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Since 36 is the LCM of 4 and 9, the beepers will beep together every 36 seconds. One hour = 60 minute = 3600 seconds, and so the simultaneous beeping will occur 100 times. (100).

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Choose a appropriate number. The LCD of  1/4 and 2/5 is 20, so assume that there were 20 applicants. Then1/4(20) = 5 failed to meet the minimum standards. Of the remaining 15 applicants,2/5 or 6, were accepted, so 6 of every 20 applicants were accepted. Set up a proportion: 6/20=1200/x⇒x = 4000

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Solution
Since you want the least number, start with the smallest answer, E. If Jessica had 200 books, Karen would have 40; but Karen has more than 40, so 200 is too small. Neither 205 (D) nor 210 (C), is a multiple of 4, so John wouldn’t have a whole number of books. Finally 220 works. (So does 240, but shouldn’t even test it since you want the smallest value.) Since Karen has at least 41 books, Jessica has at least 205. But Jessica’s total must be multiple of 4 and 5, hence of 20. The smallest multiple of 20 greater than 205 is 220.
(B)

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Add the two equation to get 10a + 10b + 10 ⇒ a + b = 1⇒(a + b)2 = 1/2= 0.5. (B)

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