Data Sufficiency

If the positive integer x is rounded to the nearest ten, will the result be greater than x ?

(1) If x is divided by 10, the remainder is even.

(2) If x is divided by 5, the remainder is odd.

OAC

rsarashi wrote:If the positive integer x is rounded to the nearest ten, will the result be greater than x ?

(1) If x is divided by 10, the remainder is even.

(2) If x is divided by 5, the remainder is odd.

OAC

1) This is simply telling us that x is EVEN. Pick some numbers.
x = 12. Rounded to the nearest tens = 10. NO, the result is not greater than x.
x = 18. Rounded to the nearest tens = 20. YES, the result is greater than x.

2) x = 18. (18/5 yields a remainder of 3.) Rounded to the nearest tens = 20. YES, the result is greater than x.
x = 13. (13/5 yields a remainder of 3.) Rounded to the nearest tens = 10. NO, the result is not greater than x.

Combined. Statement 1 tells us that x must be EVEN. For an EVEN number to give an ODD remainder when divided by 5, the units digit must be 6 or greater. (You can see this by testing numbers. If x = 12, 12/5 will give an EVEN remainder - this violates statement 2. If x = 14, 14/5 will give an EVEN remainder, again violating statement 2. But if x = 16, 16/5 will give an ODD remainder. If x = 18. 18/5 will give an ODD remainder.) If the units digit is 6 or greater, when we round to the nearest tens, we will always be rounding up, meaning that the answer to the question will always be YES, once we round to the nearest tens, the result will be greater than x. Together the statements are sufficient. The answer is C

If the positive integer x is rounded to the nearest ten, will the result be greater than x ?

(1) If x is divided by 10, the remainder is even.

(2) If x is divided by 5, the remainder is odd.

x rounded to the nearest ten will be greater than x if the units digit of x is 5 or greater.
x=5 rounded to the nearest ten --> 10, which is greater than x=5.
x=16 rounded to the nearest ten --> 20, which is greater than x=16.
x=157 rounded to the nearest ten --> 160, which is greater than x=157.

If the units digit of x is less than 5, then x rounded to the nearest ten will be less than or equal to x.
x=10 rounded to the nearest ten --> 10, which is equal to x=10.
x=24 rounded to the nearest ten --> 20, which is less than x=24.
x=101 rounded to the nearest ten --> 100, which is less than x=101.

Question stem, rephrased:
Is the units digit of x between 5 and 9, inclusive?

Statement 1: If x is divided by 10, the remainder is even.
It's possible that x=18, since 18/10 = 1 R8.
In this case, the units digit of x is between 5 and 9, inclusive.
It's possible that x=12, since 12/10 = 1 R2.
In this case, the units digit of x is NOT between 5 and 9, inclusive.
INSUFFICIENT.

Statement 2: If x is divided by 5, the remainder is odd.
It's possible that x=18, since 18/5 = 3 R3.
In this case, the units digit of x is between 5 and 9, inclusive.
It's possible that x=13, since 13/5 = 2 R3.
In this case, the units digit of x is NOT between 5 and 9, inclusive.
INSUFFICIENT.

Statements combined:
Statement 1 requires that the units digit of x be EVEN.
Between 10 and 20, inclusive, the following integers have an even units digit:
10, 12, 14, 16, 18.
Of these options, only the options in blue yield an odd remainder when divided by 5.
Implication:
To satisfy both statements, x must have a units digit of 6 or 8.
Thus, the units digit of x must be between 5 and 9, inclusive.
SUFFICIENT.

The correct answer is C.