Choose the appropriate alternative :

Q78 – 79 : Amar, Akbar, Anthony are three friends. Only three colors are available for their shirts, viz. Red, Green and Blue. Amar did not wear red shirt. Akbar did not wear green shirt. Anthony did not wear blue shirt.

78. If Akbar and Anthony wear the same colour, then which of the following is not true?

(a) Amar wears blue and Akbar wears green.

(b) Amar wears green and Akbar wears red.

(c) Amar wears blue and Akbar does not wear blue.

(d) Anthony wears red.

79. If two of them wear the same colour then how many of the following must be false.

I.   Amar wears blue and Akbar does not wear green.

II.  Amar does not wear blue and Akbar wears blue.

III. Amar does not wear blue and Akbar does not wear blue.

IV. Amar wears green. Akbar does not wear red. Anthony does not wear green.

(a) None

(b) One

(c) Two

(d) Three

 78 (a) 79 (b)

78. Since, Amar does not wear red shirt, it has to be worn by either Akbar or Anthony. So both of them either wear red shirt or one among green or blue shirt (depending on what Amar is wearing). Now since Akbar does not wear green and Anthony does not wear blue shirt, it is confirmed that both of them wear red shirts. So Amar wears either blue or green shirt. Thus we can see that statement (a) is not true.

79. If two of them wear the same colour, the following 6 combinations will exist : Since Amar does not wear Red, he can either wear blue or green. In either case, the remaining two will have to wear red, Akbar does not wear green and Anthony does not wear blue. This gives the combination 1 & 2 below. Similarly other combinations can be worked out.

 Amar Akbar Anthony 1 Green Red Red 2 Blue Red Red 3 Green Red Green 4 Green Blue Green 5 Blue Blue Green 6 Blue Blue Red

Using this we can evaluate the statements. (a) is true as we can see that in all the cases, if Amar wears blue, Akbar does not wear green. (b) need not be false always, as in combination 4, we can see that Amar does not wear blue but Akbar wears blue. (c) is also not necessarily false as in combinations 1 & 3, both Amar & Akbar do not wear blue. Statement (d) is necessarily false as, if Amar wears green and Akbar does not wear red then combination 4 is the only combination possible and hence Anthony should wear green So only one of the four statements must always be false.

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