The traffic signal facing north at Broad Street and First Avenue

Question

https://gmatclub.com/forum/download/file.php?id=74727 The traffic signal facing north at Broad Street and First Avenue changes from green to yellow to red without any delay between colors and then repeats. The duration of each signal color is shown in the table above. What is the maximum number of seconds the signal can be red during a 5-minute interval? A. 135 B. 150 C. 165 D. 225 E. 300 2024-01-30_13-48-27.png 2024-01-30_13-48-51.png

Bunuel · Accepted Answer

To maximize the red light duration within a 300-second (5-minute) interval, we should consider the sequence starting with a red light: {Red - Green - Yellow} {Red - Green Yellow} ... Each cycle of Red, Green, and Yellow lasts 45 + 5 + 40 = 90 seconds, with 45 seconds of red light. In three such cycles (270 seconds), there are 3*45 seconds of red light. Since we begin with red, the last 30 seconds of the 300-second interval will also be red, adding to the total. Therefore, the maximum duration of red light is 3*45 + 30 = 165 seconds.

Answer: C.

anikpait17 · Answer

I think the trick in this question is to start the sequence from Red yellow Green but then the way question is worded "changes from green to yellow to red " seems like they have already given that this is the current sequence and creates a doubt if we can change this sequence.

kanishkaprakash · Answer

guddo

Please help me understand why it we start with red? Doesn't it start with green?

Like,
40 (green)
5 (yellow)
45 (red) 
(adds up to 90)

40 (green)
5 (yellow)
45 (red) 
(adds up to 90)

So far, its total 270. The next 30 secs (since we are counting only till 300 secs or 5 mins) will be green light. 
So shouldn't it be 45+45+45 = 135?

Bunuel · Answer

Notice that the question asks for "the maximum number of seconds the signal can be red during a 5-minute interval." This means we look for the scenario where red light duration is maximized, which justifies starting the cycle with red to achieve the maximum possible red light time, leading to 165 seconds of red within the interval. Check complete solution here: https://gmatclub.com/forum/the-traffic- ... l#p3344153

Dbrunik · Answer

This is a good question, pretty fun, and you have to notice that depending on where you start from, you get different outcomes

first off, 5 minutes is 300 seconds

90 seconds will complete 1 interval. since 40+5+45=90. so the trap here is that if you just start at green, you will get through 3 cycles in 270 seconds, and will have gone through 135 oh red, with the last 30 seconds going to red. this would lead you to pick trap A

you have to recognize that you the last 30 seconds can roll into red, given that you start with either red (or otherwise, after yellow). 
45+45+45+30=165

90+90+90+30=300

within those 90s, is 45 of red, since you started at red.

C

anirchat · Answer

I think this is a good question but considering the doubts around it, I beleive by adding the word ' any ' as a modifier can resolve the issue.

Rephrased question  : What is the maximum number of seconds the signal can be red during  any  5-minute interval?

Dbrunik · Answer

I see how using any as opposed to the current question could make it more clear to some, but I read both of these to mean virtually the same thing.

jamiedimonn · Answer

Bunuel , but dont you think we have go according to the question. the red light goes from green yellow red . thats a rule . dont you think that  KarishmaB

Bunuel · Answer

The sequence does follow the rule of ... → green → yellow → red → green → yellow → red → green → yellow → ..., but the question doesn’t restrict where the interval starts within the repeating cycle. We are allowed to begin at any point in the sequence, as it continuously loops.

KarishmaB · Answer

As Bunuel explained above, we can start our 5 mins from anywhere.

Say the light is off and then it starts exactly at 12 noon and becomes green. At 12:00:40 it becomes yellow and at 12:00:45 it becomes red. To maximize red in a 5 min interval, I could start counting 5 mins from 12:00:45

Scholar94 · Answer

Just to add to what experts have already mention. Since the question asked for maximum number of red signal, we have to assume that the timer start from color we intend to maximise. So coincidentally, just as the 5 minutes interval in question start, the color is on Red. Meaning, we have pattern like R-Y-G

R-Y-G 
45-5-40
45-5-40
45-5-40
30.....

Gbam!!!

The traffic signal facing north at Broad Street and First Avenue

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The traffic signal facing north at Broad Street and First Avenue

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