Question 1
What is the value of the digit 6 in the number 43.762?
A. Six hundred
B. Six
C. Six tenths
D. Six hundredths
E. Six Thousands
Solution:
The number 43.762 can be written as:
43 + 7/10 + 6/100 + 2/1000
The digit 6 is in the hundredths place.
Therefore, the value of the digit 6 in the number 43.762 is six hundredths.
Therefore, the value of the digit 6 in the number 43.762 is six hundredths.
Question 2
One of the angles in an isosceles triangle is 40°.
Which of these is a possible other angle in the triangle?
Solution:
In an isosceles triangle, two angles are equal.
Therefore, the other two angles in the triangle are equal.
Let the other two angles be x.
The sum of all angles in a triangle is equal to 180°.
Therefore, x + x + 40 = 180
2x + 40 = 180
2x = 180 – 40
2x = 140
x = 140 ÷ 2
x = 70
Therefore, the other two angles in the triangle are 70° each.
Question 3
Two runners are having a race. Adam starts running from the start line at 10m/s. Two second later Andy starts running from the start line at 12m/s.
How far are they both from the start line when Andy catches up with Adam?
Solution:
Given: Speed of Andy = 10m/s
Speed of Adam = 12m/s
Let the time taken by Adam to catch up with Andy be ‘t’.
Distance covered by Adam in time ‘t’= 10t {Distance= Speed x Time}
As Andy starts running after 2 seconds, time taken by him = t-2
Distance covered by Andy= 12(t-2)
Distance covered by Adam and Andy will be same as they will catch each other at same point.
Therefore, 10t= 12(t-2)
10t= 12t-24
2t = 24
t = 12
Distance at which they will catch up with each other = 10t = 10×12 = 120m
Therefore, they are 120m away from the starting point when Andy catches up with Adam.
Question 4
David, Mark and Wyn all buy gummy bear sweets at 6 pence each. David buys two more gummy bears than Mark.
Mark buy eight more gummy bears than Wyn.
Together the three boys spend £3.42 on gummy bears. How many gummy bears David buys?
Solution:
Let’s assume the number of gummy bears Wyn buys is x.
Mark buys eight more gummy bears than Wyn, so Mark buys x + 8 gummy bears.
David buys two more gummy bears than Mark, so David buys (x + 8) + 2 gummy bears.
The cost of each gummy bear is 6 pence, which is equivalent to £0.06.
The total cost spent by the three boys is £3.42.
Therefore, we can write the equation:
(x * 0.06) + ((x + 8) * 0.06) + ((x + 8 + 2) * 0.06) = 3.42
Taking 0.06 common
0.06 { x+ (x+8)+(x+10)}= 3.42
x+x+8+x+10= 3.42/0.06
3x+18=57
3x= 57-18
x=Â 39/3
x=13
Therefore, Wyn buys approximately 13 gummy bears.
Mark buys x + 8 = 13 + 8 = 21 gummy bears.
David buys (x + 8) + 2 = 13 + 8 + 2 = 23 gummy bears.
Therefore, David buys 23 gummy bears.
Question 5
A concert hall has sold 60% of its tickets for a particular night.
36 tickets remain unsold. How many people can the concert hall hold in total?
Solution:
Let the total number of tickets the concert hall can hold be x.
60% of the tickets have been sold, which means 40% of the tickets remain unsold.
Therefore, 40% of the tickets = 36
40% of x = 36
(40/100) * x = 36
0.4x = 36
x = 36 / 0.4
x = 90
Therefore, the concert hall can hold 90 people in total.
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