if P+Q= 12, is PQ?

Question

GMATBusters’ Quant Quiz Question -5

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if P+Q= 12, is P>Q?
1) P^2>Q^2 
2)Q<0

GMATBusters · Answer

The solution of the question shall be as follows: 
 https://www.youtube.com/watch?v=XWYDKXNemUo

Archit3110 · Answer

if P+Q= 12, is P>Q? 1)P2>Q2P2>Q2 2)Q<0 #1 p can be +/-8 and q +/-4 ; sufficient #2 q<0 so P has to be >0 so p>q sufficient IMO D

ashwini2k6jha · Answer

P>Q? STATE-1:SUFFICIENT P^2-Q^2>0 P-Q*P+Q>0 GIVEN P+Q >0 HENCE P-Q>0 STATE-2 SUFFICIENT Q<0 12-P<0 P>12 HENCE P>Q SUFFICIENT ANSWER D

Raxit85 · Answer

if P+Q= 12, is P>Q?
1)P^2>Q^2
P>Q if both are positive and P has greater than 6.
P can not be > Q if P is -ve and Q >12.
Insufficient.

2)Q<0

As Q is -ve and P+Q = 12. P has to > Q.
Sufficient.

Ans. B

Kinshook · Answer

Asked: If P+Q= 12, is P>Q?

1)P^2>Q^2
|P| > |Q|
Case 1: IF Q<=0; P>=12>Q; For example Q=-3; P=15; P>Q; SUFFICIENT
Case 2: BUT IF Q>0; P>0 since if P<=0; |P| <|Q|; for example Q=18; P=-3; |P|<|Q|
Since magnitude of P > magnitude of Q and P & Q both are positive; P>Q; SUFFICIENT
In both cases P>Q
SUFFICIENT

2)Q<0
IF Q<=0; P>=12>Q; For example Q=-3; P=15; P>Q
SUFFICIENT

IMO D

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uc26 · Answer

P+Q=12. P will be greater than Q if P>6. So the question basically asks if P>6?

(1)  P^2>Q^2.  
(P+Q)*(P-Q)>0.
We know that (P+Q)=12
So, we get 12*(P-Q)>0
This means (P-Q) has to be positive which implies that P>Q.
Sufficient.

(2) Q<0.
If Q is negative, then we have P+ (negative number)=12
Thus, P>12. And P>Q.
Sufficient.

Answer: D

Tommy6e · Answer

Answer is D
if P+Q= 12, is P>Q?
We know that P+Q=12 --> P=12-Q --> if Q<6 then P>Q.

Statement 1: sufficient
1)P^2>Q^2

P=12-Q, so P^2 = (12-Q)^2
(12-Q)^2 > Q^2
144 -24Q + Q^2 > Q^2
144>24Q
6>Q

Since Q<6, P must be >6, thus P>Q

Statement 2: sufficient
2)Q<0
Q<0, which means Q<6, then P>6 and thus P>Q

1BlackDiamond1 · Answer

if P+Q= 12, is P>Q?
1)P^2>Q^2

p q p+q p^2 Q^2
6 6 12 36 36 - does not satifsy the equation
7 5 12 49 25 - Satisfies the quation and the P > Q
-P is not possible 
-q will always result in P > Q

Thus statement I is sufficient.

2)Q<0
-q will always result in P > Q since P+Q = 12
Thus statement II is sufficient.

Answer is D

kapilagarwal · Answer

ANS: D each alone sufficient

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SR71Blackbird · Answer

The answer to this question is D.

Statement 1: can be formed as |P|^2 > |Q|^2, P and Q can be either +ve or -ve. 
We can say the distance of P from zero is greater than distance of Q from zero. P can be +ve and Q can be -ve, P can be -ve and Q can be +ve, both -ve, and both +ve. 
Both -ve is not viable as the sum is positive. P is extremely -ve and Q is small +ve, the sum cannot be 12. 
The remaining two conditions both say P>Q, Q -ve and P+ve or Q small +ve and P large +ve

Statement 2:Q <0 means P +ve P>Q

zs2 · Answer

if P+Q= 12, is P>Q?
1)P2>Q2P2>Q2
2)Q<0

STATEMENT 1 -
P^2>Q^2
(P-Q)(P+Q) >0
P+Q=12 >0 GIVEN
THIS MEANS P-Q >0 I.E. P>Q Sufficient

STATEMENT 2-
Q<0
P+Q=12. IF Q<0 THEN P HAS TO BE >0 For sum to be 12
which mean p>q sufficient

HENCE D IS ANSWER

lacktutor · Answer

if P+Q= 12, is P >Q?
—> P—Q > 0 ?

(Statement1): P^{2} > Q^{2}
(P—Q)(P+Q) > 0
(P—Q)*12 > 0
—> P—Q > 0
Sufficient

(Statement2): Q < 0
Q= 12 —P
12–P < 0
—> P > 12
Sufficient

Answer (D)

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firas92 · Answer

if P+Q= 12, is P>Q?
1)P^2>Q^2
P^2-Q^2>0 or (P+Q)(P-Q)>0
Since P+Q>0, P-Q>0 or P>Q

1 is sufficient

2)Q<0

P = 12-(negative) or 12+positive

This means P is positive and Q is negative and so P>Q

2 is sufficient

Answer is (D)

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the27s · Answer

(D)

Condition (1) is sufficient to conclude P-Q > 0 because P^2-Q^2 > 0 and P + Q = 12.
Condition (2) is sufficient to conclude P>Q because, Q is negative and P+Q = 12, making P>0 and this making P>Q.

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jrk23 · Answer

i think its "D".

option a and b are equally sufficient.

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if P+Q= 12, is P>Q?

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