Quantitative Aptitude

Last lesson left a promise: the numerical half of GA has its own smuggler, and it is not your knowledge but your intuition. A shirt marked down 20% and then taxed 10% — almost every gut says “10% off.” It is wrong, and the question is engineered to catch precisely that reflex. The arithmetic itself is 8th-to-10th grade; the difficulty is unlearning a feeling and reading the words carefully (“after a 20% discount and then a 10% tax”, “if the ratio changes from 3:5 to 2:3”).

So Quantitative Aptitude is the bucket where you grind points fastest — build a small toolkit of formulas, recognise which one a question wants, and these become 90-second answers. (The toolkit never retires: percentage change, weighted averages, and ratios are the daily bread of reading dashboards, comparing model scores, and sizing A/B tests.)

The toolkit

A handful of patterns covers the vast majority of GA quant questions. Internalise these and the rest is reading carefully.

Percentages

• X% of Y = X · Y / 100. So 20% of 250 = 50.
• Going from A to B is a percentage change of (B − A) / A · 100.
• “Increase by p%” = multiply by (1 + p/100); “decrease by p%” = multiply by (1 − p/100).

Ratios and proportions

• a : b = c : d ⇔ a · d = b · c (cross-multiply).
• To split a total T in ratio a : b, the parts are T · a/(a+b) and T · b/(a+b).

Powers and logs

• a^x = b ⇔ x = log_a(b).
• log(xy) = log(x) + log(y); log(x/y) = log(x) − log(y); log(x^n) = n · log(x).

Averages

• Simple average of n numbers = sum / n.
• Weighted average when items have different counts: Σ(weight · value) / Σ(weight).

Time, speed, distance & work

• Distance = Speed · Time. Average speed over a journey of equal distances at speeds v₁ and v₂ is the harmonic mean 2v₁v₂ / (v₁ + v₂), NOT the arithmetic mean.
• Work mirrors speed: if A finishes a job in a days, A’s rate is 1/a per day; A and B together do 1/a + 1/b per day.

Basic mensuration

• Square (side s): area s², perimeter 4s.
• Rectangle (l × w): area l · w, perimeter 2(l + w).
• Circle (radius r): area π r², circumference 2 π r.
• Triangle (base b, height h): area (1/2) · b · h.
• Right triangle: hypotenuse c = √(a² + b²) (Pythagoras).

Why percentages don’t add

This trips up more aspirants than anything else, and it is the intuition the last lesson told you to kill. A 20% discount followed by a 10% tax is not a 10% net change — each step multiplies the running price, not the original:

The 10% tax applies to the discounted ₹800, not the original ₹1000 — which is why multiplying factors (0.80, then 1.10) is the only safe procedure.

Worked example — discount then tax

“A shirt is marked at ₹1000. The shop offers a 20% discount, and the customer then pays a 10% tax on the discounted price. What does the customer actually pay?”

Translate each step into a multiplicative factor on the running price:

Step 1 (discount):  1000 × (1 − 0.20)  =  1000 × 0.80  =  800
Step 2 (tax):        800 × (1 + 0.10)  =   800 × 1.10  =  880

Customer pays = ₹880

The net effective change is 0.80 × 1.10 = 0.88, a 12% net decrease from ₹1000 — not 10%, and below ₹900, against the gut’s guess. That 2-percentage-point gap is exactly the trap.

How GATE asks this

Mostly NAT (numeric answer), occasionally MCQ. The 2-mark quant questions often chain two or three steps — a ratio change followed by a percentage, or a speed problem with two legs. Read the entire question once before computing; the last sentence usually tells you which number is being asked for, and a classic mistake is to compute everything correctly and then mark the intermediate value.

In one breath

GA quant yields to a small toolkit — percentages (X% of Y, and “increase/decrease by p%” as a multiply by 1 ± p/100), ratios (cross-multiply, split a total by a/(a+b)), powers/logs, simple and weighted averages, time-speed-distance (equal-distance average speed is the harmonic mean 2v₁v₂/(v₁+v₂), not the arithmetic), and mensuration — and its single most-tested trap is that successive percentages multiply, not add, so a 20%-off-then-10%-tax shirt costs 1000 × 0.80 × 1.10 = ₹880, a 12% net cut, never the gut’s 10%.

Practice

A question to carry forward

Every quant question here handed you the numbers in words — “marked at ₹1000,” “60 km at 30 km/h,” “average score 72.” The arithmetic was the whole task. But GATE’s reasoning slot often does something sneakier: it hides the numbers in a picture — a bar chart, a pie, a table — and pairs two questions you cannot even begin until you have read the figure correctly.

And the figure is where fresh marks leak away. The sums will be the very ones you just drilled — a percentage change, a ratio, a difference of two quantities — but first you must lift exact values off a chart that may have a truncated axis, a “percentage of which total?”, or a legend you glanced past. Here is the thread onward: how do you read a data-interpretation figure for the exact numbers it encodes, turn them into the deltas and ratios the paired questions demand, and avoid being misled by the way the data is drawn rather than what it says?