If n denotes a decimal, then is n > 0.9?

[BTGmoderatorLU]

If n denotes a decimal, then is n > 0.9?

(1) When n is rounded to the nearest integer, the result is 1.

(2) When n is rounded to the nearest tenth, the result is 0.9.

The OA is E.

Can any expert explain this DS question please? I don't understand it.

[GMATGuruNY]

If n denotes a decimal, then is n > 0.9?

(1) When n is rounded to the nearest integer, the result is 1.

(2) When n is rounded to the nearest tenth, the result is 0.9.

Moving left to right on the number line:
We ROUND UP when we reach HALFWAY between two values.
Otherwise, we ROUND DOWN.

Statement 1:
0-----0.5-----1-----1.5-----2
Any value in the green range is rounded to 1.
Thus:
0.5 ≤ n < 1.5.
If n=0.5, then n < 0.9, with the result that the answer to the question stem is NO.
If n=1, then n > 0.9, with the result that the answer to the question stem is YES.
INSUFFICIENT.

Statement 2:
0.8-----0.85-----0.9-----0.95-----1
Any value in the blue range is rounded to 0.9.
Thus:
0.85 ≤ n < 0.95.
If n= 0.85, then n < 0.9, with the result that the answer to the question stem is NO.
If n=0.949, then n > 0.9, with the result that the answer to the question stem is YES.
INSUFFICIENT.

Statements combined:
n=0.85 satisfies both statements, since it is included in both the blue range and the green range.
In this case, the answer to the question stem is NO.
n=0.949 satisfies both statements, since it is included in both the blue range and the green range.
In this case, the answer to the question stem is YES.
INSUFFICIENT.

The correct answer is E.

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Hi LUANDATO,

We're told that N denotes a decimal. We're asked if N > 0.9 This is a YES/NO question. To answer this question, we need to use 'rounding' rules.

When a digit is 5-9, we round up. For example, 1.7 rounded to the nearest integer would be 2.
When a digit is 0-4, we round down. For example, 1.2 rounded to the nearest integer would be 1.

(1) When N is rounded to the nearest INTEGER, the result is 1.

With this Fact, we have a range of possible values for N:

0.5 <= N < 1.5
IF....
N = .85 then the answer to the question is NO
N = .91 then the answer to the question is YES
Fact 1 is INSUFFICIENT

2) When nN is rounded to the nearest TENTH, the result is 0.9

With this Fact, we have a range of possible values for N:

0.85 <= N < 0.95
IF....
N = .85 then the answer to the question is NO
N = .91 then the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we already have 2 values that 'fit' both Facts (.85 gives us a 'NO' answer; .91 gives us a 'YES' answer).
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich