11plus Daily Free Practice Paper – 27 May 2024

Solution:

Let the cost of a chocolate frog be x and the cost of a truffle be y.
From the information given, we can form two equations:
7x + 5y = 60 (1)
3x + 2y = 25.45 (2)
Multiply equation (2) by 5 and equation (1) by 2:
15x + 10y = 127.25 (3)
14x + 10y = 120 (4)
Subtract equation (4) from equation (3):
15x + 10y – 14x – 10y = 127.25 – 120
15x – 14x + 10y – 10y = 7.25
x = 7.25
Therefore, a chocolate frog costs £7.25.

Solution:

Let x be the length of small rectangle and a be the width
As all rectangles are identical
x = 3a (a+a+a).
or a = x/3

Now according to question,
The area of the larger rectangle is 48cm².
The area of each of the four identical rectangles is 48/4 = 12cm².
x × a = 12cm²
x × x/3 = 12cm²
x² = 12 × 3
x² = 36
x = √36 = 6cm
Therefore, the length of the side labelled x is 6cm.

Solution:

3 cat bowls cost £36.
1 cat bowl costs £36/3 = £12.
9 cat bowls cost £12 x 9 = £108.
9 cat bowls cost the same as 4 dog leads.
4 dog leads cost £108.
1 dog lead costs £108/4 = £27.
Therefore, a dog lead costs £27.

Solution:

To solve this, convert the mixed numbers to improper fractions.
14+(3/5) – 3+(2/10)
(14 x 5 + 3) / 5 – (3 x 10 + 2) / 10
(70 + 3) / 5 – (30 + 2) / 10
73 / 5 – 32 / 10
73 / 5 – 16 / 5
(73 – 16) / 5
57 / 5
Therefore, 14(3/5) – 3(2/10) = 57/5.

Solution:

Let the smallest whole number be x.
x = 57n + 2
x > 120
57n + 2 > 120
57n > 118
n > 118/57
n > 2.07
n = 3
x = 57 x 3 + 2 = 171 + 2 = 173
Therefore, the smallest whole number, above 120, which when divided by 57, leaves a remainder of two is 173.