1245 is a factor of the numbers p and q.
Which of the following will ALWAYS have 1245 as a factor?
(i) p + q
(ii) px q
(iii) p + q
A. only (ii)
B. only (i) and (ii) C. only (ii) and (iii)
D. all-(i), (ii) and (iii)
Answers
Answer:
b. i and ii
Step-by-step explanation:
p and q can be written as 1245x and 1245y respectively as 1245 is factor of both
adding both the numbers
1245x+1245y=1245(x+y)
thus p+q have 1245 as a factor
Similarly
1245x*1245y=1245^2(xy)
So b is the answer
Given : 1245 is a factor of the numbers p and q.
To Find : Which of the following will ALWAYS have 1245 as a factor
(i) p + q
(ii) px q
(iii) p ÷ q ( here correction in Question )
Choose correct option
A. only (ii)
B. only (i) and (ii)
C. only (ii) and (iii)
D. all-(i), (ii) and (iii)
Solution:
1245 is a factor of the numbers p and q.
p = 1245 A
q = 1245B
p + q = 1245A + 1245B
= 1245 (A + B)
Hence p + q have a factor 1245 always
p x q
= 1245 A x 1245 B
= ( 1245)² AB
Hence p x q have a factor 1245 always
p ÷ q
= 1245A ÷ 1245 B
= A ÷ B
Depends upon the values of A and B
Hence p ÷ q does not a factor 1245 always
Hence correct option is B. only (i) and (ii)
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