Is x a negative number? (1) 9x > 10x (2) x + 3 is positive

SOLUTION

Is x a negative number?

(1) 9x > 10x --> rearrange: \(0>10x-9x\) --> \(0>x.\) Sufficient.
(2) x + 3 is positive --> \(x+3>0\) --> \(x>-3\). Not sufficient.

Answer: A.
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From Statement -1 : 9 X > 10 X
Case -1 :Assuming X > 0
Dividing by X , 9>10 - Which is no true - So X <0 - Sufficient

Case-2 : X+3 >0
i.e X> -3 ....X can be any number greater than -3 -Not sufficient

Answer -

Now let us take it down fat and very fast, cos this is a very wussy question where we have to save time for the other tough problems we should not take more than 10 seconds to solve it .
9x>10x implies x < 0 9 (Awesome )
x+3 > 0 implies x > -3 ( not good )
Answer is A

IMO A

st 1: sufficient x is -ve
st 2: not sufficient x can be +ve, -ve or zero

Is x a negative number?

(1) 9x > 10x
(2) x + 3 is positive.

i would like to know if my process is correct

1) 9x - 10x >0 ----> x (9-10) > 0 -----> x > 0 suff

2) x + 3 = pos x can be a positive value 4 + 3 = 7 or negative -1 + 3 = 2 always positive insuff

In particular I wish to know about the first stat.

Thanks
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9x>10X only if x is -ve it cant be greater when x is + ve
hence 1 is sufficient
but statement 2 is insufficient as x can hav the value as 0 and any + ve num
zero is neither +ve nor - ve
hence insufficient
A is the answer

Hi Bunuel.

What is unclear for me is not the probelm by itself (I picked the right answer but the first statement

1) 0 > of something then X must be negative. The answer is definitevely YES.

Instead, I have obtained YES too but X is definetevely positive. In this scenario is the same, the most imprtant thing is to have a definitive answer, or is wrong thinking in this way??

Thanks
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Well, from (1) we have that x<0, so x is negative not positive.

As for your question: in a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

Hope it's clear.
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1) tells us that 0 > 10x - 9x ---> 0 > x , so 1 is sufficient
2) x could be 1 or -1, for instance.. So insufficient..

We go with A

Hi....in this why cant the value of x lie between 0 or 1? like a fraction 1/3?

Hi mandakini,

Fact 1 tells us that 9X > 10X. That is a specific "restriction" that eliminates certain possible values of X.

ANY POSITIVE value for X (even a positive fraction), won't "fit" with that inequality. Neither will the value 0.

IF....X = 1/3
9(1/3) = 3
10(1/3) = 3.3333
3 is NOT > than 3.3333, so X CANNOT be 1/3.

9(0) is NOT > than 10(0), so X CANNOT be 0.

You can also do algebra to simplify the inequality....

9X > 10X
-9X -9X
0 > X

In either approach, you can prove that X CANNOT be positive and CANNOT be 0. Negative values are all that are left, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

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

statement 1) 9x > 10x: only true if X is negative


(2) x + 3 is positive. x can be from -2 to +infinity , insufficient

hence A

HI mrslee,

With 9X > 10X... If you use X = 2/90, then you will end up with....

9(2/90) > 10(2/90)
2/10 > 2/9
1/5 > 2/9
.2 > .222222

This is NOT true, so X CANNOT be 2/90.

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

Solution:

We need to determine whether x is a negative number.

Statement One Alone:

9x > 10x

We can subtract 9x from both sides of the inequality:

9x – 9x > 10x – 9x

0 > x

Since 0 is greater than x, x is less than 0. In other words, x must be negative.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and E.

Statement Two Alone:

x + 3 is positive.

From statement two we see that x itself could be either positive or negative. Let’s use a few convenient values to illustrate.

If x is positive

Let x = 1:

1 + 3 = 4, which is positive.

If x is negative

Let x = -1:

-1 + 3 = 2, which is also positive.

Statement two alone is not sufficient to answer the question.

The answer is A.
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To determine if x is a negative number, we need to evaluate the given statements.

Statement (1): 9x > 10x
From this statement, we know that 9x is greater than 10x. This implies that x is negative because if x were positive, multiplying it by 9 would yield a larger value than multiplying it by 10. Therefore, statement (1) alone is sufficient to determine that x is negative.

Statement (2): x + 3 is positive
This statement tells us that x + 3 is positive. However, it does not directly provide information about the sign of x. x could be positive or negative, as long as x + 3 is positive.

Therefore, the information provided by statement (1) is sufficient to determine that x is a negative number.