CAT 2022 Slot 1 DILR Set 4 Q16–Q20

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2022 Slot 1, with 5 questions (Quant-based Puzzles). Answers are CAT's official key.

The set

Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only. Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.
Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000.

The following additional facts are known:
1. Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.
2. Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.
3. Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.

Question 16

How many tokens did Qahira receive?

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

Answer: 2 Quant-based Puzzles TITA

Solution

  1. In thousands: 390 = 2·3·5·13, 210 = 2·3·5·7, 165 = 3·5·11, 77 = 7·11, 66 = 2·3·11.
  2. Fathima's value divides every amount but Qahira's: only 3 does (missing 77), so F = 3 and Qahira = 77. Adhara's value divides only Pragnyaa's: only 13 does, so A = 13 and Pragnyaa = 390.
  3. Rasheeda has the most tokens (4) among the rest: Rasheeda = 210 = 2·3·5·7 without Esther, so B, C, D hold 2, 5, 7 and Esther = 11. Dhanavi gave to Qahira (7·11), so D = 7; Bithi and Chhaya are 2 and 5 in some order.
  4. Smera and Tantra are 165 and 66 in some order: Bithi (2 or 5) gives to Smera either way, so both arrangements are possible.
  5. Qahira = 77 = 7 × 11: tokens from Dhanavi and Esther, so 2 tokens.

Question 17

Who among the following definitely received a token from Bithi but not from Dhanavi?
  1. A
    Qahira
  2. B
    Tantra
  3. C
    Pragnyaa
  4. D
    Rasheeda

Answer: (C) Pragnyaa Quant-based Puzzles MCQ

Solution

  1. In thousands: 390 = 2·3·5·13, 210 = 2·3·5·7, 165 = 3·5·11, 77 = 7·11, 66 = 2·3·11.
  2. Fathima's value divides every amount but Qahira's: only 3 does (missing 77), so F = 3 and Qahira = 77. Adhara's value divides only Pragnyaa's: only 13 does, so A = 13 and Pragnyaa = 390.
  3. Rasheeda has the most tokens (4) among the rest: Rasheeda = 210 = 2·3·5·7 without Esther, so B, C, D hold 2, 5, 7 and Esther = 11. Dhanavi gave to Qahira (7·11), so D = 7; Bithi and Chhaya are 2 and 5 in some order.
  4. Smera and Tantra are 165 and 66 in some order: Bithi (2 or 5) gives to Smera either way, so both arrangements are possible.
  5. Pragnyaa = 390 contains both 2 and 5 (so Bithi's value either way) but no 7 (Dhanavi): definitely Bithi but not Dhanavi.
  6. Rasheeda got Dhanavi's 7, Qahira got no Bithi token, and Tantra's tokens depend on the arrangement.

Question 18

How many tokens did Chhaya award?

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

Answer: 3 Quant-based Puzzles TITA

Solution

  1. In thousands: 390 = 2·3·5·13, 210 = 2·3·5·7, 165 = 3·5·11, 77 = 7·11, 66 = 2·3·11.
  2. Fathima's value divides every amount but Qahira's: only 3 does (missing 77), so F = 3 and Qahira = 77. Adhara's value divides only Pragnyaa's: only 13 does, so A = 13 and Pragnyaa = 390.
  3. Rasheeda has the most tokens (4) among the rest: Rasheeda = 210 = 2·3·5·7 without Esther, so B, C, D hold 2, 5, 7 and Esther = 11. Dhanavi gave to Qahira (7·11), so D = 7; Bithi and Chhaya are 2 and 5 in some order.
  4. Smera and Tantra are 165 and 66 in some order: Bithi (2 or 5) gives to Smera either way, so both arrangements are possible.
  5. If Chhaya is 2: Pragnyaa, Rasheeda and whoever has 66. If Chhaya is 5: Pragnyaa, Rasheeda and whoever has 165. Either way 3 tokens.

Question 19

How many tokens did Smera receive?

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

Answer: 3 Quant-based Puzzles TITA

Solution

  1. In thousands: 390 = 2·3·5·13, 210 = 2·3·5·7, 165 = 3·5·11, 77 = 7·11, 66 = 2·3·11.
  2. Fathima's value divides every amount but Qahira's: only 3 does (missing 77), so F = 3 and Qahira = 77. Adhara's value divides only Pragnyaa's: only 13 does, so A = 13 and Pragnyaa = 390.
  3. Rasheeda has the most tokens (4) among the rest: Rasheeda = 210 = 2·3·5·7 without Esther, so B, C, D hold 2, 5, 7 and Esther = 11. Dhanavi gave to Qahira (7·11), so D = 7; Bithi and Chhaya are 2 and 5 in some order.
  4. Smera and Tantra are 165 and 66 in some order: Bithi (2 or 5) gives to Smera either way, so both arrangements are possible.
  5. Smera has 165 or 66, each a product of three tokens, so 3 tokens.

Question 20

Which of the following could be the amount of funding that Tantra received?
(a) Rs. 66,000
(b) Rs. 165,000
  1. A
    Neither (a) nor (b)
  2. B
    Only (a)
  3. C
    Both (a) and (b)
  4. D
    Only (b)

Answer: (C) Both (a) and (b) Quant-based Puzzles MCQ

Solution

  1. In thousands: 390 = 2·3·5·13, 210 = 2·3·5·7, 165 = 3·5·11, 77 = 7·11, 66 = 2·3·11.
  2. Fathima's value divides every amount but Qahira's: only 3 does (missing 77), so F = 3 and Qahira = 77. Adhara's value divides only Pragnyaa's: only 13 does, so A = 13 and Pragnyaa = 390.
  3. Rasheeda has the most tokens (4) among the rest: Rasheeda = 210 = 2·3·5·7 without Esther, so B, C, D hold 2, 5, 7 and Esther = 11. Dhanavi gave to Qahira (7·11), so D = 7; Bithi and Chhaya are 2 and 5 in some order.
  4. Smera and Tantra are 165 and 66 in some order: Bithi (2 or 5) gives to Smera either way, so both arrangements are possible.
  5. If Bithi = 2, Smera = 66 and Tantra = 165; if Bithi = 5, Smera = 165 and Tantra = 66. Both are possible.

More Quant-based Puzzles questions from CAT

All 127 Quant-based Puzzles questions asked since 2017.