{x | x is a positive integer <10 and 3x is even}
Answers
If x is a positive number, is x an even integer?
Notice that we are not told that x is an integer.
(1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.
(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.
(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x-3x=even-even --> 2x=even --> x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer.
If x is a positive number, is x an even integer?
Notice that we are not told that x is an integer.
(1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.
(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.
(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x-3x=even-even --> 2x=even --> x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.
Answer C