Numerical Ability & Data Interpretation

The GAT's numerical block is pitched at Class 8 to 10, not Class 12 — there is no calculus, no trigonometry and no coordinate geometry. What there is instead is arithmetic under a clock: percentage, ratio, average, profit and loss, simple and compound interest, time-speed-distance, time and work, and a data table or graph to read. That is perhaps 10 to 12 of the 50 questions, and they are the most winnable in the paper for a specific reason: the mathematics is easy enough that your score is decided by method, not by knowledge. A student who converts percentages to fractions and works from the options finishes comfortably; a student who does long multiplication does not.

The Fraction Table — the Single Biggest Time Saver

Almost every percentage question becomes a one-step calculation if you know the fraction that the percentage equals. Finding 12.5% of 640 by multiplication is slow; recognising 12.5% as ⅛ and dividing 640 by 8 gives 80 instantly. Learn this table cold — it is the highest-return twenty minutes available anywhere in the GAT.

Percentage to fraction — memorise both directions
Percentage	Fraction	Use it like this
50% · 25% · 75%	½ · ¼ · ¾	75% of 480 = 480 × ¾ = 360
33⅓% · 66⅔%	⅓ · ⅔	33⅓% of 987 = 329
20% · 40% · 60% · 80%	⅕ · ⅖ · ⅗ · ⅘	60% of 250 = 150
16⅔% · 83⅓%	⅙ · ⅚	16⅔% of 720 = 120
12.5% · 37.5% · 62.5% · 87.5%	⅛ · ⅜ · ⅝ · ⅞	37.5% of 640 = 240
11⅑% · 9¹⁄₁₁%	⅑ · ¹⁄₁₁	These appear in "increase/decrease by" questions

🧠 Successive percentage change in one step

If a quantity rises by a% and then by b%, the net change is a + b + ab/100, and a fall is entered as a negative. So +20% then −20% gives 20 − 20 − 400/100 = −4%, not zero — which is why a shopkeeper who raises a price 20% and then offers 20% off still ends 4% below where he started. The same formula answers discount-on-discount and population-growth questions, so one line replaces three calculations. A related identity worth holding: to reduce a number by 20% you multiply by 0.8, and to undo that you divide by 0.8, not multiply by 1.2.

The Seven Topics and the One Formula Each Needs

Everything you actually need to remember
Topic	The formula	The point the examiner tests
Profit & loss	Profit % = (SP − CP)/CP × 100	Always on cost price. Computing on SP is the standard wrong answer
Simple interest	SI = PRT/100	Interest is the same every year
Compound interest	A = P(1 + R/100)ᵗ; CI = A − P	For 2 years, CI − SI = PR²/100² — a one-line shortcut
Average	Average = sum ÷ count	When one value is replaced, work with the change in the sum, not fresh totals
Ratio	Write parts as 3x, 5x and solve for x	Turning a ratio into actual quantities is the whole skill
Time, speed, distance	D = S × T; km/h → m/s by × 5/18	Average speed for equal distances is the harmonic mean 2ab/(a+b), not (a+b)/2
Time & work	Work per day = 1/days; add the rates	A in 10 and B in 15 → 1/10 + 1/15 = 1/6, so 6 days together

⚠️ Average speed is not the average of the speeds

Travel 60 km at 30 km/h and 60 km back at 60 km/h. The tempting answer is 45 km/h; the correct one is 40 km/h. Total distance 120 km, total time 2 + 1 = 3 hours, so 120/3 = 40. The intuition fails because you spend more time at the slower speed, which drags the average down. For two equal distances use 2ab/(a+b) directly. Note the contrast: if the two speeds are held for equal times rather than equal distances, then the ordinary average (a+b)/2 is right — so read which quantity is equal before choosing the formula.

Data Interpretation — Reading Before Calculating

A DI set gives a table, bar chart, line graph or pie chart with three to five questions hanging off it. The marks are lost not in the arithmetic but in misreading the chart, so spend fifteen seconds on the frame before touching a number.

Read the units and the title. "Figures in lakhs" or "in ₹ crore" changes every answer, and a chart whose axis starts at 40 rather than 0 exaggerates differences to the eye.
Check whether the figures are absolute or percentages. A pie chart is always shares of a whole, so a bigger slice of a smaller total can be a smaller number — the most common DI trap.
In a pie chart, degrees convert at 3.6° per 1%. So a 90° sector is 25% and a 54° sector is 15%.
Estimate before you calculate. Options are usually far apart, so "a bit more than a quarter of 8,000" often identifies the answer without any long division.
Answer the easy questions of a set and skip its hardest. The questions of one set are independent, so a difficult ratio-of-ratios item need not cost you the three simple ones beside it.

A worked mini-table: students enrolled (in hundreds)
Year	Arts	Science	Commerce
2022	12	18	10
2023	15	21	14
2024	18	24	18

🧠 How to read that table fast

Three questions and three shortcuts. Total in 2023? 15 + 21 + 14 = 50 hundreds = 5,000 students — the unit line is doing real work here. Percentage growth in Commerce from 2022 to 2024? From 10 to 18 is a rise of 8 on a base of 10, so 80% — always divide by the earlier value. Which stream grew fastest overall? Commerce, at 80%, beats Arts (12→18, 50%) and Science (18→24, 33⅓%), even though Science added the same six hundreds as Arts. That last point is the lesson: percentage growth and absolute growth rank differently, and DI questions are written precisely to catch a candidate who computes one and answers the other.

🎯 Why this block, not GK, decides most GAT scores

Put the numbers together. Reasoning is about 12–15 questions and numeracy with DI about 10–12, so the two aptitude blocks are roughly half the paper — and both are closed sets that respond directly to practice. GK and current affairs together are perhaps 20–25, but they are unbounded, so the last mark there always costs more than the last mark here. The practical plan follows: build the fraction table and the seven formulas first, then do one timed DI set and fifteen arithmetic questions a day, logging every error by type. Two hundred practice questions is usually enough to move from half-right to four-fifths-right, and that swing alone is worth more than a month of newspapers.

Key takeaways

The numerical block is Class 8–10 arithmetic — about 10–12 of 50 questions, no calculus or trigonometry.
Memorise percentage-to-fraction: 12.5%=⅛, 16⅔%=⅙, 33⅓%=⅓, 37.5%=⅜ — the best twenty minutes in the GAT.
Successive change = a + b + ab/100, so +20% then −20% is −4%, not zero.
Profit percentage is always on cost price; computing it on selling price is the standard wrong answer.
For two years, CI − SI = PR²/100². Convert km/h to m/s by multiplying 5/18.
Average speed over equal distances is 2ab/(a+b); the plain average applies only for equal times.
In DI, read units and axis start first; in a pie chart 1% = 3.6°.
Percentage growth and absolute growth rank differently — compute the one that was asked.

Practice questions (8)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

What is 37.5% of 640?
1. 200
2. 240
3. 250
4. 280
Show answer
Answer: B — 240
37.5% = ⅜, so 640 × 3/8 = 240. Doing it as 640 × 0.375 by long multiplication gets the same answer but costs three times the time — which over ten questions is the difference between finishing the section and not.
A shopkeeper raises a price by 20% and then offers a 20% discount. The net effect on the original price is:
1. No change
2. A 4% decrease
3. A 4% increase
4. A 2% decrease
Show answer
Answer: B — A 4% decrease
Net change = a + b + ab/100 = 20 − 20 − 400/100 = −4%. Check it on ₹100: it becomes ₹120, then 20% off gives ₹96. The discount is taken on the higher price, which is why the two changes do not cancel.
A man travels 60 km at 30 km/h and returns the same 60 km at 60 km/h. His average speed for the whole journey is:
1. 45 km/h
2. 40 km/h
3. 50 km/h
4. 36 km/h
Show answer
Answer: B — 40 km/h
Total distance 120 km; time = 60/30 + 60/60 = 2 + 1 = 3 hours; so 120/3 = 40 km/h. Equivalently 2ab/(a+b) = 2×30×60/90 = 40. The tempting 45 is the plain average, which would be right only if the two speeds were held for equal times rather than equal distances.
A can finish a job in 10 days and B in 15 days. Working together they will finish it in:
1. 12.5 days
2. 6 days
3. 5 days
4. 25 days
Show answer
Answer: B — 6 days
Add the rates, never the days: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6, so 6 days. A useful sanity check — working together must take less time than the faster worker alone, which immediately rules out 12.5 and 25.
An article bought for ₹800 is sold for ₹1,000. The profit percentage is:
1. 20%
2. 25%
3. 22.5%
4. 80%
Show answer
Answer: B — 25%
Profit is ₹200 on a cost price of ₹800, so 200/800 × 100 = 25%. The tempting 20% comes from dividing by the selling price instead — profit and loss percentages are always computed on cost price, and this is the single most common error in the topic.
In a pie chart, a sector of 54° represents what percentage of the total?
1. 10%
2. 15%
3. 18%
4. 20%
Show answer
Answer: B — 15%
The whole circle of 360° is 100%, so 1% equals 3.6°. Therefore 54 ÷ 3.6 = 15%. Keeping the 3.6° figure ready turns every pie-chart question into a single division.
Enrolment (in hundreds) — Arts 12→18, Science 18→24, Commerce 10→18 from 2022 to 2024. Which stream grew fastest in percentage terms?
1. Arts
2. Science
3. Commerce
4. Arts and Science equally
Show answer
Answer: C — Commerce
Arts rose 6 on 12 = 50%; Science 6 on 18 = 33⅓%; Commerce 8 on 10 = 80%. Commerce is fastest. Note that Arts and Science added the same absolute six hundreds but rank differently in percentage — which is exactly the distinction such questions are built to test.
For a sum of ₹5,000 at 10% per annum for 2 years, the difference between compound and simple interest is:
1. ₹100
2. ₹50
3. ₹250
4. ₹500
Show answer
Answer: B — ₹50
For two years the difference is PR²/100² = 5000 × 100/10000 = ₹50. Checking the long way: SI = 5000×10×2/100 = ₹1,000, while CI = 5000(1.1)² − 5000 = 6050 − 5000 = ₹1,050. The shortcut saves the whole calculation.