GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jun 2019, 08:10 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Is x<0?

Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42 GPA: 3.82

Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 44% (00:52) correct 56% (00:49) wrong based on 84 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

$$Is x<0?$$

$$1) |x|=-x$$
$$2) |x|>x$$

_________________
Manager  G
Joined: 07 Aug 2018
Posts: 110
Location: United States (MA)
GMAT 1: 560 Q39 V28 GMAT 2: 670 Q48 V34 Show Tags

MathRevolution wrote:
[Math Revolution GMAT math practice question]

$$Is x<0?$$

$$1) |x|=-x$$
$$2) |x|>x$$

S(1)$$|x|=-x$$

This transalte into $$x<=0$$. So x could also be 0.

Insufficient.

S(2) $$|x|>x$$

This translate into x<0.

Sufficient.

_________________
Director  S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India

Show Tags

1
Hi,

This is pretty-straight forward question. Modulus function basic understanding is what it requires.

Question: Is x < 0 ?

Statement I is insufficient:

|x| = -x

According to the definition of the modulus

|x| = x , whenever x > = 0

|x| = -x, whenever x < = 0.

So here, x < 0 and also it could be equal to zero.

So not sufficient. Alternatively, u can try plugging in the values in the given statement too, you can see zero and the negative values will work.

Statement II is sufficient:

|x| > x

If “x” values are positive, then the given statement won’t be true.

Its true only for the negative value of x.

So sufficient. So the answer is B.
_________________
GMAT Mentors CEO  V
Joined: 12 Sep 2015
Posts: 3777

Show Tags

1
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

$$Is x<0?$$

$$1) |x|=-x$$
$$2) |x|>x$$

Target question: Is x < 0?

Statement 1: |x| = -x
Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = -1. Notice that |-1| = -(-1). In this case, the answer to the target question is YES, x IS less than 0
Case b: x = 0. Notice that |0| = -0. In this case, the answer to the target question is NO, x is NOT less than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x| > x
If |x| > x, then we can be certain that x does not equal 0.
So, let's see what happens if x is POSITIVE, and what happens if x is NEGATIVE

If x is positive, then |x| > x becomes |POSITIVE| > POSITIVE
This doesn't work, because |some POSITIVE number| is always equal to that same number.
For example, |3| = 3 and |12.9| = 12.9
So, if x is POSITIVE, it cannot be the case that |x| > x
In other words, x CANNOT by positive

So, if x does not equal 0 and x CANNOT by positive, then we can be certain that x is negative
In other words, the answer to the target question is YES, x IS less than 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
_________________
GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936

Show Tags

MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is $$x<0?$$

$$1) |x|=-x$$
$$2) |x|>x$$

$$x\,\,\mathop < \limits^? \,\,0$$

$$\left( 1 \right)\,\,\,\left| x \right| = - x\,\,\,\,\, \Leftrightarrow \,\,\,\,x \leqslant 0\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,x = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,x = - 1\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \end{gathered} \right.$$

$$\left( 2 \right)\,\,\,x < \left| x \right|\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,x < 0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}{\text{.}}\,\,\,\,$$

$$\left( * \right)\,\,x \geqslant 0\,\,\,\, \Rightarrow \,\,\,x = \left| x \right|$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42 GPA: 3.82

Show Tags

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
$$|x| = -x$$
$$=> x ≤ 0$$
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient.
Since the solution set “$$x<0$$” of the question doesn’t include the solution set “$$x ≤ 0$$” of the condition 1), condition 1) is not sufficient.

Condition 2)
$$|x|>x$$
$$=> x < 0$$
Since condition 2) is equivalent to the question, condition 2) is sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________
Manager  S
Joined: 24 Dec 2017
Posts: 191
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21

Show Tags

Is x < 0?

A. |x| = -x

Two possible cases

1. x=-5
|-5|=-(-5)
5=5, From this we can say that x<0. Now let's try to disprove it.

2. x=0
|0|=0, 0 is neither positive not negative

Hence A is insufficient.

B. |x|>x
Let's analyse the statement. If the RHS is positive and greater than LHS, it means x is a -ve value.

Let x be -2
|-2|>-2
2>-2

Hence we can conclude that St 2 alone(B) is sufficient to answer the question.

Thank you
Arjun Re: Is x<0?   [#permalink] 17 Sep 2018, 03:42
Display posts from previous: Sort by

Is x<0?  