If points p and q are distinct points equidistant from zero on a numbe

Question

If points p and q are distinct points equidistant from zero on a number line, which of the following could be true about p^2 – q?

I. It is less than zero

II. It is between 0 and 1

III. It equals zero

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

dave13 · Answer

let p and q be -2 and 2 respectivily -----> -2(2)-2 = -6 let p and q be -1/2 and 1/2 respectively -----> -1/2 *2 -1/2 = -3/2 IMO: A. I only

NandishSS · Answer

aragonn   Bunuel  Need to clarify, Is it p2 – q? or p^2-q?

Bunuel · Answer

__________________________
It's p^2 – q. Edited. Thank you.

eswarchethu135 · Answer

p^2 - q = ?

I. It is less than zero -- possible when p = -0.5 and q = 0.5

II. It is between 0 and 1 -- possible when p = 0.5 and q = -0.5

III. It equals zero -- possible when p = -1 and q = 1

OPTION:  E

pandeyashwin · Answer

Case 1 : p = -1/2 , q = 1/2
Case 2 : p = -1.5 , q = 1.5
Case 3 : p = -1 , q = 1

Ans E

duchessjs · Answer

My confusion comes from when we use a possible combination of  p=-1  and  q=1 , to determine if option III is possible.

If  p^2 - q  is used with  p=-1  and  q=1 , then would you use...

(-1)^2 -1  which equals  0 
OR
 -1^2 -1  which equals  -2

Where are these magical parentheses around the  -1  coming from? Or is there a rule I'm neglecting to remember about plugging in values to given equations?
The squaring of a negative rule and negative squared rule both keep swirling around in my head.

I originally came across this question on Magoosh, which used the first layout with parentheses around the  -1 , equaling zero. However, I used the second equation layout with no parentheses and answered the question incorrectly. I was hoping someone on GMAT Club could help explain.

Ypsychotic · Answer

The question asks for what could be true not for what must be true, so we have to concentrate on what must not be true.

1) Let p=-1/2, q= 1/2, p^2-q=1/4-1/2=-1/4, the expression could be less than zero.

2) Let p=1/2, q=-1/2, p^2-q=1/4-(-1/2)=3/4. the expression could be between 0 and1.

3) Let p=-1, q=1, p^2-q=(-1)^2-1=0, it equals zero, so, the expression could equal to zero.

So, i, ii and iii could be true for the expression. IMO, option E.

aragonn · Answer

Official Explanation:

This is a good number sense problem. We have to pick numbers guided by number sense.

It’s important to remember that when we square a positive fraction between 0 and 1, the square is a smaller positive number. Of course, the negative of such a fraction would have the same square.

I. If p = - \frac{1}{2}  and q = 1/2 , we get 1/4 - 1/2 = -1/4 Therefore, I works.

II. If p = 1/2​​ and q = – 1/2, we get 1/4 - (-1/2) = 3/4​​. Therefore, II works.

III. If p = –1 and q = 1, we get (–1)^2 – 1 = 0. Therefore, III works.

All three are possible. Answer = (E)

shaurcastic · Answer

My only question is, though not specifically mentioned in the answer choices, can it be > 0 also, right?

Bunuel · Answer

Since the correct answer is E, which means "It is between 0 and 1" could be true (for example, if p = 1/2 and q = -1/2), then yes, p^2 - q could be more than 0.

If points p and q are distinct points equidistant from zero on a numbe

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If points p and q are distinct points equidistant from zero on a numbe

Prep Toolkit

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