Question 1
When my age is divided by 2, 3, 4, and 6. There is always a remainder of 1. But when divided by 7. there is no remainder. What is my age?
Solution:
Here, We need to look for the least common multiple (LCM) of the divisors 2, 3, 4, and 6, and then find a number that is 1 more than a multiple of that LCM and divisible by 7.
Here are the steps to find the age:
Find the LCM of 2, 3, 4, and 6:
LCM(2, 3, 4, 6) = 12
The LCM of 2, 3, 4, and 6 is 12.
Find a number that is 1 more than a multiple of 12 and divisible by 7:
Starting from 13 (1 more than the LCM), we can check multiples of 12 until we find a number divisible by 7.
Multiples of 12: 13, 25, 37, 49, 61
Among these numbers, 49 is divisible by 7.
Therefore, the age that satisfies the given conditions is 49.
Question 2
Adam is booking 14 – night holiday. Package A charges £53.75 per night. Package B charges £50.25 per night, plus a £50 booking fees. What is the difference in the total cost between the two packages?
Solution:
Package A:
Cost per night = £53.75
Total cost for 14 nights = 53.75 * 14 = £752.5
Package B:
Cost per night = £50.25
Total cost for 14 nights = 50.25 * 14 = £703.5
Booking fees = £50
Total cost for Package B = 703.5 + 50 = £753.5
Difference in total cost = 753.5 – 752.5 = £1
Therefore, the difference in the total cost between the two packages is £1.
Question 3
Work out the missing value.
(33+(1/3))% of ____ = 60
Solution:
Let x be the missing value.
(33 + 1/3)% of x = 60
(100/3)% of x = 60
(1/3) * x = 60
x = 60 * 3 = 180
Therefore, the missing value is 180.
Question 4
What is the probability of scoring a 2 on this spinner?
Solution:
Here we can see that 2 covers 1 out of 4 portion of the total circle.
The probability of scoring a 2 on this spinner is 1/4.
Therefore, the probability of scoring a 2 on this spinner is 1/4.
Question 5
What is the largest number of 30cm by 60cm by 40cm shoe boxes that can be fit in a 2m by 6m by 4m crate?
Be careful – you can’t chop the shoe boxes!
Solution:
The dimensions of the crate are 2m by 6m by 4m.
The dimensions of the shoe box are 30cm by 60cm by 40cm.
Convert the dimensions of the shoe box to meters:
30cm = 0.3m
60cm = 0.6m
40cm = 0.4m
The dimensions of the shoe box in meters are 0.3m by 0.6m by 0.4m.
Calculate the volume of the crate:
Volume of the crate = 2m * 6m * 4m = 48m^3
Calculate the volume of the shoe box:
Volume of the shoe box = 0.3m * 0.6m * 0.4m = 0.072m^3
Divide the volume of the crate by the volume of the shoe box to find the maximum number of shoe boxes that can fit:
Maximum number of shoe boxes = 48m^3 / 0.072m^3 = 666.67
Since we can’t have a fraction of a shoe box, the maximum number of shoe boxes that can fit in the crate is 666.
Therefore, the largest number of 30cm by 60cm by 40cm shoe boxes that can be fit in a 2m by 6m by 4m crate is 666.
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