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CAT Data Interpretation & Logical Reasoning Clock Test 1

25924.The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
0$^\circ$
10$^\circ$
5$^\circ$
20$^\circ$
Explanation:

Angle traced by hour hand in$ \dfrac{13}{3} $hrs =$\left(\dfrac{360}{12}\times\dfrac{13}{3}\right)^\circ$= 130$^\circ$

Angle traced by min. hand in 20 min. =$ \left(\dfrac{360}{60} \times 20\right)^\circ $= 120$^\circ$.

$\therefore$ Required angle = (130 - 120)$^\circ$ = 10$^\circ$.

25925.At what angle the hands of a clock are inclined at 15 minutes past 5?
58$ \dfrac{1}{2} ^\circ $
64$^\circ$
67$ \dfrac{1}{2}^\circ $
72$ \dfrac{1}{2} ^\circ $
Explanation:

Angle traced by hour hand in$ \dfrac{21}{4} $hrs =$\dfrac{360}{12}\times\dfrac{21}{4} ^\circ $=157$ \dfrac{1}{2} ^\circ $

Angle traced by min. hand in 15 min. =$ \left(\dfrac{360}{60} \times 15\right)^\circ $= 90$^\circ$.

$\therefore$ Required angle =$ \left(157\dfrac{1}{2} \right)^\circ $- 90$^\circ$ = 67$ \dfrac{1}{2} ^\circ $

25927.How many times are the hands of a clock at right angle in a day?
22
24
44
48
Explanation:

In 12 hours, they are at right angles 22 times.

$\therefore$ In 24 hours, they are at right angles 44 times.

25929.How many times in a day, are the hands of a clock in straight line but opposite in direction?
20
22
24
48
Explanation:

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours.

(Because between 5 and 7 they point in opposite directions at 6 oclcok only).

So, in a day, the hands point in the opposite directions 22 times.

25933.How many times do the hands of a clock coincide in a day?
20
21
22
24
Explanation:

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 oclock)

AM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

PM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

The hands overlap about every 65 minutes, not every 60 minutes.

$\therefore$ The hands coincide 22 times in a day.

25934.How many times in a day, the hands of a clock are straight?
22
24
44
48
Explanation:

In 12 hours, the hands coincide or are in opposite direction 22 times.

$\therefore$ In 24 hours, the hands coincide or are in opposite direction 44 times a day.

25936.How many times are the hands of a clock at right angle in a day?
48
44
24
22
Explanation:

In 12 hours, hands of a clock are at right angles 22 times.

In 24 hours, hands of a clock are at right angles 44 times.

25937.How many times will the hands of a clock coincide in a day?
24
22
20
21
Explanation:

The hands of a clock coincide 11 times in every 12 hours (Between 11 and 1, they coincide only once, at 12 oclock).

12:00 am

1:05 am

2:11 am

3:16 am

4:22 am

5:27 am

6:33 am

7:38 am

8:44 am

9:49 am

10:55 am

12:00 pm

1:05 pm

2:11 pm

3:16 pm

4:22 pm

5:27 pm

6:33 pm

7:38 pm

8:44 pm

9:49 pm

10:55 pm

Hence the hands coincide 22 times in a day.

25938.How many times in a day, the hands of a clock are straight?
22
44
48
24
Explanation:

The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 o clock only. Hence the hands point in the opposite directions 22 times in a day.

The hands of a clock coincide(0° between them) 11 times in every 12 hours (between 11 and 1, they coincide only once, at 12 oclock). Hence the hands coincide 22 times in a day.

So In 24 hours, the hands come in opposite direction or coincide 44 times.

This is already given as a formula and its is better to learn the answer by heart as 44

which can save time in competitive exams.(However you should know the theory behind).

25939.How many times in a day, are the hands of a clock in straight line but opposite in direction?
48
22
24
12
Explanation:

The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 o clock only.

Hence the hands point in the opposite directions 22 times in a day.

This is already given as a formula and its is better to learn the answer by heart as 22 which can save time in competitive exams.(However you should know the theory behind).

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