GATE EC 2014 Set 2 — Question 7
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Question
Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct?
Correct answer
(D) The sum of the red and blue lights is equal to the sum of the green and yellow lights
Solution
Based on the rules provided:
(A) is always correct.
(B) is always correct.
(C) . Since and , then is always true.
(D) . This simplifies to , or . This is only true if the number of steps with red-blue pairs equals the number of steps with green-yellow pairs. This is not necessarily true as the problem does not specify the distribution of steps.
1.If a step has a red light, the other must be blue. This implies red and blue lights always occur in pairs . Thus, the total number of red lights equals the total number of blue lights ().
2.If a step has a green light, the other must be yellow. This implies green and yellow lights always occur in pairs . Thus, the total number of green lights equals the total number of yellow lights ().
Evaluating the options:(A) is always correct.
(B) is always correct.
(C) . Since and , then is always true.
(D) . This simplifies to , or . This is only true if the number of steps with red-blue pairs equals the number of steps with green-yellow pairs. This is not necessarily true as the problem does not specify the distribution of steps.
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