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CAT 2022 Slot 1 DILR · Set 2 of 4Logical ReasoningModerate DifficultyQ6–Q10 · 2 MCQ + 3 TITA

CAT 2022 Slot 1 DILR Set 2: Arrangements (5 Questions) with Solutions

The Arrangements set from the official CAT 2022 Slot 1 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2022 Slot 1 DILR · Questions 6–10
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
Rasheeda 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.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q6. Arrangements

TITA · +3 / 0
How many tokens did Qahira receive?
Correct Answer
2
Step-by-step solution
📌 Core Concept
Each funding amount factorises into prime face values. Each interviewer awards one prime only, so each interviewer matches a prime and each candidate's product tells who awarded tokens to them.
🔢 Step-by-Step Solution
1
Factorise the funds (in thousands): 390=2⋅3⋅5⋅13390=2\cdot3\cdot5\cdot13, 210=2⋅3⋅5⋅7210=2\cdot3\cdot5\cdot7, 165=3⋅5⋅11165=3\cdot5\cdot11, 77=7⋅1177=7\cdot11, 66=2⋅3⋅1166=2\cdot3\cdot11. The six interviewers carry the six primes 2, 3, 5, 7, 11, 13, one each.
2
Fact 1 says Adhara awarded only Pragnyaa. The only prime in a single product is 13, found only in 390. So Adhara = 13 and Pragnyaa = Rs.390,000.
3
Fact 1 also says Fathima awarded everyone except Qahira. The prime 3 is in four products (390, 210, 165, 66) and missing only from 77. So Fathima = 3 and Qahira = Rs.77,000 = 7⋅117\cdot11.
4
Qahira's product has exactly two primes, so she received 2 tokens.
Quick Check
Facts 1 and 3 rule out Fathima, Adhara and Bithi for Qahira. Dhanavi plus one other interviewer remain, which is 2 tokens.
Correct Answer: 2

Q7. Arrangements

MCQ · +3 / −1
Who among the following definitely received a token from Bithi but not from Dhanavi
  1. A) Rasheeda
  2. B) Pragnyaa
  3. C) Tantra
  4. D) Qahira
Correct Answer
B) Pragnyaa
Step-by-step solution
📌 Core Concept
Each interviewer is matched to one prime. Working out which prime belongs to Bithi and which to Dhanavi shows who must have received which tokens.
🔢 Step-by-Step Solution
1
Factorise the funds (in thousands): 390=2⋅3⋅5⋅13390=2\cdot3\cdot5\cdot13, 210=2⋅3⋅5⋅7210=2\cdot3\cdot5\cdot7, 165=3⋅5⋅11165=3\cdot5\cdot11, 77=7⋅1177=7\cdot11, 66=2⋅3⋅1166=2\cdot3\cdot11.
2
Fact 1 gives Adhara = 13 (only Pragnyaa, Rs.390,000). Fathima = 3, since 3 is missing only from 77, so Qahira = Rs.77,000.
3
Rasheeda has the most tokens, 4, so she is Rs.210,000 (2⋅3⋅5⋅72\cdot3\cdot5\cdot7). Fact 2 says Esther gave her nothing, so Esther is not 2, 5 or 7. Esther = 11.
4
Qahira (7⋅117\cdot11) gets 11 from Esther, so Dhanavi, who also awarded her, must be 7. Bithi and Chhaya then hold 2 and 5.
5
Pragnyaa's 2 and 5 come from Bithi and Chhaya, so Bithi awarded her. Her product has no 7, so Dhanavi did not. Pragnyaa definitely qualifies.
Why Not the Others
Rasheeda: her 7 comes from Dhanavi, so she is out.
Tantra: Tantra is Rs.165,000 or Rs.66,000, and either way Bithi's token may be absent, so it is not definite.
Qahira: Fact 3 says Bithi did not award her.
Correct Answer: B

Q8. Arrangements

TITA · +3 / 0
How many tokens did Chhaya award?
Correct Answer
3
Step-by-step solution
📌 Core Concept
The funds are products of distinct primes, and each prime belongs to one interviewer. Identifying Chhaya's prime gives the number of candidates she awarded.
🔢 Step-by-Step Solution
1
Factorise the funds (in thousands): 390=2⋅3⋅5⋅13390=2\cdot3\cdot5\cdot13, 210=2⋅3⋅5⋅7210=2\cdot3\cdot5\cdot7, 165=3⋅5⋅11165=3\cdot5\cdot11, 77=7⋅1177=7\cdot11, 66=2⋅3⋅1166=2\cdot3\cdot11.
2
Fact 1 gives Adhara = 13 and Fathima = 3, so Pragnyaa = Rs.390,000 and Qahira = Rs.77,000.
3
Rasheeda has 4 tokens, so she is Rs.210,000. Fact 2 excludes Esther, so Esther = 11. Qahira (7⋅117\cdot11) then makes Dhanavi = 7.
4
Bithi and Chhaya hold 2 and 5 in some order.
5
If Chhaya = 2, she awarded the products containing 2: 390, 210 and 66, which is 3 candidates.
6
If Chhaya = 5, she awarded the products containing 5: 390, 210 and 165, which is also 3 candidates.
Quick Check
The primes 2 and 5 each appear in exactly three products, so the count is 3 either way.
Correct Answer: 3

Q9. Arrangements

TITA · +3 / 0
How many tokens did Smera receive?
Correct Answer
3
Step-by-step solution
📌 Core Concept
Match each prime to an interviewer from the clues, then work out which product belongs to Smera.
🔢 Step-by-Step Solution
1
Factorise the funds (in thousands): 390=2⋅3⋅5⋅13390=2\cdot3\cdot5\cdot13, 210=2⋅3⋅5⋅7210=2\cdot3\cdot5\cdot7, 165=3⋅5⋅11165=3\cdot5\cdot11, 77=7⋅1177=7\cdot11, 66=2⋅3⋅1166=2\cdot3\cdot11.
2
Fact 1 gives Adhara = 13 and Fathima = 3, so Pragnyaa = Rs.390,000 and Qahira = Rs.77,000.
3
Rasheeda has the most tokens (4), so she is Rs.210,000. Fact 2 excludes Esther, so Esther = 11. Qahira (7⋅117\cdot11) with Dhanavi's token makes Dhanavi = 7.
4
Dhanavi (7) awarded exactly the products containing 7, which are 210 and 77. Fact 3 says Dhanavi did not award Smera, so Smera is not 210 or 77.
5
Pragnyaa, Rasheeda and Qahira are already fixed, so Smera is Rs.165,000 or Rs.66,000.
6
Both of these products have 3 primes, so Smera received 3 tokens.
Quick Check
165=3⋅5⋅11165=3\cdot5\cdot11 and 66=2⋅3⋅1166=2\cdot3\cdot11 each have 3 factors.
Correct Answer: 3

Q10. Arrangements

MCQ · +3 / −1
Which of the following could be the amount of funding that Tantra received?
a
Rs. 66,00066,000
b
Rs. 165,000165,000
  1. A) Only (b)
  2. B) Only (a)
  3. C) Neither (a) nor (b)
  4. D) Both (a) and (b)
Correct Answer
D) Both (a) and (b)
Step-by-step solution
📌 Core Concept
After the interviewers are matched to primes, only Smera and Tantra are left with the two remaining funds. The question is whether Tantra can hold each of them.
🔢 Step-by-Step Solution
1
Factorise the funds (in thousands): 390=2⋅3⋅5⋅13390=2\cdot3\cdot5\cdot13, 210=2⋅3⋅5⋅7210=2\cdot3\cdot5\cdot7, 165=3⋅5⋅11165=3\cdot5\cdot11, 77=7⋅1177=7\cdot11, 66=2⋅3⋅1166=2\cdot3\cdot11.
2
Fact 1 gives Adhara = 13 and Fathima = 3, so Pragnyaa = Rs.390,000 and Qahira = Rs.77,000.
3
Rasheeda has the most tokens (4), so she is Rs.210,000. Fact 2 excludes Esther, so Esther = 11. Qahira makes Dhanavi = 7. Bithi and Chhaya hold 2 and 5.
4
The funds left for Smera and Tantra are Rs.165,000 (3⋅5⋅113\cdot5\cdot11) and Rs.66,000 (2⋅3⋅112\cdot3\cdot11).
5
Fact 3 needs Bithi to have awarded Smera, and Dhanavi (7) did not. Both leftover funds lack 7. If Bithi = 5, Smera = 165 and Tantra = 66. If Bithi = 2, Smera = 66 and Tantra = 165.
6
Both assignments satisfy every fact, so Tantra could have received either Rs.66,000 or Rs.165,000.
Why Not the Others
Neither (a) alone nor (b) alone works, because each choice for Bithi is consistent with the clues.
Correct Answer: D
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CAT 2022 Slot 1 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Bangalore

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