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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

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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

by BTGmoderatorDC » Mon Jun 07, 2021 4:44 pm

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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


OA B

Source: Magoosh
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Re: 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,

by swerve » Tue Jun 08, 2021 7:13 am
BTGmoderatorDC wrote: ↑
Mon Jun 07, 2021 4:44 pm
 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


OA B

Source: Magoosh
It doesn’t matter what the values of \(A\) and \(B\) are. What matters is that we can add the remainders. Then,

If \(A\) leaves a remainder \(85, 2A\) will leave \(2\cdot 85=170.\)
If \(B\) leaves a remainder \(41, 3B\) will leave \(3\cdot 41=123.\)

Therefore, \(2A+3B\) will leave \(170+123=293,\) but \(293=237+56,\) so the final remainder is \(56.\)
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