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02 Dec 2021, 05:29
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If \(x = 1998*1999*2000\), what is the remainder when \(x\) is divided by 7?
A. \(0\)
B. \(1\)
C. \(2\)
D. \(3\)
E. \(4\)
A. \(0\)
B. \(1\)
C. \(2\)
D. \(3\)
E. \(4\)
02 Dec 2021, 05:29
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Official Solution:
If \(x = 1998*1999*2000\), what is the remainder when \(x\) is divided by 7?
A. \(0\)
B. \(1\)
C. \(2\)
D. \(3\)
E. \(4\)
Express 1998, 1999 and 2000 as (a multiple of 7) + (something). The closest multiple of 7 to these numbers is 1995, so
\(x = (1995 + 3)*(1995 + 4)*(1995 + 5)\).
When we expand this expression, all terms there will have \(1995*\) in them (so all these terms will be divisible by 7), except the last term, which will be \(3*4*5=60\).
60 divided by 7 gives the remainder of 4.
Answer: E
If \(x = 1998*1999*2000\), what is the remainder when \(x\) is divided by 7?
A. \(0\)
B. \(1\)
C. \(2\)
D. \(3\)
E. \(4\)
Express 1998, 1999 and 2000 as (a multiple of 7) + (something). The closest multiple of 7 to these numbers is 1995, so
\(x = (1995 + 3)*(1995 + 4)*(1995 + 5)\).
When we expand this expression, all terms there will have \(1995*\) in them (so all these terms will be divisible by 7), except the last term, which will be \(3*4*5=60\).
60 divided by 7 gives the remainder of 4.
Answer: E
MayaLove
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27 May 2024, 22:13
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I multiplied each by 7 (got 3,4 & 5 as remainders) and then took the product of the remainders (60) and divided once again by 7 - got 4
