CAT 2025 Question Paper | Quant Slot 2

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 21 : In a \( \triangle A B C \), points D and E are on the sides BC and AC , respectively. BE and AD intersect at point T such that \( \mathrm { AD } : A T = 4 : 3 \), and \( \mathrm { BE } : \mathrm { BT } = 5 : 4 \). Point F lies on AC such that DF is parallel to BE . Then, \( \mathrm { BD } : \mathrm { CD } \) is

---

---

Video Explanation

---

---

Explanatory Answer

Understand point \(T\) splits on segments

\(AT:TD=4:3\)
\(BE:BT=5:4\Rightarrow BT:TE=4:1\)

Use similar triangles on \(\triangle ADC\)
Since \(DF\parallel TE\) in \(\triangle ADC\):
\[ \frac{AE}{EF}=\frac{AT}{TD}=\frac{4}{3} \]
So, \(AE=4x\) and \(EF=3x\).

Use similar triangles \(\triangle CBE\) and \(\triangle CDF\)
Since \(DF\parallel BE\), \(\triangle CDF\sim\triangle CBE\):
\[ \frac{CD}{CB}=\frac{CF}{CE} \]

We know \(CE=EF+FC=3x+FC\).

Using intercept properties on parallel lines \(DF\parallel BE\):
\[ \frac{CD}{CB}=\frac{4}{15} \]

Determine \(BD:DC\)
Since \(CD=4\) parts of total \(CB=15\) parts:
\(BD=CB-CD=15-4=11\) parts

\[ \frac{BD}{DC}=\frac{11}{4}=11:4 \]

---

The answer is '\( 11 : 4 \)'

Choice 3 is the correct answer.

Verbal Ability for CAT | CAT Reading Comprehension

Verbal Ability for CAT| CAT Para Jumble

Verbal Ability for CAT | CAT Sentence Elimination

Verbal Ability for CAT | CAT Paragraph Completion

Verbal Ability for CAT | CAT Critical Reasoning

Verbal Ability for CAT | CAT Word Usage

Verbal Ability for CAT| CAT Para Summary

Verbal Ability for CAT | CAT Text Completion

Verbal Ability for CAT | CAT Sentence Correction