CAT 2022 Slot 1 — DILR Question 11
Answer the next 5 questions based on the information given below:
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 Qahira receive?
Answer & solution
Answer: 2
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 product of tokes = 390, 210, 165, 77, 66
⇒ Break of tokens received
390 = 2 × 3 × 5 × 13
210 = 2 × 3 × 5 × 7
165 = 3 × 5 × 11
77 = 7 × 11
66 = 2 × 3 × 11
From (1): Fathima awarded tokens to everyone except Qahira,
∴ Fatima must have awarded token number 3 to everyone and Qahira received tokens whose product is 77.
From (1): Adhara awarded tokens to no one except Pragnyaa
∴ Adhara must have awared token 13 and Pragnyaa received tokens whose product is 390.
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From (2): Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.
∴ Rashida must have received 4 tokes whose product can only be 210. Also, since Esther did not give her the token, hence Esther must have distributed token number 11.
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From (3): Dhanavi awarded a token to Qahira but not to Smera.
∴ Dhanavi must have awared token number 7.
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From (3): Bithi awarded a token to Smera but not to Qahira
∴ Bithi/Chhaya could have awared token 2/5 in any order.
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If Bithi gives token number 2 to S/T, then Chhaya will given token number 5 to T/S and vice-a-versa.
∴ Qahira received two tokens i.e., 7 and 11.
Hence, 2.