Positive integer \(A > 10,000\) and \(B > 20,000.\) When \(A\) is divided by \(237,\) the remainder is \(85.\) When \(B\) is divided by \(237,\) the remainder is \(41.\) What is the remainder when \(2A + 3B\) is divided by \(237?\)
a) 0
b) 56
c) 123
d) 170
e) 211
Answer: B
Source: Magoosh
Positive integer \(A > 10,000\) and \(B > 20,000.\) When \(A\) is divided by \(237,\) the remainder is \(85.\) When
This topic has expert replies
It doesn’t matter what the values of \(A\) and \(B\) are. What matters is that we can add the remainders. Then,Vincen wrote: ↑Sat Jan 23, 2021 6:50 amPositive integer \(A > 10,000\) and \(B > 20,000.\) When \(A\) is divided by \(237,\) the remainder is \(85.\) When \(B\) is divided by \(237,\) the remainder is \(41.\) What is the remainder when \(2A + 3B\) is divided by \(237?\)
a) 0
b) 56
c) 123
d) 170
e) 211
Answer: B
Source: Magoosh
\(\cdot\) If \(A\) leaves a remainder \(85,\) then \(2A\) will leave \(2\cdot 85=170.\)
\(\cdot\) If \(B\) leaves a remainder \(41,\) then \(3B\) will leave \(3\cdot 41=123.\)
So, \(2A+3B\) will leave \(170+123=293,\) but \(293=237+56.\) Therefore, the final remainder is \(56.\)
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When A is divided by 237, the remainder is 85
Watch this video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
A -> Dividend
237 -> Divisor
a -> Quotient (Assume)
85 -> Remainders
=> A = 237*a + 85 = 237a + 85
When B is divided by 237, the remainder is 41
Let quotient be b
=> B = 237*b + 41 = 237b + 41
What is the remainder when (2A + 3B) is divided by 237
2A + 3B = 2*(237a + 85) + 3*(237b + 41) = 237*2a + 170 + 237*3b + 123 = 237*(2a + 3b) + 237 + 56 = 237*(2a + 3b + 1) + 56
=> 2A + 3B when divided by 237 gives 2a + 3b + 1 as quotient and 56 as remainder.
So, Answer will be B
Hope it helps!
Watch this video to learn the Basics of Remainders
Watch this video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
A -> Dividend
237 -> Divisor
a -> Quotient (Assume)
85 -> Remainders
=> A = 237*a + 85 = 237a + 85
When B is divided by 237, the remainder is 41
Let quotient be b
=> B = 237*b + 41 = 237b + 41
What is the remainder when (2A + 3B) is divided by 237
2A + 3B = 2*(237a + 85) + 3*(237b + 41) = 237*2a + 170 + 237*3b + 123 = 237*(2a + 3b) + 237 + 56 = 237*(2a + 3b + 1) + 56
=> 2A + 3B when divided by 237 gives 2a + 3b + 1 as quotient and 56 as remainder.
So, Answer will be B
Hope it helps!
Watch this video to learn the Basics of Remainders
Ankit
How to Solve:
Inequality Problems || Statistics || Functions & Custom Characters || Remainders
How to Solve:
Inequality Problems || Statistics || Functions & Custom Characters || Remainders