Quantitative Aptitude

This is the bucket where you can grind points fastest. The math is 8th-to-10th grade, but the questions are deliberately phrased to confuse — “after a 20% discount and then a 10% tax”, “if the ratio changes from 3:5 to 2:3”, “find the average speed for the round trip”. Build a small toolkit of formulas, recognise which one the question wants, and these are 90-second answers. (This 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 problems mirror 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. A 20% discount followed by a 10% tax is not a 10% net change. Each step multiplies the previous price:

The 10% tax applies to the discounted price ₹800, not the original ₹1000. That’s 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, i.e. a 12% net decrease from ₹1000 — not 10%. 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 common mistake is to compute everything correctly and then mark the intermediate value.

A note on units

Always check units before computing. Speed in km/h with time in minutes? Convert. Area in m² when the question asks for cm²? Multiply by 10⁴. A units mismatch is the cheapest way to lose a mark you otherwise had.

Quick check