CAT 2026 · Slot 1 · Expected paper

CAT 2026 › Slot 1 paper › Quant

CAT 2026 Slot 1 Quant: Geometry & Mensuration Questions with Solutions

3 questions: Q1, Q4, Q20. Solve each one here: tap the answer, press Check, then open the solution.

Question 1Geometry – Polygons

MCQ · +3 / −1

A and B are two regular polygons with $a$ and $b$ sides respectively. The interior angle of polygon A is 3 times the exterior angle of polygon B. Which of the following is correct?
Answer and solution

Correct answer: C

Solution

Interior angle of A $= \dfrac{180(a-2)}{a}$, exterior angle of B $= \dfrac{360}{b}$.
Condition: $\dfrac{180(a-2)}{a} = 3 \times \dfrac{360}{b}$.
Try $a = 6$ (hexagon): interior $= 120^\circ$. Then $120 = \dfrac{1080}{b} \Rightarrow b = 9$ (valid polygon). Interior angle of A $= 120^\circ$.

Question 4Geometry – Triangles

MCQ · +3 / −1

In triangle ABC, $AB = 12$ cm, $AC = 15$ cm and $BC = 18$ cm. Find the length of the median AD (in cm).
Answer and solution

Correct answer: A

Solution

D is midpoint of BC, $BD = 9$.
Apollonius: $AB^2 + AC^2 = 2(AD^2 + BD^2)$
$144 + 225 = 2(AD^2 + 81) \Rightarrow 369 = 2\,AD^2 + 162 \Rightarrow AD^2 = \tfrac{207}{2} \Rightarrow AD = \sqrt{103.5}$

Question 20Geometry – Quadrilaterals

MCQ · +3 / −1

Three sides of a quadrilateral are 3 cm, 2 cm and 6 cm, and the fourth side is an integer. How many lengths are possible for the fourth side?
Answer and solution

Correct answer: C

Solution

Let fourth side = x. Quadrilateral inequality: each side < sum of other three.
$x<3+2+6=11$ and $6<3+2+x\Rightarrow x>1$. So $x\in\{2,3,4,5,6,7,8,9,10\}$ = 9 values.

An expected paper by Cetking, not the actual CAT paper. CAT is conducted by the IIMs.

Admit cards · CAT admit card · © Cetking Universe · Terms & Privacy · By using this site, you agree to Cetking's Terms.