Fence posts and gaps, letters passed on in rounds, people meeting on a road, gear wheels, clock angles and rules with a part for each one.
OftenIn many papers, especially GL AssessmentAbout 60 seconds a question in the test
The big idea
These are the problems entrance papers set about everyday things. Most have one idea that makes them easy and one trap that makes them hard.
Fence posts: in a straight line there is always one more post than gaps, and round a loop there are as many posts as gaps. Two people walking towards each other close the gap at their two speeds added together.
Gear wheels pass on one tooth at a time, so count the teeth that pass and divide by the teeth on the gear you want. On a clock, each number is thirty degrees apart.
Tips that save marks
Draw a tiny picture: three posts, two gaps.
With a rule such as forty minutes for each kilogram plus twenty, add the fixed part once.
Remember the hour hand moves too: at half past three it is halfway to the four.
A worked example
A straight fence is twenty metres long, with a post at each end and one every five metres. How many posts are there?
Twenty metres in fives makes four gaps.
A straight line has one more post than gaps.
Answer: five posts.
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 1Aim for about 60 seconds
A straight path has 8 trees, 6 m apart, with one at each end. How long is the path?
Show the worked answer
Answer: B, 42 m
How to work it out
8 trees in a line have 7 gaps between them, so the path is 7 × 6 = 42 m long.
Why the other options are wrong
A (14 m): This adds the number of trees to the gap; multiply the number of gaps by the gap.
C (54 m): This counts a gap before the first and after the last tree; the path starts and ends at a tree.
D (36 m): This has one gap too few: 8 trees make 7 gaps.
E (48 m): This gives every tree a gap; 8 trees in a line have only 7 gaps.
Question 2Aim for about 60 seconds
Kiran and Yusuf live 130 km apart. They set off at the same time towards each other, Kiran at 22 km/h and Yusuf at 30 km/h. How far from Kiran's home do they meet?
Show the worked answer
Answer: D, 55 km
How to work it out
Together they close the gap by 22 + 30 = 52 km every hour, so they meet after 130 ÷ 52 = 2.5 hours.
In that time Kiran has gone 22 × 2.5 = 55 km.
Why the other options are wrong
A (77 km): This is how far Kiran goes in 3.5 hours; they meet after 2.5 hours.
B (108 km): This takes one hour of Kiran's walking from the whole distance.
C (65 km): This is halfway; they only meet halfway if they go at the same speed, and Yusuf is faster.
E (75 km): This is how far Yusuf has gone, so it is the distance from Yusuf's home.
Question 3Aim for about 60 seconds
What is the smaller angle between the hands of a clock at 3 o'clock?
Show the worked answer
Answer: C, 90°
How to work it out
The hands are 3 numbers apart.
Each number is 360° ÷ 12 = 30°, so the angle is 3 × 30° = 90°.
Why the other options are wrong
A (270°): This is the larger angle, the long way round; the question asks for the smaller one.
B (120°): This counts one number too many; the hands are 3 numbers apart.
D (15°): This counts the minute marks between the hands as degrees; each number is 30°, not 5°.
E (18°): This uses 6° for each number; 6° is one minute mark. Each number is 30°.
Question 4Aim for about 60 seconds
Parcels A and B together balance parcel C. The three parcels weigh 1040 g altogether. Parcel A weighs 300 g. How much does parcel B weigh?
Show the worked answer
Answer: C, 220 g
How to work it out
C balances A and B, so C is half of the total: 1040 ÷ 2 = 520 g.
A and B together are also 520 g, so B = 520 − 300 = 220 g.
Why the other options are wrong
A (370 g): This shares what is left after A equally between B and C, but C weighs as much as A and B together.
B (820 g): This adds A to half the total; take A away from the half instead.
D (520 g): This is parcel C, half of the total; B is what is left of that half after A.
E (740 g): This is B and C together; C is half of the total, 520 g, and must be taken away too.
Question 5Aim for about 60 seconds
In round 1, Isla sends a letter to 4 people. In round 2, each of them sends a copy to 4 new people, and so on. How many people receive a letter in round 3?
Show the worked answer
Answer: B, 64
How to work it out
Each round multiplies the number of people by 4: 4, 16, 64.
Round 3 has 4 multiplied by itself 3 times = 64.
Why the other options are wrong
A (256): This is round 4, one step too far.
C (84): This counts everyone who has had a letter by the end of round 3, not just in round 3.
D (16): This is round 2; round 1 already has 4 people, so round 3 is one more step.
E (12): This multiplies 4 by the round number; each round multiplies the number of people by 4 again.
Want a plan built around the topics your child finds hardest?
Practise straight away at your child’s school year in maths and English, with verbal and non-verbal reasoning for the 11 Plus, and every answer explained. A free check, whenever you like, shows what to practise next and builds a weekly plan, for their year or for your target schools. Parents follow progress free.