How the Graphic Arithmetic test works
The test is part of CAST and CAST-R, the batteries for construction and skilled trades jobs such as line work, substation maintenance and meter service. You get 16 questions in 30 minutes, set on two drawings with several questions each, which is nearly two minutes a question.
The drawings carry their dimensions, and EEI warns that they are not necessarily drawn to scale. Every answer comes from arithmetic on the printed numbers: a missing length in a chain of dimensions, a distance between centres, an area, or how many times longer one part is than another. Each question has five answers, the last being N or none of the above.
The CAST-R brochure says a calculator is permitted. The 2009 CAST brochure does not mention one, so ask your utility. TECH has a similar subtest, Graphic Problem Solving, with one small drawing and four answers per question; it is reported as 21 questions in 19 minutes.
How to solve a Graphic Arithmetic question
Treat each drawing as a set of numbers, not a picture:
- Before the first question, spend 30 seconds reading every dimension and what it runs between.
- Convert mixed units, such as feet and inches, into one unit before adding or subtracting.
- For a missing length, take the overall dimension and subtract every known part along the same line.
- Never measure with your eye or a ruler. A line that looks longer may be shorter.
- Check that the answer is sensible for the drawing, then choose N only if your checked value is missing.
Worked example
A drawing shows a pipe run in three straight sections. The first is labelled 6 ft 4 in, the second 9 ft 10 in, and the third has no label. The whole run is labelled 22 ft 6 in. How long is the third section? a: 5 ft 2 in. b: 6 ft 2 in. c: 6 ft 4 in. d: 7 ft 4 in. e: none of the above.
Add the known sections: 6 ft 4 in + 9 ft 10 in = 15 ft 14 in, which is 16 ft 2 in. Subtract from the total: 22 ft 6 in − 16 ft 2 in = 6 ft 4 in. Check: 6 ft 4 in + 9 ft 10 in + 6 ft 4 in = 21 ft 18 in = 22 ft 6 in. The answer is c.
Tips for the real Graphic Arithmetic test
- Use the generous clock. At almost two minutes a question, checking each answer is affordable.
- Practise feet-and-inches arithmetic until carrying 12 inches into a foot is automatic.
- Mark the drawing with the values you work out. Later questions often reuse them.
- If a calculator is allowed, use it for multiplication and division, but do the unit conversion first.
- Leave nothing blank. CAST does not penalise wrong answers.
Practise Graphic Arithmetic on CogniPrep
There are three set-ups to choose from. CAST-R gives 16 questions in 30 minutes with an on-screen calculator; CAST is the same paper without the calculator; and TECH Graphic Problem Solving gives 21 questions in 19 minutes, one drawing and four answers each, on the reported clock. You can move freely between questions and hand in from a review grid, and your score out of 100 counts every question on the paper. The drawings are our own.