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# M31-38

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Math Expert
Joined: 02 Sep 2009
Posts: 47898

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20 Jun 2015, 10:17
00:00

Difficulty:

35% (medium)

Question Stats:

76% (00:34) correct 24% (00:30) wrong based on 46 sessions

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On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers $$x$$, $$y$$, and $$z$$ must be true?

I. $$xyz < 0$$

II. $$x + z = y$$

III. $$z(y - x) > 0$$

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

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Math Expert
Joined: 02 Sep 2009
Posts: 47898

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20 Jun 2015, 10:17
Official Solution:

On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers $$x$$, $$y$$, and $$z$$ must be true?

I. $$xyz < 0$$

II. $$x + z = y$$

III. $$z(y - x) > 0$$

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

The tick marks are equally spaced, so let's assign such values to the variables that satisfy this requirement. Say $$x = -1$$, $$y = 1$$ and $$z = 2$$. We can see that all three options are true.

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Intern
Joined: 29 Nov 2014
Posts: 22

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27 Oct 2015, 12:12
I think this is a high-quality question and I don't agree with the explanation. -1, 1 and 2 are not equally spaced. -1, 1 and 3 would be equally spaced. So the answer should be I and III only.
Current Student
Joined: 18 Jun 2015
Posts: 41

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10 Sep 2016, 08:36
1
The question clearly says the tick mark are equaly spaced. "0" is one of the tick mark. Hence the origiona explanation is correct. al three options are feasibe and correct.
Intern
Joined: 20 Sep 2016
Posts: 3
Location: Spain
GMAT 1: 740 Q50 V40
GPA: 2.45

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15 Jan 2017, 05:59
Hi,

Should we assume that the positive numbers go from zero to right and the negatives from zero to left?

In my opinion it is not clear the direction in which numbers increase. For example, 1, 0, -1, -2 could be possible and then statement 1 wouldn't be true.

Thank you!
Math Expert
Joined: 02 Sep 2009
Posts: 47898

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15 Jan 2017, 09:08
nachobs wrote:
Hi,

Should we assume that the positive numbers go from zero to right and the negatives from zero to left?

In my opinion it is not clear the direction in which numbers increase. For example, 1, 0, -1, -2 could be possible and then statement 1 wouldn't be true.

Thank you!

Positive numbers are numbers that are greater than 0 and are to the right of 0 on the number line.
Negative numbers are numbers that are less than 0 and are to the left of 0 on the number line.

0 is neither positive nor negative.
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Joined: 26 Mar 2013
Posts: 1777

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16 Jan 2017, 03:01

On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers $$x$$, $$y$$, and $$z$$ must be true?

I. $$xyz < 0$$

II. $$x + z = y$$

III. $$z(y - x) > 0$$

Let x= -2 , y=2 and z=4

I. $$xyz < 0$$

-2 *2 *4 = -16 <0 .........True

II. $$x + z = y$$

-2+ 4=2 =y..........True

III. $$z(y - x) > 0$$

4 [2 - (-2)]= 4 *4 =16>0.............True

Manager
Joined: 23 Sep 2016
Posts: 227

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22 Mar 2018, 00:24
1
Bunuel wrote:

On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers $$x$$, $$y$$, and $$z$$ must be true?

I. $$xyz < 0$$

II. $$x + z = y$$

III. $$z(y - x) > 0$$

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

sorry, but i think this one also have same problem please edit this one also.
Math Expert
Joined: 02 Sep 2009
Posts: 47898

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22 Mar 2018, 01:38
rishabhmishra wrote:
Bunuel wrote:

On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers $$x$$, $$y$$, and $$z$$ must be true?

I. $$xyz < 0$$

II. $$x + z = y$$

III. $$z(y - x) > 0$$

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

sorry, but i think this one also have same problem please edit this one also.

_______________
Edited. Thank you.
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Status: Turning my handicaps into assets
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15 May 2018, 06:43
I think in MUST BE question it’s risky to check with only one set of numbers since we have to be assured that condition works for all the numbers. Below is how I solved this question:

First, looking at the number line we can infer that since it is evenly spaced set absolute value of x is equal to the absolute value of y, or in other words y=-x, where x<0. For example, if x=-3, then y= -(-3)=3.

Now, let’s analyze the options.

I. xyz<0 - Must be true, since x is negative, while others are positive.

II. x+z=y - to be sure for this one, I’ve checked two sets: -1,1,2 and -2,2,4. Both yields true. So, it must be true

III. z(y−x)>0- here both multiples (z and (y-x)) must be positive or negative. Now, since z is positive, (y-x) must be positive. Since y is positive and x is negative, the answer must be positive i.e. 2- (-1)=3>0.

Hence, all of them MUST be true. Answer is E.
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M31-38 &nbs [#permalink] 15 May 2018, 06:43
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# M31-38

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