Graphic Arithmetic: Reading Drawings Under a Clock

Graphic Arithmetic is the CAST test's drawing section: 16 questions in 30 minutes, worked from two drawings. The arithmetic itself is straightforward — adding, subtracting, multiplying, working with dimensions and scales. What the section actually measures is whether you can pull the right numbers off a technical drawing without misreading it, which is a different skill from being good at math, and a much more job-relevant one.

It appears in both the original CAST and the revised CAST-R with identical parameters. It is also the closest documented relative of the TECH battery's Graphic Problem Solving and Interpreting Diagrams tests, so practicing it is worth doing even if TECH is the battery you face.

Why 112 seconds a question is not generous

Sixteen questions in thirty minutes works out at nearly two minutes each, which sounds comfortable next to the 27 seconds a question you get on Mechanical Concepts. It is not, for one reason: you are not answering 16 independent questions. You are learning two drawings and then answering eight questions about each.

That structure rewards front-loading. Spend the first ninety seconds on a drawing orienting yourself — what is it showing, what are the units, is there a scale, are there labels or a legend, which dimensions are given and which are implied — and every question afterward gets faster. Candidates who dive straight into question one and keep re-reading the drawing from scratch are the ones who run out of time.

Where the marks actually go

Almost all avoidable errors on a section like this fall into four buckets:

• Unit mismatch. The drawing is in feet and inches, the question asks in inches, or the drawing gives a diameter and the question wants a radius. The arithmetic is right and the answer is wrong.
• Reading an adjacent dimension. Technical drawings stack dimension lines. Under time pressure it is easy to take the overall length when the question wanted a segment of it.
• Assuming a drawing is to scale. Unless a scale is stated, the picture is a diagram, not a measurement. Work from the printed numbers only.
• Answering the wrong question. The item asks how much longer piece A is than piece B; you compute A. Distractor options are usually built from exactly these near-misses.

That last point is worth dwelling on. On a well-built multiple-choice test the wrong answers are not random — they are the results of the most common mistakes. If your answer appears in the options, that is not confirmation you got it right.

A method that survives the clock

1. Read the question fully before you look at the drawing again. Know what you are hunting for.
2. Note the units in the question and the units on the drawing before you compute anything.
3. Find the values, write them down, then do the arithmetic. Doing both at once is where transcription errors come from.
4. Sanity-check the magnitude. If you are calculating the length of a crossarm and get 400 feet, you took the wrong dimension.
5. Never leave a blank. EEI's brochures state there is no penalty for guessing or wrong answers, so a rushed answer beats an empty one.

Our Graphic Arithmetic demo runs items against a real clock with the drawing on screen, which is the part that matters: practicing this from written notes teaches a different skill from practicing it against a diagram you have to keep returning to.

The calculator question

The CAST-R brochure contains the sentence "The use of a calculator is permitted during this test", printed under Graphic Arithmetic. It is the only calculator statement in any of the EEI brochures covering the batteries on this site, and it does not appear under any other section. The original CAST brochure has no calculator statement at all.

Whether you get one on the day is a separate matter, decided by the employer and the proctor. Southern California Edison, for example, tells candidates they may not bring any electronic device including a calculator, and that it supplies all necessary equipment itself. The practical plan: build your arithmetic so you do not need a calculator, and treat one as a bonus if it appears. The employer-by-employer picture is here.

What to drill

Three things, in this order. First, unit conversion until it is reflexive — feet to inches, inches to fractions, and back. Second, reading dimensioned diagrams: circumference and area of circles, perimeters, simple volumes, and the difference between a stated dimension and one you have to derive. Third, ratio and scale, because scale questions are where the most confident candidates come unstuck.

If you have limited preparation time, pair Graphic Arithmetic with Mathematical Usage: they draw on the same arithmetic but at opposite ends of the pacing spectrum, and practicing both makes each feel easier. Full CAST practice runs them in the real order.

Frequently asked questions

How many questions is Graphic Arithmetic?

16 questions in 30 minutes, based on two drawings, in both the CAST and CAST-R batteries. That is per EEI's brochures for each battery.

What math do I need for it?

Arithmetic and basic geometry: the four operations, fractions and decimals, percentages, ratio and scale, perimeter and area, and unit conversion. Nothing that requires algebra beyond rearranging a simple relationship.

Is Graphic Arithmetic the same as Mathematical Usage?

No. Mathematical Usage is a speed test of 18 questions in 7 minutes with no drawings. Graphic Arithmetic gives you far more time per question but makes you extract the numbers yourself from a drawing.

Does it appear in POSS or MASS?

No. Graphic Arithmetic is a CAST and CAST-R section. The plant batteries use Figural Reasoning and Assembling Objects for their visual components instead. See what each tier covers.