Logical Reasoning Test - 28

Given time: 7:35 AM

To find the mirror image of the given time, use the formula:

Mirror Image Time = 11:60 - Given Time

Here, Given Time = 7:35

Therefore,

Mirror Image Time = 11:60 - 7:35

= 4:25

Hence, the correct answer is "Option 1".

We know that:

October has 31 days.

A month with 31 days has 4 full weeks (28 days) and 3 extra days.

If the month starts on a Monday, the 1st will be a Monday, and there will be Mondays on the 1st, 8th, 15th, 22nd, and 29th, which gives 5 Mondays.

So, the maximum number of Mondays that can occur in October is 5, provided the month starts on a Monday.

Hence the correct answer is "Option (3)".

Given date: 4 July 2008

So, calculating total number of odd days:

Total odd days till 4 July 2008 = 2 + 6 + 4 ⇒ 12 ÷ 7 = 5

Thus, "5" is the code for 'Friday'.

Hence, "Option 2" is the correct answer.

Key Points

When a clock is seen in a mirror, the actual time is calculated using the formula:

Actual Time=12:00 − Mirror Image Time

Given that the mirror image shows a quarter to nine (8:45).

Subtract from 12:00 − 8:45

00−45 (Not possible, so borrow 1 hour)

Convert 1 hour = 60 minutes

60−45=15 minutes

Subtract hours: 11 − 8 = 3 Hours

The actual time is 3:15.

Hence Option 1 is Correct.

At 8 : 30 PM, the hour hand is exactly between 8 and 9. The minute hand is at 6.

Total 60 minutes represents 360° 

Each 5 minutes represents = 360°/12 = 30° 

Now, the angle between hour hand and minute hand, if clock shows 8 : 30 PM = (30 + 30 + 15) = 75°

Alternate Method

Given time: 8:30

The logic followed here is:

The years divisible by 4 are leap years.

But for centuries, the century should be divisible by 400 to be a leap year.

⇒ 2800 ÷ 400 = 7 

⇒ 1800 ÷ 400 = 4.5 not completely divisible by 400.

⇒ 2600 ÷ 400 = 6.5 not completely divisible by 400.

⇒ 3000 ÷ 400 = 7.5 not completely divisible by 400.

Thus, 2800 is completely divisible by 400. is a leap year.

Hence, the correct answer is "Option 1".

Given time: 1 hour 20 minutes

Given time = 1 hour 20 minute = (1 × 60 min) + 20 min ⇒ 80 minutes

In one minutes, minutes hand covers angular distance = 6°

So, in 1 hours 20 minutes, minutes hand covers = 6° × 80 min ⇒ 480°

Hence, "Option 4" is the correct answer.

Additional Information

Movement of Hour head

12 hr = 360º

1 hr = 30º

60 min = 30º

1 min = 0.5º

Movement of Minute head

1 hr =  360º

60 min = 360º

1 min = 6º

5 min = 30º

Movement of Seconds head

1 min =  360º

60 sec = 360º

1 sec = 6º

5 sec = 30º

Gapping between hour head and minute head

​55 min = 60 min

1 min = 60/55 

Given: Year 2003

Year 2003 = (2000 + 3) ⇒ (Leap year + 3)

In case of a repeating year, we add (11) to the given year :

So, 2003 + 11 ⇒ 2014

Hence, "Option 2" is the correct answer.

Shortcut Trick

Trick to remember:

Given: A day

In one day, total minutes is ⇒ 24 hr ×  60 min = 1440 minutes.

As, hour hand and minute hand coincides every 65 minutes

⇒ 1440 ÷ 65 = 22.15

So, In 24 Hours it coincide 22 times.

Hence, "Option 4" is the correct answer.

Alternate Method

Hands coincide in 12 hours

⇒ The hands of a clock (hour hand and minute hand) coincide once every 1 hour and 5 minutes (or 1 hour + 5/11 of an hour).

⇒ In 12 hours, the hands coincide 11 times, because the first coincidence occurs at 12:00, and the next at approximately 1:05, 2:10, and so on.

Hands coincide in 24 hours

⇒  Since there are two 12-hour cycles in a day (one for AM and one for PM), the total number of coincidences is: 11(coincidences in 12 hours)×2=22.

Important Points

The reason it is 11 coincidences per 12 hours instead of 12 is that the hands coincide at the very start of the cycle and not again until the next cycle begins.

Given: 1 January 2014 was Wednesday.

Now,

2014 to 2015 = 1 Year (2014 is an ordinary year).

An ordinary year has 1 odd day.

So, 1 odd day added to the given day (Wednesday).

Wednesday + 1 odd day = Thursday.

Hence, 1 January 2015 will be a Thursday.

The correct answer is "Option 3".