(i). A, B, C, D and E are five friends.
(ii). B is elder to E, but not as tall as C.
(iii). C is younger to A, and is taller to D and E.
(iv). A is taller to D, but younger to E.
(v). D is elder to A but is shortest in the group
Which of the following statements is correct about B ?
(i). B is not the tallest.
(ii). B is shorter to E.
(iii). When they are asked to stand in ascending order with respect to their heights, B is in the middle.
Answer: A
In terms of age, we have :
E < B, C < A, A < E, A < D
So, we have : C < A < E < B < A < D.
In terms of height, we have :
B < C, D < C, E < C, D < A
B is shorter than C. So, B is not the tallest. Thus, (i) is correct.
B and E are shorter than C. So, it cannot be conclude that B is shorter to E. Thus, (ii) is incorrect.
A single definite order of heights cannot be obtained from the given information. So, (iii) is incorrect.
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Which of the following pairs of students is elder to D ?
Answer: E
In terms of age, we have :
E < B, C < A, A < E, A < D
So, we have : C < A < E < B < A < D.
In terms of height, we have :
B < C, D < C, E < C, D < A
It cannot be determined for sure.
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(i). A, B, C, D, E and F are six students in a class.
(ii). B and C are shorter than F but heavier than A.
(iii). D is heavier than B and taller than C.
(iv). E is shorter than D but taller than F.
(v). F is heavier than D.
(vi). A is shorter than E but taller than F.
Who among them is the lightest ?
Answer: E
In terms of height, we have :
B < F, C < F, C < D, E < D, F < E, A < E, F < A.
So, C < F < E < D, B < F, F < A < E
Thus, the sequence becomes :
B < C < F < A < E < D or C < B < F < A < E < D.
In terms of weight, we have :
A < B, A < C, B < D, D < F.
So, A < B < D < F, A < C.
Thus, the sequence becomes :
A < C < B < D < F or A < B < C < D < F or A < B < D < C < F.
Data is inadequate as no clue regarding E's weight is given.
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Who is third from the top when they are arranged in descending order of height ?
Answer: A
In terms of height, we have :
B < F, C < F, C < D, E < D, F < E, A < E, F < A.
So, C < F < E < D, B < F, F < A < E
Thus, the sequence becomes :
B < C < F < A < E < D or C < B < F < A < E < D.
In terms of weight, we have :
A < B, A < C, B < D, D < F.
So, A < B < D < F, A < C.
Thus, the sequence becomes :
A < C < B < D < F or A < B < C < D < F or A < B < D < C < F.
The descending order of height is :
D > E > A > F > B > C or D > E > A > F > C > B.
Clearly, A is third from the top.
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Who among them is the tallest ?
Answer: C
In terms of height, we have :
B < F, C < F, C < D, E < D, F < E, A < E, F < A.
So, C < F < E < D, B < F, F < A < E
Thus, the sequence becomes :
B < C < F < A < E < D or C < B < F < A < E < D.
In terms of weight, we have :
A < B, A < C, B < D, D < F.
So, A < B < D < F, A < C.
Thus, the sequence becomes :
A < C < B < D < F or A < B < C < D < F or A < B < D < C < F.
Clearly, D is the tallest.
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Which of the following groups of friends is shorter than A ?
Answer: D
In terms of height, we have :
B < F, C < F, C < D, E < D, F < E, A < E, F < A.
So, C < F < E < D, B < F, F < A < E
Thus, the sequence becomes :
B < C < F < A < E < D or C < B < F < A < E < D.
In terms of weight, we have :
A < B, A < C, B < D, D < F.
So, A < B < D < F, A < C.
Thus, the sequence becomes :
A < C < B < D < F or A < B < C < D < F or A < B < D < C < F.
Clearly, F, B and C are shorter than A.
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Which of the following statements is true for F as regards height and weight ?
Answer: C
In terms of height, we have :
B < F, C < F, C < D, E < D, F < E, A < E, F < A.
So, C < F < E < D, B < F, F < A < E
Thus, the sequence becomes :
B < C < F < A < E < D or C < B < F < A < E < D.
In terms of weight, we have :
A < B, A < C, B < D, D < F.
So, A < B < D < F, A < C.
Thus, the sequence becomes :
A < C < B < D < F or A < B < C < D < F or A < B < D < C < F.
Clearly F is heavier than B and C but shorter than D
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(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 socres the highest and T gets the least, or alternatively S scores the highest and U or Q scores the least.
If S is ranked sixth and Q is ranked fifth, which of the following can be true ?
Answer: D
In terms of scores, we have :
V > P, P > Q i.e. V > P > Q.
If R scores the highest, we have R > ...... > T,
If S scores the highest, we have S > ...... > Q or S > ...... > U.
If S is ranked sixth and Q is ranked fifth, we have :
? > ? > ? > ? > Q > S > ?.
In the case, R will rank the highest and thus T will rank the least.
We have :
R > ? > ? > ? > Q > S > T.
Also. the roder V > P > Q will be maintained i.e. V and P will have second, third or fourth places. So, statements (a), (b), (c) and (e) cannot follow. Thus, (d) is the answer.
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If R is ranked second and Q is ranked fifth, which of the following must be true ?
Answer: B
In terms of scores, we have :
V > P, P > Q i.e. V > P > Q.
If R scores the highest, we have R > ...... > T,
If S scores the highest, we have S > ...... > Q or S > ...... > U.
If R is ranked second, S will rank first and Q and U lowest. But Q ranks fifth. So, U ranks lowest. Also the order V > P > Q will be followed.
So ,the arrangement will be S > R > V > P > Q > ? > U. Thus, the sixth place will be occupied by T.
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If R gets most, V should be ranked not lower than :
Answer: C
In terms of scores, we have :
V > P, P > Q i.e. V > P > Q.
If R scores the highest, we have R > ...... > T,
If S scores the highest, we have S > ...... > Q or S > ...... > U.
Again, if R ranks most, T ranks lowest and occupies seventh place. Since V always rank above P and Q, so in the maximum, P and Q will occupy fifth and sixth places.
Thus, V will not rank lower than fourth.
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