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Intern  Joined: 11 Sep 2017
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Difficulty:   65% (hard)

Question Stats: 52% (01:39) correct 48% (01:38) wrong based on 91 sessions

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In which quadrant does the point P(x,y) lie?

(1) Point R(x, y+1) is in the second quadrant.
(2) Point Q(x+3, y) is in the third quadrant.
Math Expert V
Joined: 02 Sep 2009
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In which quadrant does the point P(x,y) lie? (1) Point R(x, y+1) is in the second quadrant.

In the second quadrant, x-coordinate is negative and y-coordinate is positive. So, x < 0 and y + 1 > 0 (y > -1). y > -1, means that y could be negative as well as positive, thus P(x, y) could be P(negative, negative) = III quadrant as well as P(negative, positive) = II quadrant. Not sufficient.

(2) Point Q(x+3, y) is in the third quadrant.

In the third quadrant, both x and y coordinates are negative. So, x + 3 < 0 (x < -3) and y < 0. Since, x < -3, then it's negative, thus P(x, y) = P(negative, negative) = III quadrant. Sufficient.

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1) Point R(x, y+1) is in the second quadrant.
This states that x is negative.
but we clearly don't get any idea about y.
y can be positive as well as negative.
eg: x=-3 y=2 then R(x,y+1) in II quadrant.
x=-3, y= -0.5 then R(x,y+1) in II quadrant.
Statement I is insufficient.

(2) Point Q(x+3, y) is in the third quadrant.
this states that x+3 is negative and y is negative.
if x+3 is negative then x will be negative as well for all possible cases.
hence x is negative and y is negative; means point P will be in III quadrant.
Statement II is sufficient.

Kudos if it helps.
Current Student P
Joined: 02 Jul 2017
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(1) Point R(x, y+1) is in the second quadrant.
=> As above point R lie in 2nd quadrant => x =-ve and y+1 is +ve
Now we have to find quadrant of P(x,y). As we already know x is -ve we ahve to check value of y

If R(-1,5) => P =(-1, 4) => P lies in second quadrant
if R (-1,0.5) => P =(-1, -0.5) => P lies in third quadrant.

So either P lies in second or third quadrant. here we don't know value of y . Insufficient

(2) Point Q(x+3, y) is in the third quadrant.
=> As above point Q lie in 3rd quadrant => x+3 =-ve and y is -ve
Now we have to find quadrant of P(x,y)

If Q(-0.5,-1) => x+3 = -0.5 => x =-3.5 => P =(-3.5, -1) => P lies in third quadrant

Implies for all the values of x point P will lie in 3rd quadrant. Sufficient

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_________________ Re: In which quadrant does the point P(x,y) lie?   [#permalink] 19 Mar 2019, 08:26
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# In which quadrant does the point P(x,y) lie?  