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Data Sufficiency Questions On Clocks A . Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the questi...

# Data Sufficiency Questions on Clocks and Calendars

### Data Sufficiency Questions On Clocks

A. Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question asked.
B. Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

1. What is the present time in the clock?
1. The angle between the hour hand and the minute hand is 100
2. The mirror reflection of the clock shows the time 7:40
Explanation :
Using Statement 1 alone,
The two hands in a clock form an angle of 10 degrees twice in an hour.
Also,  we cannot find the present time in the clock, because the hour is not given.
So, statement 1 alone is not sufficient.
Using Statement 2 alone,
The time in the mirror reflection of the clock is 7:40.
We can find the actual time by subtracting the time in the mirror reflection from 12:00
So statement 2 alone is sufficient to get the question.

2. Find the time shown in a wall clock?
1. The angle between the two hands is 1800
2. The hour hand of the clock is between 7 and 8 on the dial
Explanation :
Using Statement  1 alone,
The two hands of the clock are at an angle of  1800. It happens only once every hour. But we cannot tell the time because the hour is not given.
So, Statement 1 alone is not sufficient
Using Statement 2 alone,
The position of the hour hand is given, but the minute hand’s position is not given.
So statement 2 alone is not sufficient in getting the answer.
Combining both statements,
The hour hand is between 7 and 8, and the angle between the two hands is 1800.
The angle 1800 happens only once in one hour. Then we can find the present time in the clock.
Both statements together are necessary to answer the question.

3. What is the angle between the hour hand and the minute hand of the clock?
1. The two hands are $\frac{50}{3}$ minute spaces apart.
2. The minute hand is on 8, and the hour hand is between 4 and 5.
Explanation:
From statement 1 alone,
The two hands are $\frac{50}{3}$ minute spaces apart.
1 minute space = 60 .
So the two hands are  ($\frac{50}{3}$ x 60 )= 1000 apart.
We can find the angle between the two hands using the data given in statement 1 alone.
From statement 2 alone,
We can say that the time is  4:40
As the exact time is given, we can find the angle between the two hands.
So statement 2 alone is sufficient to answer the question.

4. How many minutes does a clock lose or gain in a day if it is set to correct time at noon today?
1. The clock shows 4:20 p.m when the time is 4 p.m today.
2. The clock gains 5 minutes every hour.
Explanation :
The clock is showing the correct time at noon (12 p.m).
From statement 1 alone,
The clock shows 4:20 p.m when the time is 4 p.m.
So the clock gains 20 minutes from 12  p.m. to 4 p.m.
So the clock gains 20 minutes in 4 hours => The clock gains 5 minutes in one hour.
From this, we can find the number of minutes the clock gains or loses in a day.
Statement 1 alone is sufficient to answer the question.
From statement 2 alone,
The clock gains 5 minutes every hour.
From this information, we can find the number of minutes the clock gains in a day.
Statement 2 alone is sufficient to answer the question.

5. How many minutes does clock gain in a day?  MAT September 1999
1. The clock reads 6:00 when correct the time is 5: 48
2. The clock gains 40 seconds  each hour
Explanation :
The clock reads 6:00 when the real-time is 5:48.
So the clock gains time.  But we don’t have the information about the rate of time gained by the clock
Therefore, we cannot find the time gained by the clock in 24 hours because we don’t know the time at which the clock was set to the correct time.
So statement 1 alone is not sufficient to get the answer
From statement 2 alone,
The clock gains 40 seconds every hour.
It gains (24 x 40) = 960 seconds or 16 minutes in 24 hours or day
So statement 2 alone is sufficient to get the answer
Therefore , the answer is B

### Data Sufficiency Questions On Calendars

6.  On which day of the week, Anil will celebrate his birthday if his friend Komali celebrates her birthday on Monday in the same year?
1. Komali’s birthday comes 56 days after  Anil’s birthday in the year
2. Komali’s birthday is on September 23rd and Anil’s birthday is on January 15th
Statement 1 alone :
Komali’s birthday is on Monday.
From statement 1 alone,
Anil’s birthday is 56 days before Komali’s birthday
Anil’s birthday will be on => Monday -56 = Monday
Therefore, statement 1 alone is sufficient to get the answer.
From statement 2 alone,
Komali’s birthday is on September 23rd and is a Monday
Anil’s birthday is on January 15th.
We cannot find the day of the week on 15th January because it is not clear that the February month, which occurs in this period, has 28 days or 29 days.
So data given in statement 2 is not sufficient to answer the question.

7. How many Sundays occur in a  month in a leap year?
1.1st of the month is a Sunday
2.5th of the month is a Sunday
Explanation :
The year is a leap year. So February will have 29 days
From statement 1 alone,
1st of the month is a Sunday.
So Sundays in the month are on => 1st, 8th, 15th, 22nd and 29th
All months in a leap year have 29th day. So there 5 Sundays in the month
So statement 1 alone is sufficient to get the answer.
From statement 2 alone,
5th of the month is a Sunday.
So Sundays in the month are => 5th, 12th, 19th, and 26th
It is possible in any month of a year.
There are 4 Sundays in the month
So statement 2 alone is sufficient to get the answer
Therefore , the answer is B

8. Is it a Tuesday today?
1.18th February of this year was a Wednesday
2. Today is Independence day of India
Explanation :
Taking statement 1 alone :
18th February of the year was a Wednesday, but today’s date is not given.
So statement 1 alone is not sufficient to get the answer
Taking statement 2 alone:
Today is 15th August.
We have no reference date or present year, so we cannot find the day of the week today.
Combining both statements,
18th February of the year was a Wednesday, and today is 15th August.
Yet we have no information whether the February month in the period has 28 days or 29 days.
So even when both statements are combined, we cannot find the answer.

9. In August, public holidays are only two.  One is Independence Day, and the other is Rakhi Pournami. How many total holidays will be there in the month?
1. Only Sundays are holidays except for public holidays
2.18th  March of the year is a Monday
Explanation :
There are 2 public holidays in the month.
From statement 1 alone,
All Sundays and only public holidays are holidays. We don’t know the number of Sundays in August, so we can’t find the number of holidays in the month.
From statement 2 alone,
18th March of the year is a Monday.
Hence, it can be found which day of the week is 1st August.
But that will not answer the question.
So statement 2 alone is not sufficient
Combining both statements,
Only Sundays and public holidays are holidays. We can find the number of Sundays in August , because from statement 2; we can find which day of the week 1st August was.
Both statements together are sufficient to get the answer.

10. Is the year N a leap year?
1. The year N is a multiple of 100
2. The year N is a multiple of 400