If r and s are integers and rs +r is odd which of the following is even?
r
s
r+s
rs-r
r^2+s
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integers
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GMATCRUSHER
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Mozartain
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Set up a table with three columns, and see which combinations of r and s result in an odd integer for rs+r :
r s rs+r
O O E (OxO+O = O+O = E)
O E O (OxE+O = E+O = O)
E O E (ExO+E = E+E = E)
We don't need to check r (E), s (E) combination, but if you want you can.
So rs+r would be odd only when r is odd and s is even. Plug this combination in the answer choices and see which one results in an even integer. Only the 2nd one (i.e. s) does.[/u]
r s rs+r
O O E (OxO+O = O+O = E)
O E O (OxE+O = E+O = O)
E O E (ExO+E = E+E = E)
We don't need to check r (E), s (E) combination, but if you want you can.
So rs+r would be odd only when r is odd and s is even. Plug this combination in the answer choices and see which one results in an even integer. Only the 2nd one (i.e. s) does.[/u]
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2010gmat
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imo b .. s
rs + r --> odd --> r(s+1) --> odd
say r = odd --> s+1 --> odd --> s - even
r(s+1) --> odd
say r = even --> s+ 1 --> odd --> not possible...
both r and s+1 have to be odd for the expression to be odd....
if s+ 1 is odd then we have s as even
rs + r --> odd --> r(s+1) --> odd
say r = odd --> s+1 --> odd --> s - even
r(s+1) --> odd
say r = even --> s+ 1 --> odd --> not possible...
both r and s+1 have to be odd for the expression to be odd....
if s+ 1 is odd then we have s as even
