[問題]考古題 DS Form17 Sec1-Q23

[Lian]

If x, y, and d are integers and d is odd, are both x and y divisible by d?

(1) x+y is divisible by d
(2) x-y is divisible by d

Ans:(C)

這題我帶入實際數字得知答案, 但這種方式難免會因考慮不周選錯答案, 想請問這題若運用通式應如何解題, 謝謝

[DARY]

If x, y, and d are integers and d is odd, are both x and y divisible by d?

(1) x+y is divisible by d
(2) x-y is divisible by d

Ans:(C)

這題我帶入實際數字得知答案, 但這種方式難免會因考慮不周選錯答案, 想請問這題若運用通式應如何解題, 謝謝

(x+y)+(x-y)=2x is divisible by d
(x+y)-(x-y)=2y is divisible by d
而且d is odd=>不含2的因數

所以x,y are divisible by d

[Lian]

Thank you so much


Best regards,
Lian