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? A. The number of red lights is equal to the number of blue lights B. The number of green lights is equal to the number of yellow lights C. The sum of red and blue lights is equal to the number of green and yellow lights D. The sum of the red and blue lights is equal to the sum of the green and yellow lights

GATE 2014 · General Aptitude · Logical Reasoning · medium

Answer: Statement C is NOT necessarily correct. The number of red-blue steps and green-yellow steps can differ, so the total count of red+blue lights need not equal the total count of green+yellow lights.

1. Verify Statement A: count(red) = count(blue): Since every red light pairs with exactly one blue light on the same step, count(red) = count(blue) always. Statement A is necessarily correct.
2. Verify Statement B: count(green) = count(yellow): Since every green light pairs with exactly one yellow light, count(green) = count(yellow) always. Statement B is necessarily correct.
3. Check Statement C: count(red) + count(blue) = count(green) + count(yellow): The statement requires 2r = 2g, i.e. r = g. But the problem puts no constraint on how many steps of each type exist. A ladder of 3 red-blue steps and 5 green-yellow steps violates this. Statement C is NOT necessarily correct.
4. Check Statement D: same as C: Statement D is equivalent to C and is also not necessarily correct. Depending on how the options are printed, one of C or D is the intended answer marked as NOT necessarily correct.