goyalsau wrote:I am really sorry, its my fault i copied it but didn't know the figure was not copied on the first go. I am sorry for the mistake but question is still challenging.
The name of 'Modern Food Stores' is displayed on a board at a junction using neon lights. When the board is switched on, the lights in each word follow a pattern of turning on and off. The first word remains lighted for 7/4 seconds and then remains switched off for 2 seconds. The second word remains switched on for 11/3 seconds and then remains switched off for 2 seconds. The third word remains switched on for 15/2 seconds and then remains switched off for 2 seconds. If the board is switched on, what is the smallest interval, after which the entire display will again turn on simultaneously?
(1) 61.5 seconds
(2) 97.5 seconds
(3) 807.5 seconds
(4) 4845 seconds
(5) None of these.
Good question
After the board is switched on, "Modern" would next light after (7/4 + 2) = 15/4 seconds, "Food" would next light after (11/3 + 2) = 17/3 seconds, and "Stores" would next light after (15/2 + 2) = 19/2 seconds.
The smallest interval (in seconds), after which the entire display will again turn on simultaneously, is the LCM of fractions 15/4, 17/3, and 19/2
= (LCM of 15, 17, and 19)/ (HCF of 4, 3, and 2)
= (15 × 17 × 19)/ (1)
= [spoiler]
4845 seconds
(4)
...and it's not too tough for GMAT if the choices are named A, B, C, D, and E doesn't read "none of these"[/spoiler]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
