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705-805 (Hard)|   Algebra|      
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shivanigs
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If P^2 + Q^2 =1, is P – Q =1? 25 Aug 2012, 05:32
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B
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85% (hard)

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40% (01:48) correct 60% (01:54) wrong based on 230 sessions

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If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1
(2) P is a positive integer.
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B
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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Bunuel
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If P^2 + Q^2 =1, is P – Q =1? 25 Aug 2012, 05:41
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If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.
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If P^2 + Q^2 =1, is P – Q =1? Updated on: 25 Aug 2012, 05:57
Originally posted by EvaJager on 25 Aug 2012, 05:52.
Last edited by EvaJager on 25 Aug 2012, 05:57, edited 1 time in total.
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Bunuel
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.
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Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.
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shivanigs
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If P^2 + Q^2 =1, is P – Q =1? 25 Aug 2012, 05:56
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Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.
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EvaJager
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If P^2 + Q^2 =1, is P – Q =1? 25 Aug 2012, 06:01
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shivanigs
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.
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No need for Q to be an integer. Since P = 1, it comes out that Q = 0 (from \(P^2+Q^2=1\)).
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If P^2 + Q^2 =1, is P – Q =1? 25 Aug 2012, 06:04
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shivanigs
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.
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Do you mean for (2)? Here, since we determined that P=1 we can solve P^2+Q^2=1 to get the value of Q: 1^2+Q^2=1 --> Q=0.

EvaJager
Bunuel
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.

Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.
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If the first statement were P-Q=1, then it would be sufficient, since that's exactly what we are asked - to find whether P-Q=1.
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If P^2 + Q^2 =1, is P – Q =1? 25 Aug 2012, 06:15
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Bunuel
shivanigs
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.

Do you mean for (2)? Here, since we determined that P=1 we can solve P^2+Q^2=1 to get the value of Q: 1^2+Q^2=1 --> Q=0.

EvaJager
Bunuel
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.

Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.

If the first statement were P-Q=1, then it would be sufficient, since that's exactly what we are asked - to find whether P-Q=1.
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OMG...I'm an astronaut today...
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If P^2 + Q^2 =1, is P – Q =1? 21 Oct 2013, 11:46
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EvaJager
shivanigs
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.

No need for Q to be an integer. Since P = 1, it comes out that Q = 0 (from \(P^2+Q^2=1\)).
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hi,
not sure, if iota (i) concept can be applied in here ..

i thought, in verifying S2,
P=2, Q^2=-3, Q=sqrt3 * iota
so, in this case also, p^2+Q^2=1
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If P^2 + Q^2 =1, is P – Q =1? 06 Feb 2016, 13:17
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Hi Bunuel

Can you please tell me why A cant be sufficient using below approach?

Given P^2 + Q^2 = 1.

P-Q = 1 => SQUARING BOTH SIDES => P^2 + Q^2 -2PQ = 1
=> 1 -2PQ = 1 (SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So our question becomes whether one of p or q is zero?

Now looking at A :

P+Q = 1 => Squaring both sides => P^2 + Q^2 + 2PQ = 1 => 1+2PQ = 1 ( SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So this should be sufficient right?

Bunuel
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.
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If P^2 + Q^2 =1, is P – Q =1? 07 Feb 2016, 04:34
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neeraj609
Hi Bunuel

Can you please tell me why A cant be sufficient using below approach?

Given P^2 + Q^2 = 1.

P-Q = 1 => SQUARING BOTH SIDES => P^2 + Q^2 -2PQ = 1
=> 1 -2PQ = 1 (SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So our question becomes whether one of p or q is zero?

Now looking at A :

P+Q = 1 => Squaring both sides => P^2 + Q^2 + 2PQ = 1 => 1+2PQ = 1 ( SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So this should be sufficient right?

Bunuel
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.
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You cannot square. If p - q = -1, then (p - q)^2 would be equal to 1^2 but p - q = -1 is not equal to 1.
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If P^2 + Q^2 =1, is P – Q =1? 16 Mar 2019, 04:39
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Bunuel
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.
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Hi, Any reason why we shouldn't rephrase the question ?

P-Q=1? => squaring both the sides => p^2+q^2-2pq=1 => since P^2 +Q^2 =1 => 2pq=0 => pq =0 ?????
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If P^2 + Q^2 =1, is P – Q =1? 24 Feb 2020, 00:03
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[quote="Bunuel"]If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

Why not the following reasoning?
P+Q=1
So, P=1-Q ... ... (a)

and, P^2 + Q^2 =1
So, P^2 = 1 - Q^2
So, P^2 = (1+Q)(1-Q)
So, P^2 = (1+Q)(P) ... ... apply eq. (a)
So, P = 1+Q
So, P-Q = 1
[Sufficient, Ans : D]
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If P^2 + Q^2 =1, is P – Q =1? 02 Dec 2021, 06:24
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Bunuel
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.
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Q can be imaginary number Q^2 = -1,
Does GMAT don't consider imaginary numbers?

Ambiguous question

The answer should be C
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If P^2 + Q^2 =1, is P – Q =1? 02 Dec 2021, 08:35
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iridescent995
Bunuel
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Answer: B.

Q can be imaginary number Q^2 = -1,
Does GMAT don't consider imaginary numbers?

Ambiguous question

The answer should be C
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B is correct. All numbers on the GMAT are real numbers by default.
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