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flash lights

by hemant_rajput » Wed Jan 30, 2013 11:23 am
Q17 . At a bookstore, "MODERN BOOK STORE" is flashed using neon lights. The words are individually flashed at long intervals of 5/2, 17/4 and 41/8 sec resp. , and each word is put off after a second. The least time after which the full name of the bookstore can be read again is?
a. 49.5
b. 73.5
c. 1744.5
d. 855
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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by vkb001 » Wed Jan 30, 2013 5:56 pm
Initially, every word is flashed for a second. From then, the interval for which each word is put off differs. So, the time length till the next flash for each of the words is 1+5/2, 1+17/4, 1+41/8 = 3.5, 5.25, 6.125.

We need an integer number of each of these durations so that the cumulative duration of each of these words is equal. To put it simply,

m(3.5) = n(5.25) = k(6.125) where m,n,k are all integers.

We need to find the least common multiple of the three numbers.

LCM(3.5,5.25,6.125) = 73.5.

Another way to figure this out in the exam is to check with each number.

Step 1: Try 49.5 (with the lowest)

49.5/3.5 is not an integer. So, reject this option.

Step 2: Try 73.5

73.5/3.5 = 21 (integer!)
73.5/5.25 = 14 (integer!)
73.5/6.125 = 12 (integer!)

BINGO! Answer's (b)
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