swerve wrote:A number when divided by a certain divisor left remainder 241, . Find the divisor?
A. 370
B. 365
C. 380
D. 456
E. 460
A number when divided by a certain divisor left remainder 241.
In other words, the number x is a multiple of divisor d plus 241:
x = ad + 241.
When twice the number was divided by the same divisor, the remainder was 112.
In other words, twice number x is a multiple of divisor d plus 112:
2x =
bd + 112.
Doubling the first equation, we get:
2x =
2ad + 482.
The blue expressions above are both equal to 2x and thus are equal:
bd + 112 = 2ad + 482
bd - 2ad = 370
d(b - 2a) = 370.
The resulting equation implies that d is a factor of 370.
Of the five answer choices, only
A is a factor of 370.
The correct answer is
A.
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