[DesiGuru]

Alright this one for the MegaBrains... Here's a CAT 20pointer series.
Who knows you might see this in CAT2005.
Try to get the answers on your own. I am quoting the source... So the math
professor should be content. I am eager to know how many of you can solve
this.

SELF-REFERENTIAL APTITUDE TEST, by Jim Propp (propp@math.wisc.edu)

The solution to the following puzzle is unique; in some cases the
knowledge that the solution is unique may actually give you a short-cut
to finding the answer to a particular question, but it's possible to
find the unique solution even without making use of the fact that the
solution is unique. (Thanks to Andy Latto for bringing this subtlety
to my attention.)

I should mention that if you don't agree with me about the answer to #20,
you will get a different solution to the puzzle than the one I had in mind.
But I should also mention that if you don't agree with me about the answer
to #20, you are just plain wrong. :smile:

You may now begin work.


1. The first question whose answer is B is question
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

2. The only two consecutive questions with identical answers are questions
(A) 6 and 7
(B) 7 and 8
(C) 8 and 9
(D) 9 and 10
(E) 10 and 11

3. The number of questions with the answer E is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

4. The number of questions with the answer A is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

5. The answer to this question is the same as the answer to question
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

6. The answer to question 17 is
(A) C
(B) D
(C) E
(D) none of the above
(E) all of the above

7. Alphabetically, the answer to this question and the answer to the
following question are
(A) 4 apart
(B) 3 apart
(C) 2 apart
(D) 1 apart
(E) the same

8. The number of questions whose answers are vowels is
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

9. The next question with the same answer as this one is question
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

10. The answer to question 16 is
(A) D
(B) A
(C) E
(D) B
(E) C

11. The number of questions preceding this one with the answer B is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

12. The number of questions whose answer is a consonant is
(A) an even number
(B) an odd number
(C) a perfect square
(D) a prime
(E) divisible by 5

13. The only odd-numbered problem with answer A is
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17

14. The number of questions with answer D is
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

15. The answer to question 12 is
(A) A
(B) B
(C) C
(D) D
(E) E

16. The answer to question 10 is
(A) D
(B) C
(C) B
(D) A
(E) E

17. The answer to question 6 is
(A) C
(B) D
(C) E
(D) none of the above
(E) all of the above

18. The number of questions with answer A equals the number of questions
with answer
(A) B
(B) C
(C) D
(D) E
(E) none of the above

19. The answer to this question is:
(A) A
(B) B
(C) C
(D) D
(E) E

20. Standardized test is to intelligence as barometer is to
(A) temperature (only)
(B) wind-velocity (only)
(C) latitude (only)
(D) longitude (only)
(E) temperature, wind-velocity, latitude, and longitude

K

PS: I will give hints later if needed.

[convolutedsignal]

damn spent half an hr and screwed up one clue...Amazing puzzle bro

[DesiGuru]

Hint One: Answer To Question 20 is E.

I would love if all ye believed that I could solve this puzzle.
Let me repeat there is enough information in the puzzle to solve it. Shocking as it may sound...

K

[assignus]

Originally Posted by DesiGuru

Hint One: Answer To Question 20 is E.

I would love if all ye believed that I could solve this puzzle.
Let me repeat there is enough information in the puzzle to solve it. Shocking as it may sound...

K

gotcha....

1--d
2--a
3--d
4--b
5--e
6--d
7--d
8--e
9--d
10--a
11--b
12--a
13--d
14--b
15--a
16--d
17--b
18--a
19--b
20--e

what say?

[DesiGuru]

Good Job assignus!!



If you can confirm you did it on your own I would say "Check out the big brain on assignus" quoting from pulp fiction ofcourse.

Definitely post your approach for solving this puzzle briefl. This type of puzzle is called the SRAT. Self referential apti test...

I will try and present some more interesting things about the solution later...

K

[assignus]

Originally Posted by DesiGuru

Good Job assignus!!



If you can confirm you did it on your own I would say "Check out the big brain on assignus" quoting from pulp fiction ofcourse.

Definitely post your approach for solving this puzzle briefl. This type of puzzle is called the SRAT. Self referential apti test...

I will try and present some more interesting things about the solution later...

K

...i did on my own.....but if were to come in CAT...i would have solved only this question...cuz it took more than one hour......

ill post my approach in a while......mebbe after i go home from office....

meanwhile check out the excel file attached.....rename it to .xls extension from doc (this site doesnt allow me to upload excel files.. )

[popeye]

Hi,

I think such Questions should be solved by starting with Q's that have its answer in some other Q while that Q has its answer in this particular one. This type of problems are available in a logical reasoning book(forgot its name) which I saw at British Council Library. Here we need to make one assumption or problem becomes superfluous.

REFERRING TO THE QUESTIONNAIRE
THE 'ANSWER' WORD HERE REPRESENTS THE ACTUAL ANSWER IN SOME CASES AND THE ANSWER OPTIONS IN SOME.

Somone rightly said "English is a funny language"

if we dont assume above thing the problem will take us on a never ending journey.

However in solutions answer means answer option.

Here we have Q16 & 10 and also 6 & 17 having that pattern.

Now looking at Q10 & Q16 we notice that in Q10 B,C,D,E cannot be the answer as it contradicts the condition in Q16. So answer for Q10 is A and that for Q16 is D. So we got two answers.

Q10-A Q16-D


Now for the pair 6&17 after narrowing down the options B/D can be the answer.

Next step is to look for a clue that will give you definite answer.
Look where else do Q6 or Q17 appear. After going through we notice Q.2 which has Q6 in it, but the bigger clue here is the question itself which says "The ONLY two consecutive questions with identical answers are questions"
So we know that 16 & 17 cannot have same answer. So 17 cannot have option D.
So that leaves only option B. Thus we get answer to Q6 as D.

Q6-D Q17-B

Now no more such hints are available, so I tried using the hint given. But that hint did not fit anywhere. So I decided to narrow down options from given clues by applying logic. So started from beginning.

By applying simple logic to Q1 we see that its answer can never be A 0r B because it contradicts the Q itself.

Similarly getting a clue from Q1 we see that B cannot be the answer to Q2.

Q3 & Q4 require more data so keep them aside.

Now from the clues in Q1&Q2 we can eliminate options A&B from Q5. That eliminates option E from A.

Q7 & Q8 require more data so keep them aside.

Now since we have the answer to Q10 we see that Q9 cannot have the answer as option A. That also eliminates option D from Q2

Similarly using the assumption I made Q11 too cannot have answer as A.
That also eliminates option E from Q2

Q12 requires further analysis so kept aside.

Observing Q13 we see that C cannot be the answer as it contradicts the question itself. Also we can eliminate otion E as we know answer to Q17.
Also we saw above that Q9 & Q11 cannot have answer option A.So that leaves only answer option D. That gives answers to further two more Q's.

Q13-D Q15-A Q12-A

Q18 & Q19 require more data so I went back to beginnig & applied more logic.

From Q2 again we can see that Q2 eliminates the following otions D for 5, E for 7, A&D for 14, B for 18 and E for 19(FROM HINT AS ANSWER TO Q20 IS E).
This eliminates options D&A from Q4.

Now since no. of cosonants is an even number(Q12), the vowels have to be even to add upto 20. So answer to Q8 can be A/C/E. If you see Q3 & Q4, the number of vowels has to be greater than 4. So A is also eliminated. Because of Q1 the answer to Q4 must be the remaining odd number 5 - option B.

Now since no. of vowel answer options can be 6 or 8 as seen from Q8 we can get answer to Q3. Since no. of E is 5(Q4), no. of A can be 1 or 3. But it cannot be 1 as per condition in Q1. So no. of vowels is 8 and we get answers to following questions

Q1-D Q3-D Q4-B Q8-E


So no. of consonants as answers(OPTIONS) is 12. Now as no. of answer option B as actual answers is more than 3, D cannot be more than 9. That eliminates option E from Q9 & Q14.
Now Q9 cannot have answer option(E) the answer to Q9 is the only remaining option D. So Q8&Q9 do not have same answers. That eliminates option C from Q2 leaving only option A. That means answer to Q7 is D.

Q2-A Q7-D Q9-D

We see that from Q1-10 only Q4 has answer option B.That gives answer to 11 as B.

Q11-B

Now in Q 18 as we know the number of E being 3 all which have occured we can eliminate option E here. Also B has been eliminated. So that leaves A/C/D.

No of A is 5 as seen, and only 3Q(14,18,19) are left to be answered. We have not seen a single occurrence of C. So C can be eliminated. No of D we have seen is already greater than 5, so that leaves only option A.
So no. of answers as option A=no .of answers as option B=5.

But since we have only 3 B's till now, the answers to Q14 & Q19 has to be B.

So we get the final solution(phew!!!)

1-D 2-A 3-D 4-B 5-E 6-D 7-D 8-E 9-D 10-A 11-B 12-A 13-D 14-B 15-A 16-D
17-B 18-A 19-B 20-E

Is this the solution you got?? In my case I have made several assumptions so am not sure.

Also if this occurs in CAT 2005 this will be the only problem, it requires more than an hour to get final solution.

[assignus]

Originally Posted by popeye

Hi,

Is this the solution you got?? In my case I have made several assumptions so am not sure.

heres my solution....din read ur sol...but it shud be similar if we got the same answers....btw no assumptions are required,...everything can be deduced....


First things first…..
Answer to question 20 is e (hint: hint given by DG in post # 3 J)
After reading all the questions…. Just figure out which questions to solve first…. After this basic method of approach will be elimination u should find out that question pairs 10-16 & 6-17 will be an easy one….. here we can conclude Q10=a, Q16=d.

And Q6=d, Q17=b (u may feel it can very well be other way round….but it cant be….figure it out urself)

Now, question 5 is straight……it has to be Q5=e

Now question 13, answer cannot be a,b,c,e hence it has to be Q13=d ( not a bcuz then there will be 2 odd numbered questions with answer a, namely Q9 and Q13, not b bcuz atleast one answer b has to be there…hint: Q1, it cannot be c…quite obvious, it cannot be e cuz we already have the answer for Q17=d)

From Q13=d, we also know Q15=a, Q12=a, Q9=d (u shud be able to figure it out)

Answer to question 1 cannot be a,b,c,e so it has to be d ( cant be a bcuz its contradicting the question, cant be b bcuz of the same reason, cant be c bcuz we already have 2 e’s as the answers, cant be e bcuz Q5=e)

11 questions down…9 to go….

The straight part is finished I guess…rest all is elimination….make a chart (I used excel) ….put down all the answers u know…….and put cross marks in all the places that u can eliminate….answers will follow automatically….

Question 2 is a huge advantage….the only identical answers can be between 6-11 so u can eliminate a lot of places.

Hope it helps….

[popeye]

Originally Posted by assignus

heres my solution....din read ur sol...but it shud be similar if we got the same answers....btw no assumptions are required,...everything can be deduced....

Buddy you too made the same assumptions I made but unkowingly. There is a lot of ambiguity in the way word answer is used in few Q's. It can mean actual answer or the answer option. So you need to be careful while taking correct decision.

Anywayz nice to see we got right answers.

[assignus]

Originally Posted by popeye

Buddy you too made the same assumptions I made but unkowingly. There is a lot of ambiguity in the way word answer is used in few Q's. It can mean actual answer or the answer option. So you need to be careful while taking correct decision.

Anywayz nice to see we got right answers.

can u point out a assumption that i made ?? or for that matter...what assumptions did u make??