CAT Quant Mental Math: 4 Recall Tables to Memorise

Quant

Twenty two questions, forty minutes. That is 109 seconds a question if you attempt every one, and nobody attempts every one. Watch your own rough sheet on a Quant sectional and count how many of those seconds went to the actual idea in the question, and how many went to working out that 17 squared is 289.

For most aspirants the split is worse than they expect. The thinking is fine and the arithmetic is slow, so arithmetic CAT questions that should close in ninety seconds run to three minutes. This piece is about the specific numbers worth putting into memory, the ones not worth it, and a six week schedule that makes the recall survive.

Where Your Quant Time Actually Goes

Time in a Quant section leaks in three places, and only one of them feels like a problem while it is happening. Reading and setup feel productive. Checking feels responsible. Arithmetic feels like nothing at all, which is exactly why it goes unmeasured.

The compounding is what hurts. Fifteen extra seconds on a calculation is nothing on one question. Across twelve attempts it is three minutes, and three minutes at the end of a section is roughly two more attempts you never got to. The loss shows up as a low attempt count, so aspirants diagnose it as a coverage problem and study more chapters.

• You reach for the on-screen calculator for two digit multiplication.
• You convert a fraction to a decimal by long division rather than recognising it.
• You compute a square you have seen forty times before.
• You approximate badly because you have no anchor value to approximate against.

The fix is not more practice at the same speed. It is removing the pauses, which is a different activity and takes about six weeks of very small daily sessions rather than an extra chapter.

What to Memorise, and What Not To

Memorisation gets a bad reputation in CAT preparation, and mostly deserves it. Memorising a hundred formulas produces a lookup problem. Memorising forty numbers produces recognition, and recognition is what removes the pause.

The test for whether a number belongs in memory is frequency, not difficulty. A value you will meet in half your practice sessions earns a place. A value you will meet twice a year does not, however impressive it looks on a formula sheet.

Worth memorising	Not worth memorising
Squares to 30, because they appear inside every quadratic, Pythagorean and mensuration question	Squares past 50, which two tricks generate faster than recall
Cubes to 20, because CAT number system questions lean on them	Fourth powers past 6, which almost never appear
Unit fractions to 1/20 as percentages, the single highest yield table	Long decimal expansions past two places
Powers of 2 to 12 and powers of 3 to 6	Logarithm values, which CAT supplies when needed

The Recall Bank: 4 Tables Worth Memorising

Four banks, roughly eighty values in total, and about six weeks to make them automatic. That is the entire investment, and it is smaller than one chapter.

• Squares carry the most weight, because they sit inside quadratics, right triangles and mensuration alike.
• Cubes are the smallest bank and pay almost entirely through the root direction.
• Unit fractions pay across three sections rather than one, which is why they come first in the schedule.
• Powers pay as recognition rather than as speed, and that recognition often reveals the intended method.

Why Four Banks and Not a Formula Sheet

A formula sheet answers a question you already know how to ask. A recall bank removes a pause you did not know you were taking. The two are not substitutes, and the bank is the one that changes your attempt count rather than your accuracy.

Bank 1: Squares to 30, and Two Tricks

Learn one to thirty by rote, in writing rather than by reading. There are only thirty of them, the first fifteen are already familiar, and the second fifteen take about a week. Then stop, because two patterns cover almost everything above thirty.

The Numbers Ending in Five Trick

For any number ending in 5, multiply the leading part by the next integer and write 25 after it. So 35 squared is 3 times 4, then 25, giving 1225. And 65 squared is 6 times 7, then 25, giving 4225. It is exact, not an approximation, and it works to any size.

The Near Anchor Trick

• Near 50: (50 plus x) squared is 2500 plus 100x plus x squared. So 53 squared is 2500 plus 300 plus 9, which is 2809.
• Near 100: (100 minus x) squared is 10000 minus 200x plus x squared. So 97 squared is 10000 minus 600 plus 9, which is 9409.
• Near 30 or 40: use the same expansion with 900 or 1600 as the anchor.
• Difference of squares: 43 times 37 is 40 squared minus 3 squared, which is 1591.

Bank 2: Cubes to 20, and Free Cube Roots

The twenty values are 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859 and 8000. Ten of those you already know, so the real work is the second half.

The bonus is that cube roots come free. Every digit has a unique last digit when cubed, so the last digit of a perfect cube tells you the last digit of its root immediately. Cubes ending in 1, 4, 5, 6, 9 and 0 keep their digit, and the rest swap in pairs: 2 with 8, and 3 with 7.

1. Take the cube, say 6859. The last digit is 9, so the root ends in 9.
2. Strip the last three digits, leaving 6. It sits between 1 cubed and 2 cubed, so the root starts with 1.
3. The root is 19. No division, no estimation, about four seconds.

Bank 3: The Fraction to Percentage Table

This is the highest yield bank of the four, because it converts division into recognition. Percentage, profit, ratio, data interpretation and averages all reduce to it, and it is only nineteen values.

Fraction	Percentage	Fraction	Percentage
1/2	50	1/11	9.09
1/3	33.33	1/12	8.33
1/4	25	1/13	7.69
1/5	20	1/14	7.14
1/6	16.67	1/15	6.67
1/7	14.29	1/16	6.25
1/8	12.5	1/17	5.88
1/9	11.11	1/18	5.56
1/10	10	1/19	5.26

Two habits make the table pay. First, read every percentage in a question as a fraction, so 37.5 percent becomes 3/8 and the arithmetic collapses. Second, use the table for approximation in data interpretation, where 5.9 percent is close enough to 1/17 to rank two options without dividing anything.

The Five Conversions That Appear Most

• 1/8 and its multiples, because 12.5, 37.5, 62.5 and 87.5 are the percentages CAT reuses most in profit questions.
• 1/6 and 1/12, which cover the 16.67 and 8.33 that appear in time and work.
• 1/7, whose decimal repeats in a fixed cycle and shows up in number system questions.
• 1/11 and 1/9, which give the repeating 9.09 and 11.11 that DI options are built around.
• 1/16, since 6.25 is the value aspirants most often stop to divide for.

Bank 4: Powers and the Numbers CAT Reuses

The last bank is short. Powers of 2 up to 4096, powers of 3 up to 729, and the awareness that CAT recycles a small set of friendly numbers because they make clean answers.

• Powers of 2: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096.
• Powers of 3: 3, 9, 27, 81, 243, 729.
• Powers of 5 and 7 to the fourth: 625 and 2401.
• Factorials to 6: 1, 2, 6, 24, 120, 720. Beyond that they rarely appear as values.

There is a recognition benefit as well as a speed one. CAT chooses friendly values on purpose, so a number appearing in your working that happens to be a power or a factorial is usually a signal about the structure rather than a coincidence.

Powers of 2 earn their place because they appear across number system, progressions and permutations. When a question produces 1024 or 2048, recognising it as a power of 2 usually reveals the structure the setter intended, and that recognition is worth more than the arithmetic it saves.

Drilling It: A 6 Week Schedule

Recall decays quickly and rebuilds cheaply, which makes frequency the only variable that matters. Five minutes on six days beats forty minutes on one, and the schedule below assumes nothing more than that.

1. Weeks 1 and 2. Squares 16 to 30, five minutes daily, written from memory rather than read.
2. Weeks 3 and 4. Cubes 11 to 20, plus the last digit rule for roots, in both directions.
3. Week 5. The fraction table, and the multiples of sevenths, eighths and elevenths.
4. Week 6. Powers, then mixed recall at random rather than in table order.

Write from memory every time. Reading a table feels like revision and produces recognition rather than recall, and recognition fails under exam pressure. Then test the recall where it is meant to pay, inside percentage questions for CAT preparation and timed sets rather than in the table itself.

Keep the written reference short while you drill. The free CAT formula and cheatsheet library already holds these tables, so your own page only needs the values you personally keep missing. When the recall is stable, take it into topic-wise CAT exam previous year questions, where the arithmetic is deliberately unfriendly and the saved seconds are most visible.