CAT 2022 Slot 1 · DILR · Question 14

CAT 2022 Slot 1 previous year question on Caselet DI, with the answer and a step-by-step solution.

Caselet DIData InterpretationType in the answer (TITA)Medium

Set 3: Funding Tokens from Six Interviewers — this question belongs to a set. Read the full set with all 5 questions →

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.

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.

CAT 2022 Slot 1 · DILR · Question 14

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