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.

D. EACH statement ALONE is sufficient to answer the question asked.

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

Answer : B

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.

Therefore, the answer is A

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

Answer : C

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.

Therefore, the answer is C

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.

Answer : D

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.

Therefore, the answer is D

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.

Answer : D

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.

Therefore the answer is D

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

Answer :

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 23^rd and Anil’s birthday is on January 15^th

Answer : A

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 23^rd and is a Monday

Anil’s birthday is on January 15^th.

We cannot find the day of the week on 15^th 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.

Therefore, the answer is A

7. How many Sundays occur in a month in a leap year?

1.1^st of the month is a Sunday

2.5^th of the month is a Sunday

Answer : D
Explanation :

The year is a leap year. So February will have 29 days

From statement 1 alone,

1^st of the month is a Sunday.

So Sundays in the month are on => 1^st, 8^th, 15^th, 22^nd and 29^th

All months in a leap year have 29^th day. So there 5 Sundays in the month

So statement 1 alone is sufficient to get the answer.

From statement 2 alone,

5^th of the month is a Sunday.

So Sundays in the month are => 5^th, 12^th, 19^th, and 26^th

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?

1.18^th February of this year was a Wednesday

2. Today is Independence day of India

Answer : E

Explanation :

Taking statement 1 alone :

18^th 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 15^th August.

We have no reference date or present year, so we cannot find the day of the week today.

Combining both statements,

18^th February of the year was a Wednesday, and today is 15^th 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.

Therefore, the answer is E

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

2.18^th March of the year is a Monday

Answer : C
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,

18^th March of the year is a Monday.

Hence, it can be found which day of the week is 1^st 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 1^st August was.

Both statements together are sufficient to get the answer.

Therefore, the answer is C

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

Answer : B

Explanation :

From statement 1 alone:

N is a multiple of 100. Then N is a century year.

1600 is a multiple of 100, and it is a leap year.

1700 is a multiple of 100 but not a leap year.

So we cannot determine whether N is a leap year or not.