If p and q are nonzero numbers, and p is not equal to q, in

Question

X-Ycoordinategrid.jpg If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does point (p, p – q) lie? (1) (p, q) lies in quadrant IV. (2) (q, -p) lies in quadrant III.

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=23750 
 If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does point (p, p – q) lie?

(1) (p, q) lies in quadrant IV. Points in IV quadrant have positive x-coordinate and negative y-coordinate, so p = positive and q = negative --> (p, p – q) = (positive, positive - negative) = (positive, positive) --> this point lies in the I quadrant. Sufficient.
 
(2) (q, -p) lies in quadrant III. Points in III quadrant have negative x-coordinate and negative y-coordinate, so q = negative and -p = negative, so p = positive. The same as above. Sufficient.

Answer: D.

aadi13 · Answer

how can we deduce that p>q ? Pls explain

it think (p,q) is in 4th quad which means q is already negative and hence p-q = p-(-q) =p+q is positive and hence first quadrant

Bunuel · Answer

From (1) p = positive and q = negative: p > 0 and 0 > q. Sum these two inequalities to get p > q.

TheKingInTheNorth · Answer

If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does point (p, p – q) lie?

(1) (p, q) lies in quadrant IV.
(2) (q, -p) lies in quadrant III.

very easy ....

Remember whenever there is variable in the question and variable in the ans option . Always use number to solve such question .

st 1 -- assume a number for p ,q --- and it lies in quadrant IV
let say p =1 , q = -2 
now we need to find (p, p – q) ---> 1, 3 
both are positive hence 1st quadrant

st 2 (q, -p) lies in quadrant III.
similarly use the approach like st 1 .... It is also sufficient .

hence D ans .

please post kudos if you like my post .

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does point (p, p – q) lie?

(1) (p, q) lies in quadrant IV.
(2) (q, -p) lies in quadrant III.

There are 2 variables (p,q) and 2 equations from the 2 conditions, which means that the number of variables matches the number of equations, giving high chance that (C) is going to be the answer. 
Looking at the conditions, conditions 1 and 2 actually mean the same thing, as:
both gives the range: p>0, q<0. 
Then, p>0 and p-q>0 therefore the conditions are sufficient and the answer becomes (D)

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Shruti0805 · Answer

Hi Bunuel,

If q has a larger absolute value than q, p-q would be negative and thus, (p, p-q) would be in the 4th quadrant and thus, neither of the statements are sufficient. Is this not correct?

Bunuel · Answer

Let's test your claim. Say p = 1 and q = -10, then p - q = 1 - (-10) = 11 = positive.

bumpbot · Answer

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If p and q are nonzero numbers, and p is not equal to q, in

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