If x is an even integer, which of the following must be an odd integer?
a)3x/2
b)3x/2 +1
c)3x^2
d)(3x^2)/2
e)(3x^2)/2 +1
a)3x/2
b)3x/2 +1
c)3x^2
d)(3x^2)/2
e)(3x^2)/2 +1
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Source: Beat The GMAT — Problem Solving |
I think the answer is E.
If you just plug in an even integer you can easily eliminate all the options but B and E.
Option B -- 3x/2 +1 ,
Since we are dividing by an even integer and then adding 1 to it. This option would lead to an even integer. Try pluggin in 2 in place of x you'll know what exactly I mean.
Option E -- 3x^2/2 +1
Here even when we are diving by 2 we are still left with even integer which is multiplied by an odd integer i.e. 3, therefore result will always be even. Then odd integer 1 is added to the result.
Therefore for option E no matter what the value (even) of x is, the result will always be an odd integer.
Let me know if you still have any doubts.
If you just plug in an even integer you can easily eliminate all the options but B and E.
Option B -- 3x/2 +1 ,
Since we are dividing by an even integer and then adding 1 to it. This option would lead to an even integer. Try pluggin in 2 in place of x you'll know what exactly I mean.
Option E -- 3x^2/2 +1
Here even when we are diving by 2 we are still left with even integer which is multiplied by an odd integer i.e. 3, therefore result will always be even. Then odd integer 1 is added to the result.
Therefore for option E no matter what the value (even) of x is, the result will always be an odd integer.
Let me know if you still have any doubts.
The way I found the answer is by plugging in numbers. I don't remember which book I found it in, but the book says that when plugging in numbers, if 2 or more answers give the same result try differnt numbers until only 1 choice is correct. EX:
if x=4
b)7
e)73
if x=6
b)10
e)163 => therefore e is always odd
if x=4
b)7
e)73
if x=6
b)10
e)163 => therefore e is always odd
