能力傾向 - 時鐘線上測驗

以下測驗提供與時鐘相關的選擇題 (MCQ)。您需要閱讀所有給出的答案，然後點選正確的答案。如果您不確定答案，可以使用顯示答案按鈕檢視答案。您可以使用下一題按鈕檢視測驗中的新一組問題。

Q 1 - 在 2 點到 3 點之間，時鐘的時針和分針何時重合？

答案：A

解釋

At 2 o' clock, the hour hand is at 2 and minute hand is at 12
i.e. they are 10 min spaces apart.
The minute hand has to gain 10 minute spaces
over the hour hand to be together.

The minute hand gains 55 mins in 60 mins.
∴ It will gain 10 mins in 60/55 * 10 min
= 120/11 minutes.

Hence the hands will coincide at 120/11 minutes past 2.

Q 2 - 在 4 點到 5 點之間，時鐘的時針和分針何時成直角？

答案：B

解釋

At 4 o' clock, the minute hand is 20 minute spaces behind the hour hand.
Now, when the two hands are at right angles, they are fifteen min spaces
apart. So, they are at right angles in following two cases.

Case I ? When the minute hand is 15 min spaces behind the hour hand.
In this case, min hand will have to gain (20-15) = 5 min spaces.
= (60/55)*5 = 60/11
∴ They are at right angle at 60/11 minutes past 4.
Case II ? When the minute hand is 15 minute spaces ahead of the hour hand.
In this case the minute hand will have to gain (20+15) = 35 min spaces.
= (60/55)*35 = 420/11 min
∴ They are at right angles at 420/11 min
past 4.

Q 3 - 5 點 15 分時，時鐘的兩根指標之間的角度是多少？

答案：C

解釋

At 15 minutes past 5 o' clock, the minute hand is at 3
and hour hand is slightly ahead of 5.

In 60 minutes, the hour hand moves ahead by 300
∴ In 15 minutes, the hour hand moves ahead by = (30/60)*15
= 7.5°

Angle between 3 and 5 hour spaces = 60°.
∴ The total angle between the two hands at
 15 minutes past 5 o' clock = 60 + 7.5 = 67.5°

Q 4 - 一個鐘錶在早上設定為正確時間。該鐘表在 24 小時內快走 10 分鐘。當該鐘錶顯示第二天晚上 1 點時，實際時間是多少？

答案：B

解釋

Time from 8 Am on a day to 1p.m on the accompanying day= 29 hrs.
24 hours 10 min. of this clock = 24 hrs. Of the right clock.
145/6 hrs. of this clock= 24 hrs of the right clock.
29 hrs. of this clock = (24*6/145*29)hrs of the right clock.
= 28 hrs 48 min. of right clock.
∴The right time is 28 hrs 48 min. after 8 am
This is 48 min. past. 12.

Q 5 - 一個鐘錶在 12 點開始計時。在 5 點 10 分時，時針旋轉了多少角度？

答案：C

解釋

Angle followed by hour hand in 12 hrs =360°
Point followed by hour hand in 5 hrs 10 min.
=31/6 = (360/12*31/6)°= 155°

Q 6 - 當時間是 8 點 30 分時，時鐘的時針和分針之間的夾角是多少？

答案：B

解釋

Angle followed by hour hand in 17/2hrs= (360/12*17/2)°= 255°
Point followed by min. hand in 30 min. = (360/60*30)°= 180°
∴ Required Angle = (255-180)°=75°

Q 7 - 一天中，時鐘的指標有多少次成一直線？

答案：C

解釋

In 12 hours, the hands concur or are in inverse heading 22 times.
∴ In 24 hours, the hands concur or are
in inverse heading 44 Times each day.

Q 8 - 一天中，時鐘的指標有多少次成一直線且方向相反？

答案：A

解釋

The hands of a check point in inverse headings 11 times in every 12 Hours.
(since somewhere around 5 and 7 they point in inverse headings at 6 o'clock just)
So in a day, the hands point in the inverse headings 22 times.

Q 9 - 在 9 點到 10 點之間，時鐘的時針和分針何時重合？

答案：C

解釋

To be as one somewhere around 9 and 10 o'clock,
the moment hand needs to pick up 45 min. spaces.
55 min. space are picked up in 60 min.
45 min. space are picked up in (60/55*45) min. or 540/11 min.
∴ The hands are as one at 540/11 min. past 9.

Q 10 - 一個手錶每 3 分鐘快走 5 秒。該手錶在早上設定為正確時間。在當天下午，當手表顯示 4 點 15 分時，實際時間是多少？

答案：B

解釋

Time structure 7 a.m. to 4.15 p.m.=9 hrs 15 min=37/4 hrs.
3 min. 5 sec. of this clock=3 min of the right clock.
=> 37/720hrs of this clock =1/2 hrs of the right clock
=> 37/4 hrs of this clock =(1/20*720/37*37/4)hrs of right clock
= 9hrs of the right clock
∴ The right time is 9 hrs after 7 a.m. i.e. 4 p.m.

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