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11 Nov 2021, 10:21
Kudos
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A
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Difficulty:
75%
(hard)
Question Stats:
41% (02:09) correct
59%
(02:27)
wrong
based on 68
sessions
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What is the remainder when the positive integer x is divided by 7?
1) The remainder is 1 when 3x is divided by 7.
2) The remainder is 1 when 7x is divided by 3.
1) The remainder is 1 when 3x is divided by 7.
2) The remainder is 1 when 7x is divided by 3.
12 Nov 2021, 00:36
Kudos
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sjuniv32
1) The remainder is 1 when 3x is divided by 7.
Equation: \(3x=7y+1\), where y is quotient and 1 is the remainder.
Check for value of x and y as integers.
y=2: \(3x=7*2+1=15\) or \(x=5\).........Remainder when 5 is divided by 7 is 5.
y=5: \(3x=7*5+1=36\) or \(x=12\).........Remainder when 12 is divided by 7 is 5.
y=8: \(3x=7*8+1=57\) or \(x=19\).........Remainder when 19 is divided by 7 is 5.
So remainder is 5 always.
Sufficient
2) The remainder is 1 when 7x is divided by 3.
Equation: \(7x=3y+1\), where y is quotient and 1 is the remainder.
Check for value of x and y as integers.
y=2: \(7x=3*2+1=7\) or \(x=1\).........Remainder when 1 is divided by 7 is 1.
y=9: \(7x=3*9+1=28\) or \(x=4\).........Remainder when 4 is divided by 7 is 4.
Different remainders.
Insufficient
A
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