TOUGHEST Questions of CAT EXAM 🤯

The speaker opens by recounting her personal journey through multiple competitive exams including IIT JEE, CAT, GMAT, SSC CGL, RBI Grade B, and UPSC. She shares a formative memory of a classmate who joined her IIT JEE coaching batch in 12th grade, studied for only one year, scored rank 2000 in JEE Advanced, and secured admission to IIT Kanpur — all while solving practice problems even during her auto-rickshaw commute. This story serves as the speaker's key lesson: in exams with success rates below 1%, not a single second should be wasted.

She contextualizes this for CAT aspirants, noting that roughly 2.5 lakh students appear annually, with only about 2000 seats in top IIMs, making the success rate approximately 1%. She adds that gaining admission to IIM Ahmedabad is 100 times harder than getting into Stanford. She then promotes the iQuanta app, highlighting features like free quizzes with detailed video solutions across VARC, LRDI, and Quant sections, previous year papers, customizable quiz settings (topic, difficulty, number of questions, timer), a VARC reading mode with adjustable word-per-minute speed, and a doubt resolution service promising answers within 10 minutes.

The bulk of the video is dedicated to solving four difficult CAT 2025 problems. The first is an exponential equation where x, y, z are natural numbers; by breaking all bases into prime factors (2, 3, 5) and equating powers, she derives x=10, z=42, y=60, giving x+y+z=112. The second problem involves finding the digit sum of 10^50 + 10^25 - 123; through careful place-value analysis of the subtraction, she arrives at a digit sum of 221. The third is a logarithmic equation requiring valid x values; after applying log properties and simplifying, she finds that x=3 is invalid (causes log 0) and the negative root is invalid, leaving only one valid solution (3+√33)/2, making the sum of valid x values equal to that single value. The fourth is a range-finding problem for a rational function f(x)=(2x-3)/(2x²+4x-6); by setting f(x)=y, rearranging into a quadratic in x, and applying the discriminant condition (b²-4ac ≥ 0), she determines the range is (-∞, 1/8] ∪ [1/2, ∞). Finally, she solves an LRDI puzzle involving six balls (B1–B6) and four hoops (H1–H4), using a table to track which balls pass through which hoops, deducing that B3 is larger than all hoops (zero pings) and B2 is smaller than all hoops (four pings), giving a total of six pings for B1+B2+B3.