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# If x and y are numbers on the number line above, which of the followin

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Re: If x and y are numbers on the number line above, which of the followin [#permalink]
Bunuel wrote:
Note: Figure not drawn to scale

If x and y are numbers on the number line above, which of the following statements must be true?

I. |x+y| < y
II. x + y < 0
III. xy < 0

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

Kudos for a correct solution.

Attachment:
599_1.png

given Y>0 and X<0 .

I |x+y| < y
at |X|=|Y| the inequality will change to is 0<Y? Answer YES
at |X|=|2Y| the inequality will change to is Y<Y? Answer NO

II X+Y<0 . If |X| > |Y| then YES . if |X| > |Y| then NO . also |X| can be equal to |Y| in which case X+Y =0 .

III XY <0 yes.

B
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Re: If x and y are numbers on the number line above, which of the followin [#permalink]
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A) |x+Y|<Y
Not Always True
If |X|>2|Y| then false
else true
B)X+Y<0
This is true only if |X|>|Y|
C)XY<0
This is always true since x<0 and Y>0

IMO B
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Re: If x and y are numbers on the number line above, which of the followin [#permalink]
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Bunuel wrote:
Note: Figure not drawn to scale

If x and y are numbers on the number line above, which of the following statements must be true?

I. |x+y| < y
II. x + y < 0
III. xy < 0

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

Kudos for a correct solution.

Attachment:
The attachment 599_1.png is no longer available

MAGOOSH OFFICIAL SOLUTION:
Attachment:

Arithmetic_Numberline.png [ 26.9 KiB | Viewed 21157 times ]

FAQ: Why is Statement I not correct?

The key phrasing in this questions is "which of the following statements MUST be true." Must be true means that the statement can never be false.

If x = -9 and y = 1, then statement 1 would be false. Since we have numbers that can make statement 1 false, it does not satisfy the "MUST be true" condition.

FAQ: I thought that the bars around the x and y on answer choice I meant absolute value? As in the number of places from the number line?

Those bars most certainly do mean absolute value; however, it's important to realize that you perform the operation inside the brackets before you take the absolute value. I'll give some possibilities for x and y:

In this case it works. Let's try a different set:

x = -10
y = 3

|x + y| < y
|-10 + 3| < 3
|-7| < 3
7 < 3
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Re: If x and y are numbers on the number line above, which of the followin [#permalink]
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Hi All,

On Test Day, Roman Numeral questions are not too common (you'll probably see just 1 in the Quant section). Sometimes they can be rather complex, but the answer choices tend to be written in such a way so that you can avoid doing some of the work. In this prompt, it looks like everyone was able to quickly prove that Roman Numerals 1 and 2 are NOT always true. After doing that work, you can eliminate 4 of the answers. The one that's left MUST be the correct one.....and you don't even have to deal with Roman Numeral 3 to prove it. Be on the lookout for these types of 'design' shortcuts - the GMAT writers put them into certain questions on purpose.

GMAT assassins aren't born, they're made,
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Re: If x and y are numbers on the number line above, which of the followin [#permalink]
Rushed this one so I got it wrong, but the answer is III. xy < 0 only.

The figure tells us that the following are true: x < 0 and y > 0

|x + y | < y
x = -6, y = 1 ----> | -6 + 1 | > y OUT

x + y < 0
-6 + 1 = -5 < 0
-1 + 2 = 1 > 0 OUT

xy < 0
(-)(+) is necessarily < 0
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Re: If x and y are numbers on the number line above, which of the followin [#permalink]
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Top Contributor
It is given to us that x is negative and y is positive but we do not know the actual values of x and y

Since it is a must be true question so let's take values of x and y to prove the option choices wrong

I. |x+y| < y Now on LHS (Left Hand Side) we have |x+y| and RHS (Right Hand Side) we have y
So, we need to get a value of |x+y| which is bigger or equal to y in order to prove this wrong
Lets take a small negative value of x and small positive value of y
x = -100, y = 10
|x+y| = |-100+10| = |-90| = 90 > 10 (Watch this video to learn the Basics of Absolute Value)
=> |x+y| < y MUST not be true always

II. x + y < 0
x = -10, y = 100
x+y = 90 > 0
=> x + y < 0 MUST not be true always

III. xy < 0
x = -10, y = 100
or x = -100, y = 10
In any case xy < 0 (Watch this video to learn the Basics of Inequalities)
As product of a negative number and a positive number < 0
=> xy < 0 is Always True

Hope it helps!

Watch the following video to learn the Basics of Absolute Values

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Re: If x and y are numbers on the number line above, which of the followin [#permalink]
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Re: If x and y are numbers on the number line above, which of the followin [#permalink]
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