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The two points P (p, 2) and Q (3, q) lie
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19 Dec 2024, 23:50
19 Dec 2024, 23:50
Expert Reply
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Question Stats:
42% (01:11) correct
57% (00:39) wrong based on 7 sessions
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The two points $\(P(p, 2)\)$ and $\(Q(3, q)\)$ lie in the rectangular coordinate system formed by the $\(x\)$-axis and the $\(y\)$-axis. If $\(p q \neq 0\)$, then which of the following options are true?
Indicate all that apply
A Points $\(P\)$ and $Q$ are in $\(1^{\text {st \)$ and $\(4^{\text {th \)$ quadrants respectively if $\(p q>0\)$
B Points $\(P\)$ and $Q$ are in $\(3^{\text {rd \)$ and $\(4^{\text {th \)$ quadrants respectively if $\(p q>0\)$
C Points $\(P\)$ and $Q$ are in $3^{\text {rd $ quadrant and $\(4^{\text {th \)$ quadrant respectively if $\(p q<0\)$
D None of the options above.
Indicate all that apply
A Points $\(P\)$ and $Q$ are in $\(1^{\text {st \)$ and $\(4^{\text {th \)$ quadrants respectively if $\(p q>0\)$
B Points $\(P\)$ and $Q$ are in $\(3^{\text {rd \)$ and $\(4^{\text {th \)$ quadrants respectively if $\(p q>0\)$
C Points $\(P\)$ and $Q$ are in $3^{\text {rd $ quadrant and $\(4^{\text {th \)$ quadrant respectively if $\(p q<0\)$
D None of the options above.
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Re: The two points P (p, 2) and Q (3, q) lie
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22 Dec 2024, 12:15
22 Dec 2024, 12:15
Expert Reply
There are two possibilities for the product of p and q
Case 1. $\(\mathrm{pq}<0\)$ which implies exactly one of p and q is positive and the other one is negative
(a) if we take $\(p>0 \& q<0\)$, we get point $\(P(p, 2)\)$ in the $\(1^{\text {st \)$ quadrant \& point $\(Q(3, q)\)$ in the $\(4^{\text {th \)$ quadrant.
(b) if we take $\(\mathrm{p}<0 \& \mathrm{q}>0\)$, we get point $\\(mathrm{P}(\mathrm{p}, 2)\)$ in $\(2^{\text {nd \)$ quadrant \& point $\(\mathrm{Q}(3, \mathrm{q})\)$ in the $\(1^{\text {st \)$ quadrant.
Case 2. $\(\mathrm{pq}>0\)$ which implies either both p and q are positive or both are negative.
(a) if we take $\(p>0 \& q>0\)$, we get point both the points $\(P(p, 2) \& Q(3, q)\)$ in the 1st quadrant.
(b) if we take $\(p<0 \& q<0\)$, we get point $\(P(p, 2)\)$ in $\(2^{\text {nd \)$ quadrant $\(\&\)$ point $\(Q(3, q)\)$ in the $\(4^{\text {th \)$ quadrant.
Hence using above cases, none of the given options can be true, so the answer is (D).
Case 1. $\(\mathrm{pq}<0\)$ which implies exactly one of p and q is positive and the other one is negative
(a) if we take $\(p>0 \& q<0\)$, we get point $\(P(p, 2)\)$ in the $\(1^{\text {st \)$ quadrant \& point $\(Q(3, q)\)$ in the $\(4^{\text {th \)$ quadrant.
(b) if we take $\(\mathrm{p}<0 \& \mathrm{q}>0\)$, we get point $\\(mathrm{P}(\mathrm{p}, 2)\)$ in $\(2^{\text {nd \)$ quadrant \& point $\(\mathrm{Q}(3, \mathrm{q})\)$ in the $\(1^{\text {st \)$ quadrant.
Case 2. $\(\mathrm{pq}>0\)$ which implies either both p and q are positive or both are negative.
(a) if we take $\(p>0 \& q>0\)$, we get point both the points $\(P(p, 2) \& Q(3, q)\)$ in the 1st quadrant.
(b) if we take $\(p<0 \& q<0\)$, we get point $\(P(p, 2)\)$ in $\(2^{\text {nd \)$ quadrant $\(\&\)$ point $\(Q(3, q)\)$ in the $\(4^{\text {th \)$ quadrant.
Hence using above cases, none of the given options can be true, so the answer is (D).
gmatclubot
Re: The two points P (p, 2) and Q (3, q) lie [#permalink]
22 Dec 2024, 12:15
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