If y is an integer and y = |x| + x, is y = 0?

Question

(1) x < 0
(2) y < 1

Bunuel · Accepted Answer

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Bunuel · Answer

If y is an integer and y = |x| + x, is y = 0?

Notice that from \(y=|x|+x\) it follows that y cannot be negative:
If \(x>0\), then \(y=x+x=2x=2*positive=positive\);
If \(x\leq{0}\) (when x is negative or zero) then \(y=-x+x=0\).

(1) \(x<0\) --> \(y=|x|+x=-x+x=0\). Sufficient.

(2) \(y<1\). We found out above that y cannot be negative and we are given that y is an integer, hence \(y=0\). Sufficient.

Answer: D.

Also discussed in Inequality and absolute value questions from my collection: https://gmatclub.com/forum/inequality-an ... 86939.html

Hope it's clear.

LM · Answer

Each of (1) and (2) are sufficient to answer the question. Thus the answer should be "D". 
From(1), any value of X<0, whether it's integer or fraction will lead to Y = 0 because the mode function will result in positive value and positive value added to same negative value will result in Zero.
From (2), We can have Y as negative Integer ( -1,-2....) if and only if the Right hand side of equation is different. It's just adding the same X and it can't lead to the negative value.

Yes it can definitely lead to the Zero.

Thus Answer should be D.

You can plug and play certain values ( numbers ) in order to verify the above.

KarishmaB · Answer

A word of caution: When you read "If y is an integer and y=|x|+x", analyze it there and then. y can be a positive integer when x is positive, y will be 0 when x is negative and y will be 0 when x is 0."
Another important point to note here: When the author puts in extra effort to write "y is an integer" rather than "x and y are integers" , take special note that x may not be an integer. Not that it matters very much here but in many questions such a statement will have special significance.

devinawilliam83 · Answer

If y is an integer and y = |x| + x, is y = 0?

(1) x < 0 
(2) y < 1

I rephrased the original question as Is  x<0 ?
Statement 1 : SF
Statement II : if y<1; x+|x|<1..on solving we get 2 ranges for x
 - X<0 or,
 - 0<X<0.5
Basis this II is insufficient.. Where am I going wrong ?

devinawilliam83 · Answer

Bunuel,why didn't i get it with the way i solved it? 
Am unable to understand where my approach is wrong . Thanks

Bunuel · Answer

You forgot that it's given that y=integer. (2) says y<1, thus |x|+x must also be some integer less than 1: 0, -1, ... but if you refer to my solution you'll see that |x|+x can never be negative, so the only valid solution for |x|+x (or which is the same for y) is 0.

Hope it's clear.

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If y is an integer and y = |x| + x, is y = 0?

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If y is an integer and y = |x| + x, is y = 0?

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