a2zinterviews

16.	The product of two numbers is 4107. If the H.C.F of those numbers is 37, then the greater number is
	A.  101
	B.  107
	C.  109
	D.  111

Solution

Let the numbers be 37a and 37 b. Then, 37a ×37b = 4107 ‹=› ab = 3. Now, co-primes with product 3 are (1, 3). So, the required numbers are (37 ×1, 37 ×3) i.e , (1 , 111) Therefore Greater number = 111.

17.	The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is
	A.  15 cm
	B.  25 cm
	C.  35 cm
	D.  42 cm

Solution

Required length = H.C.F of 700 cm, 385 cm and 1295 cm ‹=› 35 cm.

18.	Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
	A.  4
	B.  7
	C.  9
	D.  13

Solution

Required number = H.C.F of (91 - 43), (183 - 91) and (183 - 43) = H.C.F of 48, 92 and 140 = 4.

19.	Let N be the greatest numbers that will divide 43, 91 and 183 so as to leave the same remainder in each case.
	A.  4
	B.  7
	C.  9
	D.  13

Solution

Required number = H.C.F of (91 - 43), (183 - 91) and (183 - 43) = H.C.F of 48, 92 and 140 ‹=› 4.

20.	Product of two co-prime numbers is 117. Their L.C.M should be
	A.  1
	B.  117
	C.  equal to their H.C.F
	D.  cannot be calculated

Solution

H.C.F of co-prime numbers is 1. So, L.C.M = 117/1 ‹=› 117.