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SET 1 — 🔍 CAT Level
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 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 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
Rs.66,000
The following additional facts are known:
Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.
Rasheeda received the highest number of tokens that anyone received, but she did not receive one from Esther.
Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.
Question 1
How many tokens did Qahira receive?
Question 2
Who among the following definitely received a token from Bithi but not from Dhanavi?
A. Pragnyaa
B. Rasheeda
C. Qahira
D. Tantra
Question 3
How many tokens did Chhaya award?
Question 4
How many tokens did Smera receive?
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✅ Answers & Explanations
First convert the fund amounts into products of token values.
390 = 2 × 3 × 5 × 13
210 = 2 × 3 × 5 × 7
165 = 3 × 5 × 11
77 = 7 × 11
66 = 2 × 3 × 11
So the number of tokens received are:
390 → 4 tokens
210 → 4 tokens
165 → 3 tokens
77 → 2 tokens
66 → 3 tokens
Rasheeda received the highest number of tokens. So Rasheeda must have received either 390 or 210.
Now, Fathima gave tokens to everyone except Qahira.
So Fathima’s token value must be present in four candidates’ products and absent only in Qahira’s product.
Looking at the products:
3 appears in 390, 210, 165, 66
It does not appear in 77.
So:
Fathima = 3
Qahira = 77
Therefore, Qahira received tokens 7 and 11.
So Qahira received 2 tokens.
Answer for 35: 2
Now, Adhara gave a token only to Pragnyaa.
The only value that appears in just one product is 13, and it appears only in 390.
So:
Adhara = 13
Pragnyaa = 390
Now remaining candidates and funds:
Rasheeda, Smera, Tantra must get 210, 165, 66 in some order.
Rasheeda must receive the highest number of tokens and did not receive from Esther.
Since 210 has 4 tokens and 165, 66 have 3 tokens each:
Rasheeda = 210
210 = 2 × 3 × 5 × 7
Rasheeda did not receive from Esther. So Esther cannot be 2, 3, 5, or 7.
Therefore:
Esther = 11
Qahira = 77 = 7 × 11
Since Dhanavi gave a token to Qahira but not to Smera, Dhanavi must be 7 because Qahira has 7 and 11, and 11 is already Esther.
So:
Dhanavi = 7
Now Bithi gave a token to Smera but not to Qahira. Since Qahira has 7 and 11, Bithi cannot be 7 or 11.
Remaining values are 2 and 5 for Bithi and Chhaya.
Smera can be either 165 or 66:
165 = 3 × 5 × 11
66 = 2 × 3 × 11
So Bithi may be 5 or 2 depending on Smera’s fund.
In both cases, Chhaya gets the other value and awards tokens to exactly 3 candidates.
So Chhaya awarded 3 tokens.
Smera received either 165 or 66, and both have 3 tokens.
So Smera received 3 tokens.
Final Answers
2 tokens
Pragnyaa and Smera both fit, but among the options only Pragnyaa is given.
Answer: A3 tokens
3 tokens
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