CAT 2022 Slot 1 · DILR · Set 3: Funding Tokens from Six Interviewers

The full set and all 5 questions (Q11–Q15) from CAT 2022 Slot 1, with answers and solutions.

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 11 · Caselet DI

How many tokens did Qahira receive?
Answer & solution

Answer: 2

Solving the set

Step 1 – Factorise each funding amount (÷ 1000). Every amount is a product of distinct primes, so each interviewer has a different face value.

Funding (Rs.)

÷ 1000

Prime factors (tokens)

Number of tokens

390,000

390

2 × 3 × 5 × 13

4

210,000

210

2 × 3 × 5 × 7

4

165,000

165

3 × 5 × 11

3

77,000

77

7 × 11

2

66,000

66

2 × 3 × 11

3

Step 2 – Count how often each value appears: 2 → 3 amounts, 3 → 4, 5 → 3, 7 → 2, 11 → 3, 13 → 1.

Step 3 – Fathima gives to four candidates (all but Qahira) ⇒ her value is 3, and Qahira has 77,000. Adhara gives only to Pragnyaa ⇒ value 13, and Pragnyaa has 390,000.

Step 4 – Rasheeda has the most tokens (4) and is not Pragnyaa ⇒ 210,000 (2, 3, 5, 7). She got nothing from Esther, so Esther's value is not 2, 3, 5 or 7, and not 13 (Adhara) ⇒ 11.

Step 5 – Dhanavi gives Qahira (7 × 11); 11 is Esther's ⇒ Dhanavi = 7. Bithi and Chhaya take 2 and 5. Smera and Tantra get 165,000 and 66,000; Bithi gives Smera, so Bithi = 5 ⇒ Smera 165,000, or Bithi = 2 ⇒ Smera 66,000. Both are consistent.

Interviewer

Face value

Reason

Fathima

3

Only 3 appears in exactly four amounts (all except 77,000 = Qahira)

Adhara

13

Only 13 appears in exactly one amount (390,000 = Pragnyaa)

Esther

11

Rasheeda (4 tokens, 210,000 = 2·3·5·7) has no Esther token; 11 is the only value she lacks among 2, 5, 7, 11

Dhanavi

7

Gives Qahira (7 × 11); 11 is Esther's

Bithi

2 or 5

Gives Smera

Chhaya

5 or 2

The remaining value

Candidate

Funding (Rs.)

Tokens from

Pragnyaa

390,000

Adhara (13), Fathima (3), Bithi and Chhaya (2, 5)

Rasheeda

210,000

Fathima (3), Dhanavi (7), Bithi and Chhaya (2, 5)

Qahira

77,000

Dhanavi (7), Esther (11)

Smera / Tantra

165,000 and 66,000 in some order

Fathima (3), Esther (11) and one of Bithi/Chhaya

This question

From Step 3, Qahira's funding is 77,000 = 7 × 11: tokens from Dhanavi and Esther. 2 tokens.

Hence, the answer is 2.

Question 12 · Caselet DI

Who among the following definitely received a token from Bithi but not from Dhanavi?
  1. A
    Pragnyaa
  2. B
    Rasheeda
  3. C
    Qahira
  4. D
    Tantra
Pick an option, then check.
Answer & solution

Answer: Option A

Solving the set

Step 1 – Factorise each funding amount (÷ 1000). Every amount is a product of distinct primes, so each interviewer has a different face value.

Funding (Rs.)

÷ 1000

Prime factors (tokens)

Number of tokens

390,000

390

2 × 3 × 5 × 13

4

210,000

210

2 × 3 × 5 × 7

4

165,000

165

3 × 5 × 11

3

77,000

77

7 × 11

2

66,000

66

2 × 3 × 11

3

Step 2 – Count how often each value appears: 2 → 3 amounts, 3 → 4, 5 → 3, 7 → 2, 11 → 3, 13 → 1.

Step 3 – Fathima gives to four candidates (all but Qahira) ⇒ her value is 3, and Qahira has 77,000. Adhara gives only to Pragnyaa ⇒ value 13, and Pragnyaa has 390,000.

Step 4 – Rasheeda has the most tokens (4) and is not Pragnyaa ⇒ 210,000 (2, 3, 5, 7). She got nothing from Esther, so Esther's value is not 2, 3, 5 or 7, and not 13 (Adhara) ⇒ 11.

Step 5 – Dhanavi gives Qahira (7 × 11); 11 is Esther's ⇒ Dhanavi = 7. Bithi and Chhaya take 2 and 5. Smera and Tantra get 165,000 and 66,000; Bithi gives Smera, so Bithi = 5 ⇒ Smera 165,000, or Bithi = 2 ⇒ Smera 66,000. Both are consistent.

Interviewer

Face value

Reason

Fathima

3

Only 3 appears in exactly four amounts (all except 77,000 = Qahira)

Adhara

13

Only 13 appears in exactly one amount (390,000 = Pragnyaa)

Esther

11

Rasheeda (4 tokens, 210,000 = 2·3·5·7) has no Esther token; 11 is the only value she lacks among 2, 5, 7, 11

Dhanavi

7

Gives Qahira (7 × 11); 11 is Esther's

Bithi

2 or 5

Gives Smera

Chhaya

5 or 2

The remaining value

Candidate

Funding (Rs.)

Tokens from

Pragnyaa

390,000

Adhara (13), Fathima (3), Bithi and Chhaya (2, 5)

Rasheeda

210,000

Fathima (3), Dhanavi (7), Bithi and Chhaya (2, 5)

Qahira

77,000

Dhanavi (7), Esther (11)

Smera / Tantra

165,000 and 66,000 in some order

Fathima (3), Esther (11) and one of Bithi/Chhaya

This question

Bithi's value is 2 or 5; Dhanavi's is 7.

• Pragnyaa (2 × 3 × 5 × 13) has both 2 and 5, so she gets Bithi's token in either case, and she has no 7 – she definitely fits.

• Rasheeda has 7, so she has Dhanavi's token. Qahira has no token from Bithi. Tantra gets Bithi's token only in one of the two cases.

Hence, the answer is option 1.

Question 13 · Caselet DI

How many tokens did Chhaya award?
Answer & solution

Answer: 3

Solving the set

Step 1 – Factorise each funding amount (÷ 1000). Every amount is a product of distinct primes, so each interviewer has a different face value.

Funding (Rs.)

÷ 1000

Prime factors (tokens)

Number of tokens

390,000

390

2 × 3 × 5 × 13

4

210,000

210

2 × 3 × 5 × 7

4

165,000

165

3 × 5 × 11

3

77,000

77

7 × 11

2

66,000

66

2 × 3 × 11

3

Step 2 – Count how often each value appears: 2 → 3 amounts, 3 → 4, 5 → 3, 7 → 2, 11 → 3, 13 → 1.

Step 3 – Fathima gives to four candidates (all but Qahira) ⇒ her value is 3, and Qahira has 77,000. Adhara gives only to Pragnyaa ⇒ value 13, and Pragnyaa has 390,000.

Step 4 – Rasheeda has the most tokens (4) and is not Pragnyaa ⇒ 210,000 (2, 3, 5, 7). She got nothing from Esther, so Esther's value is not 2, 3, 5 or 7, and not 13 (Adhara) ⇒ 11.

Step 5 – Dhanavi gives Qahira (7 × 11); 11 is Esther's ⇒ Dhanavi = 7. Bithi and Chhaya take 2 and 5. Smera and Tantra get 165,000 and 66,000; Bithi gives Smera, so Bithi = 5 ⇒ Smera 165,000, or Bithi = 2 ⇒ Smera 66,000. Both are consistent.

Interviewer

Face value

Reason

Fathima

3

Only 3 appears in exactly four amounts (all except 77,000 = Qahira)

Adhara

13

Only 13 appears in exactly one amount (390,000 = Pragnyaa)

Esther

11

Rasheeda (4 tokens, 210,000 = 2·3·5·7) has no Esther token; 11 is the only value she lacks among 2, 5, 7, 11

Dhanavi

7

Gives Qahira (7 × 11); 11 is Esther's

Bithi

2 or 5

Gives Smera

Chhaya

5 or 2

The remaining value

Candidate

Funding (Rs.)

Tokens from

Pragnyaa

390,000

Adhara (13), Fathima (3), Bithi and Chhaya (2, 5)

Rasheeda

210,000

Fathima (3), Dhanavi (7), Bithi and Chhaya (2, 5)

Qahira

77,000

Dhanavi (7), Esther (11)

Smera / Tantra

165,000 and 66,000 in some order

Fathima (3), Esther (11) and one of Bithi/Chhaya

This question

If Chhaya's value is 2, she gives to Pragnyaa, Rasheeda and the 66,000 candidate; if it is 5, to Pragnyaa, Rasheeda and the 165,000 candidate. Either way 3 tokens.

Hence, the answer is 3.

Question 14 · Caselet DI

How many tokens did Smera receive?
Answer & solution

Answer: 3

Solving the set

Step 1 – Factorise each funding amount (÷ 1000). Every amount is a product of distinct primes, so each interviewer has a different face value.

Funding (Rs.)

÷ 1000

Prime factors (tokens)

Number of tokens

390,000

390

2 × 3 × 5 × 13

4

210,000

210

2 × 3 × 5 × 7

4

165,000

165

3 × 5 × 11

3

77,000

77

7 × 11

2

66,000

66

2 × 3 × 11

3

Step 2 – Count how often each value appears: 2 → 3 amounts, 3 → 4, 5 → 3, 7 → 2, 11 → 3, 13 → 1.

Step 3 – Fathima gives to four candidates (all but Qahira) ⇒ her value is 3, and Qahira has 77,000. Adhara gives only to Pragnyaa ⇒ value 13, and Pragnyaa has 390,000.

Step 4 – Rasheeda has the most tokens (4) and is not Pragnyaa ⇒ 210,000 (2, 3, 5, 7). She got nothing from Esther, so Esther's value is not 2, 3, 5 or 7, and not 13 (Adhara) ⇒ 11.

Step 5 – Dhanavi gives Qahira (7 × 11); 11 is Esther's ⇒ Dhanavi = 7. Bithi and Chhaya take 2 and 5. Smera and Tantra get 165,000 and 66,000; Bithi gives Smera, so Bithi = 5 ⇒ Smera 165,000, or Bithi = 2 ⇒ Smera 66,000. Both are consistent.

Interviewer

Face value

Reason

Fathima

3

Only 3 appears in exactly four amounts (all except 77,000 = Qahira)

Adhara

13

Only 13 appears in exactly one amount (390,000 = Pragnyaa)

Esther

11

Rasheeda (4 tokens, 210,000 = 2·3·5·7) has no Esther token; 11 is the only value she lacks among 2, 5, 7, 11

Dhanavi

7

Gives Qahira (7 × 11); 11 is Esther's

Bithi

2 or 5

Gives Smera

Chhaya

5 or 2

The remaining value

Candidate

Funding (Rs.)

Tokens from

Pragnyaa

390,000

Adhara (13), Fathima (3), Bithi and Chhaya (2, 5)

Rasheeda

210,000

Fathima (3), Dhanavi (7), Bithi and Chhaya (2, 5)

Qahira

77,000

Dhanavi (7), Esther (11)

Smera / Tantra

165,000 and 66,000 in some order

Fathima (3), Esther (11) and one of Bithi/Chhaya

This question

Smera's funding is 165,000 or 66,000; each is a product of three primes, so she got 3 tokens.

Hence, the answer is 3.

Question 15 · Caselet DI

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 (b)
  3. C
    Only (a)
  4. D
    Both (a) and (b)
Pick an option, then check.
Answer & solution

Answer: Option D

Solving the set

Step 1 – Factorise each funding amount (÷ 1000). Every amount is a product of distinct primes, so each interviewer has a different face value.

Funding (Rs.)

÷ 1000

Prime factors (tokens)

Number of tokens

390,000

390

2 × 3 × 5 × 13

4

210,000

210

2 × 3 × 5 × 7

4

165,000

165

3 × 5 × 11

3

77,000

77

7 × 11

2

66,000

66

2 × 3 × 11

3

Step 2 – Count how often each value appears: 2 → 3 amounts, 3 → 4, 5 → 3, 7 → 2, 11 → 3, 13 → 1.

Step 3 – Fathima gives to four candidates (all but Qahira) ⇒ her value is 3, and Qahira has 77,000. Adhara gives only to Pragnyaa ⇒ value 13, and Pragnyaa has 390,000.

Step 4 – Rasheeda has the most tokens (4) and is not Pragnyaa ⇒ 210,000 (2, 3, 5, 7). She got nothing from Esther, so Esther's value is not 2, 3, 5 or 7, and not 13 (Adhara) ⇒ 11.

Step 5 – Dhanavi gives Qahira (7 × 11); 11 is Esther's ⇒ Dhanavi = 7. Bithi and Chhaya take 2 and 5. Smera and Tantra get 165,000 and 66,000; Bithi gives Smera, so Bithi = 5 ⇒ Smera 165,000, or Bithi = 2 ⇒ Smera 66,000. Both are consistent.

Interviewer

Face value

Reason

Fathima

3

Only 3 appears in exactly four amounts (all except 77,000 = Qahira)

Adhara

13

Only 13 appears in exactly one amount (390,000 = Pragnyaa)

Esther

11

Rasheeda (4 tokens, 210,000 = 2·3·5·7) has no Esther token; 11 is the only value she lacks among 2, 5, 7, 11

Dhanavi

7

Gives Qahira (7 × 11); 11 is Esther's

Bithi

2 or 5

Gives Smera

Chhaya

5 or 2

The remaining value

Candidate

Funding (Rs.)

Tokens from

Pragnyaa

390,000

Adhara (13), Fathima (3), Bithi and Chhaya (2, 5)

Rasheeda

210,000

Fathima (3), Dhanavi (7), Bithi and Chhaya (2, 5)

Qahira

77,000

Dhanavi (7), Esther (11)

Smera / Tantra

165,000 and 66,000 in some order

Fathima (3), Esther (11) and one of Bithi/Chhaya

This question

From Step 5, Tantra's funding is 66,000 when Bithi's value is 5, and 165,000 when it is 2. Both cases are valid.

Hence, the answer is option 4.

Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.

Practice timed →