1. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
A. 4
B. 5
C. 6
D. 8
B. 5
C. 6
D. 8
Answer: Option A
Explanation:
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
2. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
A. 9000
B. 9400
C. 9600
D. 9800
B. 9400
C. 9600
D. 9800
Answer: Option C
Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
3. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
A. 101
B. 107
C. 111
D. 185
B. 107
C. 111
D. 185
Answer: Option C
Explanation:
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).
Greater number = 111.
4. Find the HCF of 24 X 52 X 73 X 112, 76 X 54 X 27 X 13, 56 X 22 X 74 X 17.
For this question we need to take common factors first, and then lowest powers.
Here common factors are 2, 5, 7.
Then write their lowest powers.
Answer = 22 x 52 x 73.
5. Find the LCM of 24 X 52 X 73 X 112, 76 X 54 X 27 X 13, 56 X 22 X 74 X 17.
For this question we need to write all the given numbers , and then write their Highest powers.
All the numbers are 2, 5, 7, 11, 13, 17.
Then write their Highest powers.
Answer = 27 x 56 x 76 x 112 x 13 x 17.
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