hour hand at 8 → 4 hour-gaps × 30° = 120°.

Answer: E

Approach: Odd-days method: count odd days up to the date, then map 0 = Sunday, 1 = Monday, …

Solution:
26 Jan 1950 = 1949 complete years + 26 days
1600 years → 0 odd days; 300 years → 1 odd day
49 years = 12 leap + 37 ordinary → 12 × 2 + 37 × 1 = 61 → 61 mod 7 = 5
26 days of January → 26 mod 7 = 5
Total = 0 + 1 + 5 + 5 = 11 → 11 mod 7 = 4 → Thursday

Cetking shortcut: Known anchor: India's first Republic Day (26 Jan 1950) was a Thursday.

Answer: D

Approach: The hour hand moves 30° per hour.

Solution:
8 a.m. to 2 p.m. = 6 hours
Rotation = 6 × 30° = 180°

Why the other options are wrong:
A/B/D/E: not multiples of 30° for whole hours (except D = 3 hours).

Answer: C

Approach: Going back one year shifts the day back by the number of odd days in between.

Solution:
Jan 12, 1979 → Jan 12, 1980 contains Feb 1979 only (Feb 29, 1980 comes after Jan 12)
365 days = 52 weeks + 1 odd day
So Jan 12, 1979 = Saturday − 1 = Friday

Why the other options are wrong:
D (Thursday): wrongly counts 1980 as leap for this interval (2 odd days).

Answer: E

Approach: Clock angle formula.

Solution:
At 4:20, H = 4, M = 20.
Angle = |30 × 4 − 5.5 × 20| = |120 − 110| = 10°.

Why the other options are wrong:
A, B, C, E: not |120 − 110|.

Cetking shortcut: Minute hand at 4 exactly (120°); hour hand has moved 20 × 0.5 = 10° past 4 ⇒ 10°.

Answer: D

Approach: Work backwards from the next departure using the fixed train interval.

Solution:
Trains leave every 2 h 30 min. The next train is at 18:00.
So the previous train left at 18:00 − 2:30 = 15:30.
The announcement was made 40 min after that: 15:30 + 0:40 = 16:10.

Why the other options are wrong:
A (15:30): this is when the previous train left, not when the announcement was made.
B (17:10): adds 40 min to the wrong reference time.
C (16:00), D (15:50): wrong offsets from 15:30.

Cetking shortcut: Announcement time = next departure − interval + time since the last departure = 18:00 − 2:30 + 0:40 = 16:10.

Answer: E

Approach: Calendar shift: move day by day from the reference day.

Solution:
Day before yesterday = Saturday, so yesterday = Sunday and today = Monday.
Tomorrow = Tuesday, so the day after tomorrow = Wednesday.

Why the other options are wrong:
D (Tuesday): this is tomorrow.
E (Sunday): this is yesterday.
A (Friday), B (Thursday): these count backwards.

Cetking shortcut: The day before yesterday is −2 and the day after tomorrow is +2, so the gap is 4 days: Saturday + 4 = Wednesday.

Answer: C

Approach: Day counting with remainder mod 7.

Solution:
She went 9 days ago, on a Thursday.
9 = 7 + 2. After 7 days it is Thursday again, and 2 more days gives Saturday.

Why the other options are wrong:
A (Thursday): this is the day 7 days later, not 9.
C (Sunday): this is 3 days after Thursday.
D (Tuesday): this counts back 2 days instead of forward.
E (Wednesday): this is Thursday − 1.

Cetking shortcut: Today = Thursday + (9 mod 7) = Thursday + 2 = Saturday.

Answer: B

Approach: Odd-days method: count the extra days beyond full weeks.

Solution:
17 Dec 2002 → 17 Dec 2003: 365 days = 1 odd day.
17 Dec 2003 → 17 Dec 2004: 366 days (29 Feb 2004 falls inside) = 2 odd days.
17 Dec 2004 → 22 Dec 2004: 5 days.
Total = 1 + 2 + 5 = 8, and 8 mod 7 = 1 odd day.
Saturday + 1 = Sunday.

Why the other options are wrong:
A (Monday): needs 2 odd days in total; treating 2004 as an ordinary year gives 1 + 1 + 5 = 7, which is Saturday (not offered), so this is a slip in the odd-day count.
C (Wednesday), B (Tuesday), E (Friday): wrong odd-day totals.

Cetking shortcut: Each ordinary year moves the day by 1 and each leap year by 2. Here 1 + 2 + 5 = 8 ≡ 1, so the answer is Sunday.

Answer: D

Approach: Error changes from −2 min to +4 min 48 s uniformly.

Solution: Time elapsed: Monday 12 noon → next Monday 2 pm = 7 days 2 h = 170 h.
Total gain = 2 min + 4 min 48 s = 6 min 48 s = 6.8 min.
To be correct it must gain 2 min → time needed = 170 × 2/6.8 = 50 h.
Monday 12 noon + 50 h = Wednesday 2 pm.

Answer: B

Approach: The hands coincide 11 times in every 12 hours (once every 12/11 h = 65 5/11 min).

Solution:
10:20 AM, 8 Mar → 10:20 AM, 11 Mar = 3 days = 72 hours = 6 blocks of 12 hours.
Coincidences = 6 × 11 = 66.
Counting full 12-hour blocks gives the intended answer, 66 (the last 55 minutes add one more overlap at about 10:54 AM on 11 March, but 67 is not among the options).

Why the other options are wrong: 45 and 50 undercount; 89 counts more than 11 per 12 hours; 25 is roughly one day's count.

Cetking shortcut: 22 coincidences per day × 3 days = 66.

Answer: D

Approach: Day after n days = start day + (n mod 7).

Solution:
She went on a Thursday, 9 days ago.
9 = 7 + 2 → today is 2 days after Thursday = Saturday.

Why the other options are wrong: Tuesday/Wednesday count backwards; Thursday would need a multiple of 7 days; Sunday is 10 days.

Answer: C

Approach: Minute hand gains 55 minute-spaces on the hour hand every 60 minutes.

Solution:
At 9:00 the minute hand (at 12) is 45 spaces behind the hour hand (at 9).
To be 23 spaces apart with the minute hand still behind, it must gain 45 − 23 = 22 spaces.
Time = 22 × 60/55 = 24 minutes → 9:24.
(Minute hand 23 spaces ahead would need a gain of 68 spaces = 74 2/11 min, beyond 10 o'clock.)
Check: at 9:24 the hour hand is at 47 spaces, minute hand at 24 → 23 apart ✓.

Answer: E

Approach: Count odd days from the known date.

Solution:
26 Jan 1950 → 26 Jan 1980 = 30 years, crossing 29 Feb of 1952, 56, 60, 64, 68, 72, 76 = 7 leap days.
Odd days for 30 years = 30 + 7 = 37 → 37 mod 7 = 2.
26 Jan 1980 → 15 Aug 1980: Jan 5 + Feb 29 + Mar 31 + Apr 30 + May 31 + Jun 30 + Jul 31 + Aug 15 = 202 days → 202 mod 7 = 6.
Total odd days = 2 + 6 = 8 → 1. Thursday + 1 = Friday.

Cetking shortcut: Each year shifts the weekday by 1 (2 if a 29 Feb is crossed); add the month days separately.

Answer: B

Approach: Faulty clock: the clock runs 24 h 10 min while true time runs 24 h.

Solution:
Clock time passed from 8:00 to 11:00 = 3 h = 180 min.
True time = 180 × 1440 ÷ 1450 ≈ 178.76 min = 2 h 58 min 45 s.
True time = 8:00 + 2:58:45 = 10:58:45 AM.

Why the other options are wrong:
A 11:59:35, C 11:58:45 — after 11:00; a fast clock is ahead, so true time is earlier.
B 10:50:45 — far too large a correction.
E 10:58:40 — wrong seconds.

Cetking shortcut: Gain ≈ 10 min/24 h ≈ 25 s per hour → 3 h ≈ 75 s = 1 min 15 s → 11:00 − 1:15 = 10:58:45.

Answer: D

Approach: Total minus skips.

Solution:
One day = 24 × 3600 = 86,400 s; 7 days = 604,800 s.
Skipped = 0 + 1 + 3 + 4 + 7 + 13 + 7 = 35 s.
Worked = 604,800 − 35 = 604,765 s.

Why the other options are wrong:
A 604769, B 604768, D 604764, E 604761 — skip totals of 31, 32, 36, 39 (miscounted).

Cetking shortcut: All options start 6047…; only the skip total (35) matters → last two digits 65.

Answer: C

Approach: Odd days method.

Solution:
15 Aug 1947 → 15 Aug 1956: 9 years with 29 Feb 1948, 1952, 1956 inside → odd days = 9 + 3 = 12 → 5.
15 Aug 1956 → 26 Jan 1957: Aug 16 + Sep 30 + Oct 31 + Nov 30 + Dec 31 + Jan 26 = 164 days → 164 mod 7 = 3.
Total odd days = 5 + 3 = 8 → 1.
Friday + 1 = Saturday.

Why the other options are wrong:
B Friday — 0 odd days.
C Sunday — 2 odd days (one extra leap day counted).
D Thursday, E Tuesday — counted backwards / wrong totals.

Cetking shortcut: Total days 3452 = 7 × 493 + 1 → one day ahead.

Answer: A

Approach: Hands coincide 11 times in 12 hours, i.e. 22 times in 24 hours.

Solution:
Hands overlap once every 12/11 hours, so in 12 hours they overlap 11 times (the 12th overlap falls exactly at the 12 o'clock that starts the next cycle).
In 24 hours: 2 × 11 = 22 times.
72 hours = 3 days → 3 × 22 = 66 times.

Why the other options are wrong:
24 / 72: assumes one overlap per hour.
76 / 56: no valid count gives these.

Cetking shortcut: Coincide 22/day, opposite 22/day, right angle 44/day. Multiply by days.

Answer: D