1.
The L.C.M of two prime numbers x and y (x>y) is 203, the value of 2y-x
Answer: Option 'B'
-15
2.
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
Answer: Option 'C'
Other number = (11 x 7700/275) = 308.
3.
Find the highest common factor of 36 and 84.
Answer: Option 'C'
36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.
4.
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
Answer: Option 'B'
Let the two numbers be 13a and 13b respectively.
Then, 13a x 13b = 2028
=>ab = 2028 / (13 x 13) = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4). Clearly, there are 2 such pairs.
5.
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
Answer: Option 'A'
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107 => ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Therefore, Greater number = 111.