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Too tough for Gmat.

by goyalsau » Wed Sep 01, 2010 7:58 pm
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 cyclic pattern of turning on and off. The first word remains lighted for seconds and then remains switched off for 2 seconds. The second word remains switched on for seconds and then remains switched off for 2 seconds. The third word remains switched on for 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
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by brijesh » Wed Sep 01, 2010 8:25 pm
I think u need to mention for how many seconds the words remain lighted...

suppose the first word remain lighted for A s

Second word emain lighted for B s

and the third word remain lighted for C s

the ans : LCM (A+2, B+2, C+2): i.e. the time when the entire display will again turn on simultaneously?
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by goyalsau » Wed Sep 01, 2010 10:00 pm
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.
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by sanju09 » Thu Sep 02, 2010 2:47 am
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



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by neerajkumar1_1 » Thu Sep 02, 2010 6:15 am
sanju great solving...

one thing i need ur help on...
i understood why u took the LCM...

but the thought would have probably not occurred to me straight away...

what are u looking in this problem that u got to the soln quickly...
as in let me know if i can fit this problem in some type where i can realize that such would be the soln...

thanks...
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by sanju09 » Fri Sep 03, 2010 2:43 am
neerajkumar1_1 wrote:sanju great solving...

one thing i need ur help on...
i understood why u took the LCM...

but the thought would have probably not occurred to me straight away...

what are u looking in this problem that u got to the soln quickly...
as in let me know if i can fit this problem in some type where i can realize that such would be the soln...

thanks...
Whenever a series of events is such that each event is periodic, then from the moment when all the events were made to happen simultaneously, LCM of the periods is the smallest interval, after which all the events will again happen simultaneously.
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
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