Question

SAT Questions:
1) What is the time between 1:00 and 2:00, when the minute hand and hour hand overlap?
2) There are pens and pencils in a bucket, the number of pencils is twice the number of pens. If each student was given 5 pens, there will be 2 pens left over. If each student was given 11 pencils, then 21 pencils more are needed. What was the number of students in the class?
3) In some year, July 7th was on a Wednesday. What day of the week was May 1st in that year?

Answer 1

If we keep track of the minute hand as m, minutes past 12
the hour hand starts at 1:00 which is minute 5. In 1 hour it moves to minute 10 (2:00)
so the hour hand moves 1/12 as fast as the minute hand.
so we start with h at 5 minutes moving to 5+m/12 where m is the minute hand.
they are equal when
m= 5+m/12
solve for m= 60/11 = 5 and 5/11 after 1:00 or 1:05:27 to the nearest second.

Answer 2

I don't get the first part

Answer 3

for part 1. we could say:
minute hand travels 360º every 60 minutes or 6 deg/min
hour hand travels at 360º every 12 hours (720 minutes) or 0.5 deg/min

the hour hand starts at 1:00 = 30º from the top
at 1:00 the minutes starts at the top and h starts 30º ahead of it. they meet when
6*t= 30+0.5t where t is the elapsed time in minutes
5.5t=30
t= 30/5.5 = 60/11= 5 minutes 27 seconds (rounded)

Answer 4

As 55 min are gained by minute hand in 60 min
Therefore 5 min will be gained by min hand in. (60x5)/ 55= 5. 45 min 
Hence hands will coincide at 5. 45 min past 1 ' o clock

Answer 5

Let x be no. Of pens 
Let y be no. Of pencils
Let n be the total no. Of students

Given y= 2x
No. Of pencils is twice that of pen

All students are given 5 pens each 5n
And  only two pens are left after distributing them
x-5n = 2

All students are given 11 pencils each 11 n
And 21 pencils more are needed after distributing them
11 n- y = 21

Now substituting y = 2x
  
x- 5n = 2
11n - 2x= 21

 Solving them we get n= 25