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S and T are positive integers. If S divided by 5 leaves a remainder of
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06 Feb 2022, 06:45
06 Feb 2022, 06:45
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S and T are positive integers. If S divided by 5 leaves a remainder of 3, and T divided by 5 leaves a remainder of 4, what is the remainder when S • T is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 6
(A) 0
(B) 1
(C) 2
(D) 5
(E) 6
Re: S and T are positive integers. If S divided by 5 leaves a remainder of
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11 Feb 2022, 16:09
11 Feb 2022, 16:09
1
I am probably wrong about how I went solving this:
S = (5 x A) + 3 --> S = 5A + 3
T = (5 x B) + 4 --> T = 5B + 4
First multiply both S and T:
(5A + 3) (5B + 4) = 5A5B + 20A + 15B + 12
Then divide by 5:
(5A5B + 20A + 15B + 12)/5 = AB + 4A + 3B + (12/5)
The only term that was not divisible by 5 was 12. So I found what the remainder of 12/5.
12 is 10 (divisible by 5) plus 2 . So the remainder is 2.
S = (5 x A) + 3 --> S = 5A + 3
T = (5 x B) + 4 --> T = 5B + 4
First multiply both S and T:
(5A + 3) (5B + 4) = 5A5B + 20A + 15B + 12
Then divide by 5:
(5A5B + 20A + 15B + 12)/5 = AB + 4A + 3B + (12/5)
The only term that was not divisible by 5 was 12. So I found what the remainder of 12/5.
12 is 10 (divisible by 5) plus 2 . So the remainder is 2.
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S and T are positive integers. If S divided by 5 leaves a remainder of
[#permalink]
08 Sep 2022, 10:32
08 Sep 2022, 10:32
1
S divided by 5 leaves a remainder of 3
Theory: Dividend = Divisor*Quotient + Remainder
S -> Dividend
5 -> Divisor
a -> Quotient (Assume)
3 -> Remainders
=> S = 5*a + 3 = 5a + 3
T divided by 5 leaves a remainder of 4
Let quotient be b
=> T = 5b + 4
what is the remainder when S • T is divided by 5
S • T = (5a + 3)*(5b + 4) = 25ab + 15b + 20a + 12 = 25ab + 15b + 20a + 10 + 2
= 5*(5ab + 3b + 4a + 2) + 2
=> S • T when divided by 5 gives 5ab + 3b + 4a + 2 as quotient and 2 as remainder
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
S -> Dividend
5 -> Divisor
a -> Quotient (Assume)
3 -> Remainders
=> S = 5*a + 3 = 5a + 3
T divided by 5 leaves a remainder of 4
Let quotient be b
=> T = 5b + 4
what is the remainder when S • T is divided by 5
S • T = (5a + 3)*(5b + 4) = 25ab + 15b + 20a + 12 = 25ab + 15b + 20a + 10 + 2
= 5*(5ab + 3b + 4a + 2) + 2
=> S • T when divided by 5 gives 5ab + 3b + 4a + 2 as quotient and 2 as remainder
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Remainders
