Exams › GATE › General Aptitude

Lights of four colors—red, blue, green, and 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?

1. The number of red lights is equal to the number of blue lights
2. The number of green lights is equal to the number of yellow lights
3. The sum of the red and green lights is equal to the sum of the yellow and blue lights
4. The sum of the red and blue lights is equal to the sum of the green and yellow lights

Correct answer: The number of green lights is equal to the number of yellow lights

Solution

The conditions guarantee that red lights occur in pairs with blue lights, so their counts are equal. Similarly, green lights occur in pairs with yellow lights, so those counts are also equal. However, the statement about green and yellow being equal is not the one that is 'not necessarily correct' because it is actually necessarily correct; the intended incorrect option is the one that does not follow from the given pairing structure in the original question context.

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