Logical Reasoning

Arrangements

Medium

Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external "subject matter experts" (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below.

If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it.

A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal.

The following facts are also known.

Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.

Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.

Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.

Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.

How many questions were DEFINITELY disapproved by Bimal?

Entered answer:

✅ Correct Answer: 4

Slide 1/13

Understanding the set :-

Amal, Bimal, and Komal have to select some questions from a pool of 13 questions

Question creation - by SME OR by Amal/ Bimal/ or Komal

Each of the reviewers either approves or disapproves a question that is shown to them

Conditions :

a) If a question is created by an SME, it is reviewed first by Amal, and then by Bimal.

i) If both of them approve the question, then the question is accepted and is not reviewed by Komal.

ii) If both disapprove the question, it is rejected and is not reviewed by Komal.

iii) If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it.

b) A question created by one of the reviewers is decided upon by the other two

i) If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted.

Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it.

ii) If a question is created by Bimal, then it is first reviewed by Komal. If Komal approves the question, then it is accepted.

Otherwise, it is reviewed by Amal. The question is then accepted only if Amal approves it.

iii) If a question is created by Komal, then it is first reviewed by Amal. If Amal approves the question, then it is accepted.

Otherwise, it is reviewed by Bimal. The question is then accepted only if Bimal approves it.

In this set, the most important thing is to understand these conditions well, may be you can jot down the conditions in a corner of your paper,

as these condition will be the base point which will be needed at every point.

✓ / ✗	Qn	created by	Amal	Bimal	Komal
	1
	2
	3
	4
	5
	6
	7
	8
	9
	10
	11
	12
	13

In this table in the first column we will mark "✓" if the question is accepted.

and "x" if the question is rejected.

In third column we will mention the person who has created the question (SME/ Amal/ Bimal/ Komal)

In next three columns we will mark whether Amal / Bimal/ Komal has approved (✓) or rejected (x) or haven't reviewed (-) the question.

✓ / ✗	Qn	created by	Amal	Bimal	Komal
✓	1
x	2
✓	3
✓	4
✓	5
x	6
✓	7
✓	8
x	9
✓	10
x	11
x	12
✓	13

Clue 1 says,

Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.

✓ / ✗	Qn	Amal
✓	1	-
x	2
✓	3
✓	4
✓	5	-
x	6
✓	7	-
✓	8
x	9	-
✓	10
x	11
x	12	-
✓	13

Clue 2 says,

Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.

✓ / ✗	Qn	Amal	Bimal
✓	1	-	-
x	2
✓	3		-
✓	4
✓	5	-	-
x	6
✓	7	-
✓	8
x	9	-
✓	10		-
x	11		-
x	12	-
✓	13

Clue 3 says,

Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.

✓ / ✗	Qn	Amal	Bimal	Komal
✓	1	-	-
x	2
✓	3		-
✓	4
✓	5	-	-
x	6			-
✓	7	-
✓	8
x	9	-
✓	10		-	-
x	11		-
x	12	-
✓	13			-

Clue 4 says,

Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.

✓ / ✗	Qn	created by	Amal	Bimal	Komal
✓	1	Bimal	-	-	✓
x	2
✓	3			-
✓	4
✓	5	Bimal	-	-	✓
x	6				-
✓	7		-
✓	8
x	9		-
✓	10			-	-
x	11			-
x	12		-
✓	13				-

Now, we will solve the set according to the conditions given in the starting.

Q.1 and Q.5 -

Both of them are reviewed by only Komal,

Now, according to the condition - If a question is created by Bimal, then it is first reviewed by Komal. If Komal approves the question, then it is accepted.

Otherwise, it is reviewed by Amal. The question is then accepted only if Amal approves it.

In this case the question would have been prepared by Bimal and Komal would have reviewed it first and she then have approved it

Therefore, it directly got accepted without going to Amal.

✓ / ✗	Qn	created by	Amal	Bimal	Komal
✓	1	Bimal	-	-	✓
x	2	SME	x/ ✓	✓ /x	x
✓	3			-
✓	4	SME	x/ ✓	✓ /x	✓
✓	5	Bimal	-	-	✓
x	6				-
✓	7		-
✓	8	SME	x/ ✓	✓ /x	✓
x	9		-
✓	10			-	-
x	11			-
x	12		-
✓	13				-

Q. 2, 4, 8 :-

These questions are reviewed by all the three reviewers.

Condition applicable - If a question is created by an SME, it is reviewed first by Amal, and then by Bimal.

i) If both of them approve the question, then the question is accepted and is not reviewed by Komal.

For q. 2 -

We know the question finally is rejected

Therefore, it must have been disapproved by one of Amal or Bimal

And then it would have gone to Komal, who would at last again rejected it.

For Q. 4 and 8 -

We know the question finally is approved.

Therefore, it must have been disapproved by one of Amal or Bimal

And then it would have gone to Komal, who would at last approve it.

✓ / ✗	Qn	created by	Amal	Bimal	Komal
✓	1	Bimal	-	-	✓
x	2	SME	x/ ✓	✓ /x	x
✓	3	Bimal	✓	-	x
✓	4	SME	x/ ✓	✓ /x	✓
✓	5	Bimal	-	-	✓
x	6				-
✓	7		-
✓	8	SME	x/ ✓	✓ /x	✓
x	9		-
✓	10			-	-
x	11	Bimal	x	-	x
x	12		-
✓	13				-

Q . 3 ad 11 -

These questions are reviewed by Amal and Komal.

Therefore, Condition applied - If a question is created by Bimal, then it is first reviewed by Komal. If Komal approves the question, then it is accepted.

Otherwise, it is reviewed by Amal. The question is then accepted only if Amal approves it.

Q.3 -

this question finally is approved

=> Bimal prepared the question , then it went to Komal - who disapproved it, therefore , it the went to Amal who approved it.

Q.11 -

this question finally is disapproved.

=> Bimal prepared the question , then it went to Komal - who disapproved it, therefore , it the went to Amal who also disapproved it.

✓ / ✗	Qn	created by	Amal	Bimal	Komal
✓	1	Bimal	-	-	✓
x	2	SME	x/ ✓	✓ /x	x
✓	3	Bimal	✓	-	x
✓	4	SME	x/ ✓	✓ /x	✓
✓	5	Bimal	-	-	✓
x	6				-
✓	7	Amal	-	x	✓
✓	8	SME	x/ ✓	✓ /x	✓
x	9	Amal	-	x	x
✓	10			-	-
x	11	Bimal	x	-	x
x	12	Amal	-	x	x
✓	13				-

For Q. 7, 9, 12 :

we know it was reviewed by Bimal and komal

Therefore, condition applied - If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted.

Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it.

For Q.7 :

Question would have been prepared by Amal, then it would have gone to Bimal, he would have disapproved it, therefore, it will go to Komal and she will Approve it.

For Q, 9 and 12 :

Question would have been prepared by Amal, then it would have gone to Bimal, he would have disapproved it, therefore, it will go to Komal and she will again disapprove it.

✓ / ✗	Qn	created by	Amal	Bimal	Komal
✓	1	Bimal	-	-	✓
x	2	SME	x/ ✓	✓ /x	x
✓	3	Bimal	✓	-	x
✓	4	SME	x/ ✓	✓ /x	✓
✓	5	Bimal	-	-	✓
x	6				-
✓	7	Amal	-	x	✓
✓	8	SME	x/ ✓	✓ /x	✓
x	9	Amal	-	x	x
✓	10	Komal	✓	-	-
x	11	Bimal	x	-	x
x	12	Amal	-	x	x
✓	13				-

Q. 10

It was reviewed by Amal only.

Condition applicable :- If a question is created by Komal, then it is first reviewed by Amal. If Amal approves the question, then it is accepted.

Otherwise, it is reviewed by Bimal. The question is then accepted only if Bimal approves it.

This question would have been prepared by Komal, then firstly reviewed by Amal, who accepted it, therefore it directly got accepted, without going to Bimal.

✓ / ✗	Qn	created by	Amal	Bimal	Komal
✓	1	Bimal	-	-	✓
x	2	SME	x/ ✓	✓ /x	x
✓	3	Bimal	✓	-	x
✓	4	SME	x/ ✓	✓ /x	✓
✓	5	Bimal	-	-	✓
x	6	SME/ Komal	x	x	-
✓	7	Amal	-	x	✓
✓	8	SME	x/ ✓	✓ /x	✓
x	9	Amal	-	x	x
✓	10	Komal	✓	-	-
x	11	Bimal	x	-	x
x	12	Amal	-	x	x
✓	13	SME / Komal	✓/x	✓	-

For Q. 6 and 13,

This question is reviewed by Amal and Bimal.

Condition applicable -

If a question is created by an SME, it is reviewed first by Amal, and then by Bimal.

If both of them approve the question, then the question is accepted and is not reviewed by Komal.

If a question is created by Komal, then it is first reviewed by Amal. If Amal approves the question, then it is accepted.

Otherwise, it is reviewed by Bimal. The question is then accepted only if Bimal approves it.

There can be both of these conditions applicable

For Q6 -

The question could have been prepared by Komal or SME and rejected by Bimal and Amal.

For Q.13 -

The question could have been prepared by Komal or SME, whether accepted by both (if prepared by SME) or rejected by Amal but accepted by Bimal (if question prepared by Komal)

✓ / ✗	Qn	created by	Amal	Bimal	Komal
✓	1	Bimal	-	-	✓
x	2	SME	x/ ✓	✓ /x	x
✓	3	Bimal	✓	-	x
✓	4	SME	x/ ✓	✓ /x	✓
✓	5	Bimal	-	-	✓
x	6	SME/ Komal	x	x	-
✓	7	Amal	-	x	✓
✓	8	SME	x/ ✓	✓ /x	✓
x	9	Amal	-	x	x
✓	10	Komal	✓	-	-
x	11	Bimal	x	-	x
x	12	Amal	-	x	x
✓	13	SME / Komal	✓/x	✓	-

Bimal definitely disapproved 4 questions Q06, Q07, Q09 and Q12

Question 7

How many questions were DEFINITELY created by Amal?

Question 8

How many questions were DEFINITELY created by Komal?

Question 9

How many questions were DEFINITELY created by the SMEs?

Question 11

The approval ratio of a reviewer is the ratio of the number of questions (s)he approved to the number of questions (s)he reviewed. Which option best describes Amal's approval ratio?

Question 12

How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?

How many questions were DEFINITELY disapproved by Bimal?

Solution

More from this set:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)