Q14) Find the greatest number which will divide 2113 and 2793 leaving the remainder 5 in each case. 1) 54 2) 68 3) 76 4) 72 Required number is the H.C.F. of 2108 (2113 - 5) and 2788 (2793 - 5). Hence, option 2. Q15) For two positive integers a and b define the function h(a,b) as the HCF of a,b. Let A be a set of n positive integers, G(A), the HCF of elements of A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is 1) n + 1 2) n - 1 3) (n + 1)/2 4) n n - 1 Hence, option 2. Q16) 2 pieces of cakes of weights 253 gms and 368 gms are to be divided into equal parts. Each part must be as heavy as possible. If one such part is served to each guest, then what is the weight of each piece of cake such that minimum number of guests that could be served. 1) 16 2) 11 3) 23 4) 27 Weight of a piece of cake = H.C.F.(253, 368) = 23 Hence, option 3. Q17) The L.C.M. of two numbers is 315 and their ratio is 7:9. Then the numbers are: 1) 42, 54 2) 28, 36 3) 49, 63 4) 35, 45 Let the numbers be 7y, 9y. H.C.F. = y H.C.F. × L.C.M. = 7y × 9y 315y = 63y ^{2}y = 0, 5 (y = 0 is rejected so, required value of y = 5) Numbers are 35, 45 Hence, option 4. Q18) A call center observes that it gets a call at an interval of very 6 minutes from London, at every 15 minutes from Paris, at the interval of 18 minutes from New York and after every 25 minutes from Sydney. If at 7:00 a.m. it has received the calls simultaneously from all the four destinations, then at what time will it receive the calls from all the four places on the same day? 1) 7:30 AM 2) 10:00 PM 3) 10:00 AM 4) 2:30 PM Call center gets calls from all the four places simultaneously after LCM(6, 15, 18, 25) minutes = 450 minutes So the next call will be received simultaneously from the four places at 2:30 PM Hence, option 4. Q19) If a and b are positive integers, then what is the value of 1) a 2) b 3) 1 4) Value of is equal to 1. Hence, option 1. |