Ch.4 :- Comparison of Ranks : Exercise 2


⇒ Directions for Q. No. 1 to 6 :Following questions are based on the information given below. Read the information carefully and then answer the questions that follow:

(i) Seven students P, Q, R, S, T, U and V take a series of tests.

(ii) No two students get similar marks.

(iii) V always scores more than P.

(iv) P always scores more than Q.

(v) Each time either R scores the highest and T gets the least, or alternatively S scores the highest and U or Q scores the least.

1. If V is ranked fifth, which of these must be true ?

(a) S scores the highest     (b) R is ranked second     (c) T is ranked third

(d) Q is ranked fourth        (e) U scores the least

Answer & Solution

Ans(a) On the basis of the information (iii) and (iv), if (v) is ranked fifth, then P will be ranked 6th and Q seventh (the last position) and consequently, as per information (v), if Q gets last position, S will be positioned on top.

2. If R gets the most, V should be ranked not lower than

(a) Second     (b) Third     (c) Fourth     (d) Fifth     (e) Sixth

Answer & Solution

Ans(c) If R gets the most, T will get the least. Now as per conditions, V is followed by P and P is followed by Q. Therefore, V carries two persons after him. Hence, V cannot be positioned lower than the 4th position.

3. If S is ranked second, which of the following can be true?

(a) P gets more than R    (b) V gets more than S    (c) P gets more than S

(d) T gets more than Q    (e) U gets more than V

Answer & Solution

Ans(e) If S is ranked second, then R will score the highest and T the least. On the basis of the positions of S, R and T, we observe that only U may get more than V.

4. If S is ranked sixth and Q is ranked fifth, which of the following can be true?

(a) V is ranked fifth or fourth      (b) R is ranked second or third

(c) P is ranked second or fifth     (d) U is ranked third or fourth

(e) T is ranked fourth or fifth

Answer & Solution

Ans(d) If S is ranked sixth and Q is fifth, then automatically R will be ranked at first and T at seventh positions. Now on the basis of the positions of S, Q, Rand T, only option (d), which positions U either third or fourth, can be valid.

5. If R is ranked second and Q is ranked fifth, which of these must be true?

(a) S is ranked third     (b) P is ranked third     (c) V is ranked fourth

(d) T is ranked sixth    (e) U is ranked sixth

Answer & Solution

Ans(d) If R is ranked second and Q gets fifth position, then automatically S will get the top position and U the last. Now on the basis of the positions of R, Q, S, and U obtained so far V is positioned at third and P at fourth. Therefore, only option (d) i.e., position of T at the sixth position satisfies this order of ranking.

6. Information given in which of the statement is superfluous?

(a) (ii)     (b) CO     (c) (iv)     (d) None is superfluous     (e) None of these

Answer & Solution

Ans(d) Since all the information are needed to solve the question, so none of the information given is superfluous.

⇒ Directions for Q. No. 7 to 11 : Read the following information and select the best answer choice given in each of the questions thatfollows.

In a study offive brands of pain relieving tablets P, Q, R, Sand T, the brands were tested and ranked against each other us more or less effective per dose. The following results were obtained.

(i) P was more effective than Q.

(ii) The effectiveness of R was less than that of S.

(iii) T was the least effective brand tested.

(iv) Q and R were equally effective.

(v) The effectiveness of S was greater than that of Q.

7. If the above statements are true, which of the following must also be true ?

(a) P and S were equally effective.    (b) P was the most effective.

(c) S was the most effective.              (d) R was less effective than P.

(e) T did not relieve pain.

Answer & Solution

Ans(d)On the basis of the information given in the question we find the order of their effectiveness as in the order in Fig. Drugs at the bottom being the less effective and at the top, the most effective. From the ranking order, we find that position of R keeps varying and, therefore, either P or S can be the most effective brand.

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From the order, it is clear that R was less effective than P.

8.All the information in the results given above can be derived from which of the following groups of statements?

(a) Statements (i), Cii),Ciii)     (b) Statements (i), (iii), (iv)

(c) Statements (ii), (iii), (iv)    (d) Statements (i), (ii), (iii), (iv)

(e) Statements (ii), (iii), (iv), and (v).

Answer & Solution

Ans(d) On the basis of the information given in the question we find the order of their effectiveness as in the order in Fig. Drugs at the bottom being the less effective and at the top, the most effective. From the ranking order, we find that position of R keeps varying and, therefore, either P or S can be the most effective brand.

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 Information (v) is not required to obtain the final order of ranking. Therefore, only informations (i), (ii), (iii), (iv) are sufficient to get the final ranking.

9. If a sixth brand M is tested and found to be more effective than S, then which of the followings must be true if the findings of the study are correct?

(a) M is the most effective of all the six brands tested.

(b) At least four of the six brands tested are less effective thanM.

(c) M is more effective than P.

(d) M is less effective than P.

(e) No more than four of the six brands tested are more effective than T.

Answer & Solution

Ans(b) On the basis of the information given in the question we find the order of their effectiveness as in the order in Fig. Drugs at the bottom being the less effective and at the top, the most effective. From the ranking order, we find that position of R keeps varying and, therefore, either P or S can be the most effective brand.

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  It is clear from the ranking order so obtained that brand S may be less effective than P, equal to P and more effective than P. It means that position of S is not fixed. Now as per question, sixth brand i.e., M is more effective than S which implies that whatever be the position of S, there will be atleast four brands which will be less effective than M.

10.If R is more expensive per dose than P, and T is less expensive per dose than R, which of the following must be true, according to the study, for a consumer, who wishes to buy a pain reliever with the greatest effectiveness for the amount spent per dose?

(a) P should be purchased instead of R,

(b) P should be purchased instead ofT.

(c) T should be purchased instead of R.

(d) Q should be purchased instead of R if Q is of the same price as S.

(e) Q should be purchased instead of T if Q is of the same price as R.

Answer & Solution

Ans(a) On the basis of the information given in the question we find the order of their effectiveness as in the order in Fig. Drugs at the bottom being the less effective and at the top, the most effective. From the ranking order, we find that position of R keeps varying and, therefore, either P or S can be the most effective brand.

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Now it is given that P is less expensive than R and from the order, P is more effective than R. It means that P should be purchased as it is more effective and less expensive than R.

11.If Q contains the same amount of an ingredient, X, as S does and more of that ingredient than T does, which of the following is consistent with the results of the study?

(a) The relative effectiveness of the 5 brands of pain relievers is due to the amount of X the brand contains.

(b) R does not contain X, and brands of pain relievers in which X is absent do not have any measurable effective- ness.

(c) The absent of X in R would account for R’s being more effective than T, Q and S.

(d) The absence of X in R would account for R’s being more effective than T, Q and S.

(e) The presence of X contributes to the effectiveness of T, Q and S in relieving pain.

Answer & Solution

Ans(e) On the basis of the information given in the question we find the order of their effectiveness as in the order in Fig. Drugs at the bottom being the less effective and at the top, the most effective. From the ranking order, we find that position of R keeps varying and, therefore, either P or S can be the most effective brand.

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We know that effectiveness of Sand Q is equal and it is given that amount of X in these brands is also equal. Also the effectiveness of T as well as amount of X in T is less than that of Sand Q. It means that presence of X contributes to the effectiveness of T, Q and S in relieving pain.

⇒ Directions for Q. No. 12 to 15 : Read the following information and answer the questions that follow. Sunita is taller than Seema and Renu, Renu is shorter than Radha and Gauri. Bina is taller than Radha and shorter than Sunita. Sunita is not the tallest and Renu is not the shortest.

12.Who is the tallest?

(a) Sunita     (b) Bina    (c) Gauri    (d) Data inadequate   (e) None

Answer & Solution

Ans(c) On the basis of information given in the question, final order of ranks in descending order is as follows:

Gauri, Sunita, Bina, Radha, Renu, Seema

Gauri is the tallest among all.

13.Who is the shortest?

(a) Radha    (b) Renu    (c) Bina    (d) Data inadequate    (e) None

Answer & Solution

Ans(e) On the basis of information given in the question, final order of ranks in descending order is as follows:

Gauri, Sunita, Bina, Radha, Renu, Seema

Seema is the shortest.

14.What is the position of Radha from the shorter end?

(a) Fourth    (b) Second    (c) Third    (d) Data inadequate    (e) None

Answer & Solution

Ans(c) On the basis of information given in the question, final order of ranks in descending order is as follows:

Gauri, Sunita, Bina, Radha, Renu, Seema

Radha occupies the third position from the shorter end

15.Which of the following statements is definitely correct?

(a) Bina occupies the third position from the top.

(b) Seema is taller than Renu.

(c) Gauri is shorter than Radha.

(d) None of the above.

Answer & Solution

Ans(a) On the basis of information given in the question, final order of ranks in descending order is as follows:

Gauri, Sunita, Bina, Radha, Renu, Seema

Bina occupies the third position from the top.

⇒Directions for Q. No. 16 to 20 : Study the following information carefully and then answer the questions that follow.

A blacksmith has five iron articles A, B, C, D and E each having a different weight.

(i) A weighs twice as much as B.

(ii) B weighs four and half times as much as C.

(iii) C weighs half as much as D.

(iv) D weighs half as much as E.

(v) E weighs less than A but more than C.

16.Which of the following is the lightest in weight?

(a) A      (b) B     (c) C     (d) D

Answer & Solution

Ans(c) A =2B, B=9/2C, D=2C, E=2D, A>E> or

A > B > E > D > C

C

17.E is lighter in weight than which of the other two articles?

(a) A, B     (b) D, C     (c) A, C     (d) D, B

Answer & Solution

Ans(a) A =2B, B=9/2C, D=2C, E=2D, A>E> or

A > B > E > D > C

A,B

18.E is heavier than which of the following two articles?

(a) D, B     (b) D, C     (c) A, C     (d) A, B

Answer & Solution

Ans(b) A =2B, B=9/2C, D=2C, E=2D, A>E> or

A > B > E > D > C

D,C

19.Which of the following is the heaviest in weight?

(a) A     (b) B     (c) C     (d) D

Answer & Solution

Ans(a) A =2B, B=9/2C, D=2C, E=2D, A>E> or

A > B > E > D > C

A

20.Which of the following represents the descending order of weights of the articles?

(a) A, B, E, D, C     (b) B, D, E, A, C     (c) A, B, C, D, E     (d) c, D, E, B, A

Answer & Solution

Ans(a) A =2B, B=9/2C, D=2C, E=2D, A>E> or

A > B > E > D > C

A, B, E, D, C

21.There are five friends S, K, M, A, R. S is shorter than K, but taller than R, M is the tallest. A is a little shorter than K and little taller than S. Who has two persons taller and two persons shorter than him ?

(a) R     (b) S     (c) K     (d) A

Answer & Solution

Ans(d)  Clearly A has two persons taller and two persons shorter than him.

M → K→ A → S → R.

22.Among A, B, P, Q and S, B is immediate next taller than the shortest and Q is taller than the shortest and Q is taller than P. Which of the following statement(s) is/are necessary to decide the tallest among them?

(A) P is not as tall as S

(B) A is third below Q in height

(C) P is second in height above A

(a) only (A) or (B)     (b) only (B) or (C)     (c) only (A) or CC)

(d) (A) or (B) or (C)    (e) only (A)

Answer & Solution

Ans(b) Using basic information given in the question, we find that

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Now if we use either of the information (B) or (C), we know that A is the tallest.

⇒ Directions for Q. No. 23 to 25 : Read the information given below to answer the questions that follow:

(i) There is a group of five girls.

(ii) Kamini is second in height but younger than Rupa.

(iii) Pooja is taller than Monika but younger in age.

(iv) Rupa and Monika are of the same age but Rupa is tallest between them.

(v) Neelam is taller than Pooja and elder to Rupa

23.If they are arranged in the ascending order of height, who will be in the third position?

(a) Monika     (b) Monika or Rupa     (c) Rupa     (d) None

Answer & Solution

Ans(d) Orders of height and age in descending order are given below:

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Kamini will be in the third position.

24.If they are arranged in descending order of their ages, who will be in the fourth position?

(a) Monika or Rupa     (b) Monika     (c) Kamini     (d) None of these

Answer & Solution

Ans(d) Orders of height and age in descending order are given below:

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Fourth position cannot be determined if they are arranged in descending order of their ages.

25.To answer the question “Who is the youngest person in the group”, which of the following statements is superfluous?

(a) only (i)     (b) only (v)     (c) only (ii)      (d) either (i) or (iv)

Answer & Solution

Ans(a) Orders of height and age in descending order are given below:

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Only Statement (i) is superfluous.