Inductive reasoning

What it measures

Whether you can find the rule behind a sequence of figures or numbers from the examples alone, and use it to say what comes next. Nothing is stated; you infer the rule, then apply it. The skill is naming what changes between frames and checking that it keeps changing the same way.

How it appears

• Figure sequenceFour or five frames of shapes, dots and lines, and a choice of frames for the next one. Elements rotate, move, flip, change shade or change in number, often two at once.
• Odd one out or matching setA set of figures that share a rule and one that breaks it, or two sets and a figure to place in the right one.
• Number or letter seriesA sequence of numbers or letters and the next term to find. The same skill in a different costume.
• InteractiveYou build the next frame yourself by dragging its elements into place.

Timing

24 questions in 25 minutes.

graduatesfirst.com gives 18 questions in 24 minutes for the standard version and 15 questions in 18 minutes for the interactive one. Treat 60 to 80 seconds a question as the range.

How to tell it apart

• Deductive reasoningDeductive questions hand you the rules and ask what follows. Inductive questions hide the rule inside examples and ask you to find it.
• Checking informationChecking asks whether two things are identical. Inductive asks how one thing becomes the next.

The method

Name the change, check it repeats, predict before you look.

1. Look only at frame 1 and frame 2 and name what changed. Rotation, reflection, movement, a count going up or down, a shade switching.
2. Check that the same change takes frame 2 to frame 3. If it does not, there are two rules running at once, one per element, or a rule that alternates.
3. Track one element at a time across all the frames and ignore the rest while you do it.
4. Write the rule in words, the dot moves two places clockwise and the square flips each frame, and predict the next frame before you look at the options.
5. Cross out every option that breaks any one rule. The survivor is the answer; if two survive, you have missed a rule.
6. For a number series, take the differences between terms. If they are not constant, take the differences of the differences, or check whether each term is a multiple of the last.
7. Past the pace, choose the option that fits the most obvious rule and move on.

Traps to know

• The rule that fits three terms and fails the fourth

  Two rules often agree on the first three terms and part on the fourth. The reader spots the first rule, stops checking, and predicts from it.

  Setup The series reads 2, 4, 8, 14, and the question asks for the next term.

  The trap Doubling fits 2, 4, 8, so predicting 28. But doubling gives 16 for the fourth term, not 14.

  The escape The differences are 2, 4, 6, so the next difference is 8 and the next term is 22. Test the rule on every term you have.

• Rotation read as reflection

  A shape turned through 180 degrees can look like its mirror image. The two rules predict different frames when the shape is not symmetric, and both are offered.

  Setup An arrow points up, then right, then down.

  The trap Calling it a flip about the horizontal axis, which would send up to down and then back to up.

  The escape Up, right, down is a quarter turn clockwise each frame. The next frame points left, not up.

• Two rules, one noticed

  One element moves and another changes shade at the same time. Options that get the movement right but the shade wrong are there for the reader who tracked only one element.

  Setup A dot moves round a clock face two hours at a time while a square in the centre alternates filled and empty.

  The trap Picking the option with the dot in the right place and the square in the wrong state.

  The escape Track the dot, then track the square, then combine. An option must satisfy both.

• Counting the wrong thing

  The rule is in the number of sides, or the number of shaded regions, and the reader counts shapes. The count that is going up is not always the obvious one.

  Setup A triangle, a square, a pentagon, a hexagon.

  The trap Looking for a rule in the shapes' positions or shading, which do not change.

  The escape Count sides. Three, four, five, six. The next figure has seven.

Worked examples