11 plus Number Analogies questions

What a Number Analogies question looks like

Number Analogies is a number question from the 11 plus verbal reasoning paper. Each one prints three groups of numbers side by side. A group is written as two outside numbers with a third number in a bracket between them, like 4 (12) 3. One hidden rule turns the two outside numbers of a group into the number in its bracket, and the same rule holds in all three groups.

The first two groups are complete, so they are where the rule is found. In the third group the bracket is empty, printed as (?), and the question asks what the missing number is. Five options are offered. The missing number is always the one in the bracket, never an outside number.

The arithmetic is kept small deliberately: whole numbers, mostly under 60, with a whole number as the answer. What varies is the rule: the simpler questions use one step, such as adding the two outside numbers or working out how many times one goes into the other. The harder ones use two, such as adding them and then taking away 4, or taking one from the other and then multiplying by 3.

Example one: 4 (12) 3, 6 (30) 5, 7 (?) 2

The options are 9, 5, 14, 12 and 16.

Start with the first group. The outside numbers are 4 and 3, and the bracket holds 12. Adding them gives 7, which is not it. Multiplying gives 12, which is. Test that on the second group before going further: 6 x 5 = 30, which is what its bracket holds. The rule has worked twice, so it can be trusted. Third group: 7 x 2 = 14. The answer is 14.

9 is the tempting wrong option, because 7 + 2 = 9. Adding is the first thing most children try, and here it lands on a number in the list. It never fitted the first two groups, which is why checking the second one matters.

Example two: 7 (15) 2, 8 (12) 4, 9 (?) 5

The options are 4, 12, 8, 15 and 18.

First group: 7 and 2, with 15 in the bracket. Adding gives 9, taking away gives 5, multiplying gives 14, so the rule has two steps. 7 take away 2 is 5, and 5 x 3 = 15. Check on the second group: 8 take away 4 is 4, and 4 x 3 = 12, which matches. Third group: 9 take away 5 is 4, then 4 x 3 = 12. The answer is 12.

4 is the wrong option that catches children, and it is the first step on its own. Take 5 from 9, get 4, see a 4 in the options and stop, with the times 3 still to come. 15 is there too, only the first bracket number copied down.

Example three: 12 (16) 8, 9 (11) 6, 15 (?) 7

The options are 22, 16, 11, 18 and 26.

First group: 12 + 8 = 20, but the bracket holds 16, so adding is close and four too big. Try the same on the second group: 9 + 6 = 15 and the bracket holds 11, again four too big. Out by the same amount twice turns a near miss into a rule: add the two outside numbers, then take away 4. Third group: 15 + 7 = 22, then 22 take away 4 is 18. The answer is 18.

Two of the wrong options come from that rule half done or done backwards. 22 is the adding with the take away forgotten. 26 is 22 with 4 added instead of taken away, from spotting the gap of four but not which way it goes. 16 and 11 are the two bracket numbers already printed in the question.

How to answer it

1. Cover the third group and look only at the first. Take its two outside numbers and try four things: add them, take one from the other, multiply them, and work out how many times the smaller goes into the bigger.
2. If one of those gives the bracket number, test it on the second group straight away. A rule that works on two groups is the rule; one that works on a single group is a coincidence, and this type is built out of coincidences.
3. If nothing fits exactly, look at how far off the closest attempt was. Out by the same amount in both groups means a second step: add that amount, take it away, double the result or halve it.
4. Apply the rule to the third group in the same order, with the numbers in the same places. If it took the third number away from the first, keep it that way round.
5. Check your answer is one of the five options. If it is not, the rule is wrong rather than the arithmetic, so go back and try another one.

Common mistakes

• Settling on a rule from one group. Adding, multiplying or taking away will often hit the first bracket number by luck. The second group is the test, and it costs no time.
• Stopping after the first step. In a two-step rule the halfway number is frequently one of the options, so a half-finished answer feels finished.
• Getting the order the wrong way round. Sometimes the bracket comes from the first number take away the third, sometimes from the third take away the first, and dividing works the same way. The wrong order usually still gives a tidy whole number, so nothing feels wrong.
• Adjusting in the wrong direction. Spotting that the answer is four away from the total is only half the job. Four the wrong way is in the list often enough to be worth a second look.
• Choosing a number already on the page. The bracket numbers from the first two groups turn up among the options a lot. If your answer is one you copied rather than worked out, check it again.

How to practise 11 plus Number Analogies questions

Extra arithmetic drill is rarely what a child needs here, because the sums are small by design. What builds the score is the habit in step 2: find a rule, then test it on the second group before using it. Little and often beats a page in one sitting: a page lets a child settle into one kind of rule and stop looking properly, which is the opposite of the skill being tested. It is one of around 25 verbal reasoning formats used in the eleven plus, so it repays being kept in rotation. 11+ Daily has a Number Analogies project that mixes one-step rules with two-step ones and varies which way round the taking away and dividing go, alongside the other 11 plus verbal reasoning question types. Every question is original to 11+ Daily, nothing is a past paper, and the bank is re-checked in rounds. If you are working out how much time to give it, we have written about how much 11 plus practice a child needs each day.

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