Interviewers, Candidates, and Funding Tokens

CAT 2022 Slot 1 · DILR · Medium · Number Properties

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Passage / data 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 1 of 5

How many tokens did Qahira receive?

Answer

2

Explanation

Funding amounts in thousands divided by 1000 are 390, 210, 165, 77, 66. Prime factorizations: 390=2×3×5×13390 = 2 \times 3 \times 5 \times 13 210=2×3×5×7210 = 2 \times 3 \times 5 \times 7 165=3×5×11165 = 3 \times 5 \times 11 77=7×1177 = 7 \times 11 66=2×3×1166 = 2 \times 3 \times 11 Qahira receives funding of 77 (7 and 11), so she receives 2 tokens.

Question 2 of 5

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

Explanation

Matching prime values (2, 3, 5, 7, 11, 13) to interviewers show that Pragnyaa received a token from Bithi but not from Dhanavi.

Question 3 of 5

How many tokens did Chhaya award?

Answer

3

Explanation

Chhaya corresponds to the face value assigned to her, awarding tokens to 3 candidates.

Question 4 of 5

How many tokens did Smera receive?

Answer

3

Explanation

Smera receives 3 tokens.

Question 5 of 5

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

Explanation

Depending on the valid assignment of candidates to the amounts 165, 66, etc., Tantra could receive either Rs. 66,000 or Rs. 165,000.

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