Free CCAT practice test: 50 questions in 15 minutes

The answer is A.

Long rules are easier to judge once you strip them to their connectors. This one says: allowed if you are 17 or older, or if you have written permission. The word or means either condition on its own is enough, so both are never required at the same time. Maria meets the first, which settles it, and the missing permission is the distractor the sentence is built around.

The habit worth keeping: circle the connector before you weigh the facts. And answers you when both conditions must hold; or answers you when either one will do, and mixing the two up produces a confident wrong answer faster than any other mistake in this section.

The answer is D, $12.

The arithmetic is the easy part; the second line is the question. Thirty-two eggs are two boxes and eight eggs over, and since you cannot buy eight loose eggs, those eight cost a whole third box: 3 × $4 = $12.

Every wrong answer is a correct calculation for a different shopping trip. $10.67 is what 32 eggs would cost if you could buy them one at a time, $8 buys two boxes and leaves you eight eggs short, $16 pays for a box you do not need, and $11 rounds the money up when it is the number of boxes that has to be rounded.

The habit worth keeping: when something can only be bought in whole units, divide, round UP to the next whole unit, and only then multiply by the price. Fractions of a box do not exist, and the line that says so is the easiest line to skip when the clock is running.

The answer is D, $75.

Work backwards through the discount before you go anywhere near the four items. At 40% off, the customer pays 60% of the original price, so $180 is 60% of what the goods cost before the sale. Since 10% is $30, 100% is $300, and the average of four items is $300 ÷ 4 = $75.

The trap is choice C. Adding 40% back to what was paid feels like undoing the discount and is not the same operation: $45 plus 40% is $63, because the 40% was taken off the larger number and added back to the smaller one. Choice B is the average actually paid, which is the answer to a question about today rather than before the sale; choice A applies the discount a second time; and choice E is the pre-sale total with the last step forgotten.

The habit worth keeping: a price after a discount is a percentage OF the original, so you divide to get back, never add the percentage on. And decide before you calculate whether the answer has to be larger or smaller than the number in the question. Here it has to be larger than $45, which removes two options in a second.

The answer is E, Bared 120.

Profit is the sale price minus everything in the cost columns, so the first move is to notice that the three cost columns have to be added before anything can be compared.

Two rows go without arithmetic: Bared 260 costs at least as much as Bared 120 in every cost column, more in two of them, and sells for less, so it loses on both counts, and Calir XR costs about as much as Calir XC but sells for almost $400 less, so it cannot win either. That leaves three rows to compute: Bared 120 makes $552, Calir XC $549, Bared 450 $522.

And that is the point of this question. The top two are three dollars apart, so estimating would have handed you the wrong product. Some questions invite an estimate and some punish it; a table with several columns to add is usually the second kind.

The habit worth keeping: scan for rows that cannot win, because they lose on every column or because a similar row sells for far more, and delete them first; then do the arithmetic only for what survives. Here that turns five calculations into three.

The answer is D, 9.

Chain questions read long and solve fast if you start at the only number you are given and follow the links in order: Jean is 10, Alice is a fifth of that, so 2. Jonathan is twice Alice, so 4. Dave is five years older, so 9.

Now look at what the wrong answers are made of. Choice B is Jonathan’s age and choice A is Alice’s, which is where you land by stopping one or two links early; 7 adds the five years to Alice and skips Jonathan; 15 adds them to Jean, the only age the question states.

In chain questions the wrong answers are built from the steps of the correct path, so an answer that turns up halfway through your own calculation deserves a second look rather than relief.

The answer is D, 0.0077.

Give every number the same number of decimal places by padding with zeros, then read left to right and stop at the first column where they differ. That column decides, and no digit to its right can overturn it: 0.07000, 0.00900, 0.00810, 0.00770, 0.00779. Two candidates survive the third decimal place, they agree on the fourth as well, and the fifth decides: 0 against 9, so 0.0077 is the smaller one.

The trap is the length of the number: 0.00779 has the most digits in the list, which makes it look like the smallest for the wrong reason, when the extra digit is exactly what makes it larger. Padding removes the illusion and costs you two seconds.

The answer is D, gik.

Letters are hard to compare and positions are easy, so translate first: c, e, g is 3, 5, 7. The next group, d, f, h, is 4, 6, 8, then 5, 7, 9, then 6, 8, 10.

Two rules fall out at once. Inside a group the step is always two, one letter skipped each time, and from group to group everything shifts up by one. So the next group is 7, 9, 11, which reads back as g, i, k.

Check what the wrong answers do with that: ghj starts correctly but drops the skip between the first two letters, gjl stretches the first gap to three, hjk starts on the wrong letter and compresses the last gap, and hjl is the dangerous one, because it keeps both skips and only starts one letter too far, which is what you get by shifting the last group by two instead of one. Each breaks at least one half of the rule, which is why a quick glance is not enough.

The habit worth keeping: a letter series is a number series in disguise. Write the alphabet positions, or count them on your fingers, and you are back on ground where the pattern is obvious.

The answer is D, 22.

The series looks erratic because two simple series are woven into one. Read every second number instead of every number: 7, 2, -3 falls by five each step, and 12, 17 rises by five each step. The question mark belongs to the rising strand, so it is 17 plus 5.

If you would rather work with the gaps, they run +5, -10, +15, -20, growing by five and flipping sign every step, which makes the next gap +25, and -3 plus 25 is 22 again.

Now look at what the wrong answers are made of: -8 continues the falling strand, which is where you land if you find the two strands and then forget to check which one the question mark sits in; -23 repeats the last gap unchanged, and -28 lets the gap grow to 25 but keeps its sign, so both miss the flip; and 27 takes two rising steps from 17 because two positions have passed, when the strand has moved only once. Finding the two strands is only half the work, and checking which one the question mark sits in is the other half.

The habit worth keeping: when a series swings up and down, stop reading it as one series. Alternating direction is the signature of two interleaved ones, and splitting them turns one hard question into two easy ones.

Two series in one. The upper arcs fall by five, the lower arcs rise by five, and the question mark sits on the rising strand.

The answer is C, $40.

This question hands you more numbers than it needs, and finding the two that matter is the whole exercise. The factory earns $5,760 over 48 hours, so it currently earns $120 an hour. Adding a fourth machine to three raises output by one third, the same job finishes in proportionally less time, and the hourly earnings rise by that same third: a third of $120 is $40. The 720 toys and the output per machine never enter the calculation.

If you prefer the long road it also works, four machines wrap 20 toys an hour and finish in 36 hours, so $5,760 over 36 hours is $160 an hour, and $160 minus $120 is $40.

Notice the distractors that come from that road: $160 is the new hourly figure, correct but not what was asked, $120 is the old one, and $20 is the four machines’ combined output in toys per hour. The most dangerous option is $30: adding a fourth machine feels like adding a quarter, but the quarter is measured against the new four, and against the original three it is a third.

The habit worth keeping: before calculating, ask which of the given numbers the question actually needs. Word problems of this kind regularly supply figures that only exist to make the long path look compulsory.

The answer is C, 16.

Translate the condition once instead of testing each option: the sum sits between 36 and 64, and an average is the sum divided by four, so the average sits between 9 and 16. Now read the options against that range and only 16 falls outside it. It fails by the smallest possible margin, which is the entire point of the question: an average of 16 needs a sum of exactly 64, and the sum has to be smaller than 64.

The other four correspond to sums of 37, 44, 52 and 63, all inside: 9.25 and 15.75 sit one unit of the sum away from the ends and are still possible, because 37 is greater than 36 and 63 is smaller than 64.

Two things make this question harder than the arithmetic in it. The word NOT means four of the five options are possible, so the first option that fits will feel like the answer if you read past it. And the ends of the range are not included, so the endpoint that looks like it belongs is the one that does not, while the two values that look too close to the edge are fine.

The habit worth keeping: when a question gives you a range, convert it once and mark whether the ends are included. Questions of this type almost always live at the ends.

The answer is E, 880.

Start with direction, not arithmetic. You are given a part and asked for the whole, so the answer has to be larger than 616. That alone removes 88 and 431 before you calculate anything, and 431 is exactly what you get by multiplying when the question calls for dividing, which is the mistake this question is built to catch.

Then take the short path: 70% is seven tenths, so one tenth is 616 divided by 7, which is 88, and ten tenths is 880.

Notice where that leaves choice A. 88 is not a wrong calculation, it is the right one stopped a step early, sitting in the options waiting for someone in a hurry. Choice C, 801, is the other tempting road: adding the missing 30% of 616 back on, as if 30% of the part were 30% of the whole. And 862 is what an estimate produces when the reciprocal of 0.7 is rounded down to 1.4; the short path is exact and just as fast, so there is no reason to estimate here. Confirm in two seconds if you like: 70% of 880 is 616.

The habit worth keeping: decide whether the answer must be bigger or smaller than the number you were given before you touch the numbers. On reverse percentage questions the instinct to multiply produces a plausible option every time.