CAT 2025 Slot 2 DILR Set 2 Q6–Q9

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2025 Slot 2, with 4 questions (Grids & Matrices). Answers are CAT's official key.

The set

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4.

Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a "ping". Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping.

The following additional information is known:
1. B1 and B6 each made a ping on H4, but B5 did not.
2. B4 made a ping on H3, but B1 did not.
3. All balls, except B3, made pings on H1.
4. None of the balls, except B2, made a ping on H2.

Question 6

What was the total number of pings made by B1, B2, and B3?

TITA: type in the answer. There are no options and no negative marking.

Answer: 6 Grids & Matrices TITA

Solution

  1. H1: everyone except B3 pings, so B3 is bigger than H1, and H1 is at least as big as every other ball. H2: only B2 pings, so \(B2 \le H2 <\) every other ball.
  2. B1 pings H4 but not H3, so \(H3 < B1 \le H4\). B4 pings H3, so \(B4 \le H3\). B5 does not ping H4 but pings H1, so \(H4 < B5 \le H1\).
  3. Chain: \(B2 \le H2 < B4 \le H3 < B1 \le H4 < B5 \le H1 < B3\); B6 satisfies \(H2 < B6 \le H4\), its position relative to H3 (and to B4, B1) is unknown.
  4. B1 pings H1 and H4 (2); B2 is the smallest ball and pings all 4; B3 is bigger than every hoop (0). Total \(= 6\).

Question 7

Which of the following statements about the relative sizes of the balls is NOT NECESSARILY true?
  1. A
    B4 < B5 < B3
  2. B
    B1 < B6 < B3
  3. C
    B1 < B5 < B3
  4. D
    B2 < B1 < B5

Answer: (B) B1 < B6 < B3 Grids & Matrices MCQ

Solution

  1. H1: everyone except B3 pings, so B3 is bigger than H1, and H1 is at least as big as every other ball. H2: only B2 pings, so \(B2 \le H2 <\) every other ball.
  2. B1 pings H4 but not H3, so \(H3 < B1 \le H4\). B4 pings H3, so \(B4 \le H3\). B5 does not ping H4 but pings H1, so \(H4 < B5 \le H1\).
  3. Chain: \(B2 \le H2 < B4 \le H3 < B1 \le H4 < B5 \le H1 < B3\); B6 satisfies \(H2 < B6 \le H4\), its position relative to H3 (and to B4, B1) is unknown.
  4. A, C and D follow from the chain. In B, \(B1 < B6\) is not forced, since B6 only needs \(B6 \le H4\) and could be smaller than B1.

Question 8

Which of the following statements about the relative sizes of the hoops is true?
  1. A
    H2 < H4 < H3 < H1
  2. B
    H1 < H3 < H4 < H2
  3. C
    H2 < H3 < H4 < H1
  4. D
    H1 < H4 < H3 < H2

Answer: (C) H2 < H3 < H4 < H1 Grids & Matrices MCQ

Solution

  1. H1: everyone except B3 pings, so B3 is bigger than H1, and H1 is at least as big as every other ball. H2: only B2 pings, so \(B2 \le H2 <\) every other ball.
  2. B1 pings H4 but not H3, so \(H3 < B1 \le H4\). B4 pings H3, so \(B4 \le H3\). B5 does not ping H4 but pings H1, so \(H4 < B5 \le H1\).
  3. Chain: \(B2 \le H2 < B4 \le H3 < B1 \le H4 < B5 \le H1 < B3\); B6 satisfies \(H2 < B6 \le H4\), its position relative to H3 (and to B4, B1) is unknown.
  4. Reading the hoops off the chain: \(H2 < H3 < H4 < H1\).

Question 9

What BEST can be said about the total number of pings from all the tests undertaken?
  1. A
    13 or 14
  2. B
    12 or 13
  3. C
    At least 9
  4. D
    12 or 13 or 14

Answer: (B) 12 or 13 Grids & Matrices MCQ

Solution

  1. H1: everyone except B3 pings, so B3 is bigger than H1, and H1 is at least as big as every other ball. H2: only B2 pings, so \(B2 \le H2 <\) every other ball.
  2. B1 pings H4 but not H3, so \(H3 < B1 \le H4\). B4 pings H3, so \(B4 \le H3\). B5 does not ping H4 but pings H1, so \(H4 < B5 \le H1\).
  3. Chain: \(B2 \le H2 < B4 \le H3 < B1 \le H4 < B5 \le H1 < B3\); B6 satisfies \(H2 < B6 \le H4\), its position relative to H3 (and to B4, B1) is unknown.
  4. Pings: H1 5, H2 1, H4 4 (B1, B2, B4, B6). H3: B2 and B4 surely, B6 maybe, so 2 or 3.
  5. Total \(= 12\) or \(13\).

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