Question #228290

The remainder of n7 is 4. The remainder of m9 is 7. Which of the following is a potential value for n×m?

(A) 24

(B) 44

(C)22

(D) 126

(E) 55


1
Expert's answer
2021-08-24T08:24:04-0400

Let n=7x+4,x=0,1,2,...n=7x+4, x=0,1,2,... and let m=9y+7,y=0,1,2,...m=9y+7,y=0,1,2,... Then


n×m=(7x+4)(9y+7)=63xy+49x+36y+28n\times m=(7x+4)(9y+7)=63xy+49x+36y+28

y=0,y=0, if n×mn\times m is divided by 77 the remainder is 0.0.

126÷7=18126\div7=18

m=9(0)+7=7,n=7(2)+4=18m=9(0)+7=7, n=7(2)+4=18

y=1,y=1, if n×mn\times m is divided by 77 the remainder is 1.1.

22÷7=3,remainder 122\div7=3, remainder \ 1

m=9(1)+7=16m=9(1)+7=16

But 2222 is not divisible by 16.16.


y=2,y=2, if n×mn\times m is divided by 77 the remainder is 2.2.

44÷7=6,remainder 244\div7=6, remainder \ 2

m=9(2)+7=25m=9(2)+7=25

But 4444 is not divisible by 25.25.



y=3,y=3, if n×mn\times m is divided by 77 the remainder is 3.3.

24÷7=2,remainder 324\div7=2, remainder \ 3

m=9(3)+7=34m=9(3)+7=34

But 2424 is not divisible by 34.34.


y=4,y=4, if n×mn\times m is divided by 77 the remainder is 4.4.

44÷7=6,remainder 244\div7=6, remainder \ 2

m=9(2)+7=25m=9(2)+7=25

But 4444 is not divisible by 25.25.



55÷7=7,remainder 655\div7=7, remainder \ 6

y=6,y=6, if n×mn\times m is divided by 77 the remainder is 6.6.

m=9(6)+7=61m=9(6)+7=61

But 5555 is not divisible by 61.61.


(D) 126

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