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

Question

Note: Figure not drawn to scale https://gmatclub.com/forum/download/file.php?id=26103 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 599_1.png

shreyast · Accepted Answer

I thought option D would be correct but later realised that option B is correct.

So from diagram we know that x < 0 and y > 0.

if x = -100 and y = 1, I is false
if x = -1 and y = 100, II is false
III, will always be true since neither x or y is 0.

BrentGMATPrepNow · Answer

I. |x+y| < y  
Statement I is not necessarily true. 
For example, if x = -5 and y = 1, the inequality |x+y| < y becomes: |(-5) + 1| < 1, which simplifies to be: 4 < 1, which is not true. 
This means we can eliminate answer choices A, D and D since they state that statement I is true.

II. x + y < 0  
Statement II is not necessarily true.
For example, if x = -1 and y = 2, the inequality x + y < 0 becomes: (-1) + 2 < 0, which simplifies to be: 1 < 0, which is not true. 
This means we can eliminate answer choice E since it states that statement II is true.

By the process of elimination, the correct answer is B

Lucky2783 · Answer

given Y>0 and X<0 . I |x+y| < y at |X|=|Y| the inequality will change to is 0 |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 . Answer B

mehtakaustubh · Answer

A) |x+Y|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

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: Arithmetic_Numberline.png 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

EMPOWERgmatRichC · Answer

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,
Rich

CEdward · Answer

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
IN

BrushMyQuant · Answer

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

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

bumpbot · Answer

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