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Statement 1: pz^4 < 0 i.e. p is Negative because z^4 must be positive for given Inequation But since the sign of z is still unknown hence, NOT SUFFICIENT
Statement 2: p + z^4 = 14 As per this inequation p and z can have any sign positive or negative hence nothing can be concluded NOT SUFFICIENT
Combining the two statements p is Negative but even after combining the two statement we can't conclude the sign of z. Hence, NOT SUFFICIENT
Answer: Option E
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(1) pz^4 < 0 => p<0 but we do not know the sign of z => Do not know the sign of pz => Insufficient (2) p + z^4 = 14 We do not know the sign of both p and z => Insufficient (1) + (2): insufficient
Considering statement (1) pz^4 < 0 , as z has even power we cannot say anything about whether z is + or -. It follows BCE.
Now consider statement (2) p + z^4 = 14, => p=14-z^4, now this leads us to options p can be + or negative based on z's values. For example, p=14-16 is -2 and p=14-1^4 is 13.
Even combining both of them does not provide any solution so I go for option E.
Sol. zp is negative when either z or p is negative 1) pz^4 <0 so z^4 is always +ve sp p is -ve but we dont know anything about z so insufficient 2) p + z^4 = 14 Dont know anything about p and z so insufficient
1) + 2) p(14-p) <0 either p <0 or 14 - p <0 or p >14 so noot sufficient
E must be the correct answer
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In order for \(zp<0\), only one out of z and p must be negative and not both.
Statement 1 tells that \(p<0\) but nothing about z (as \(z^4\) will always be positive whether z is positive or negative). Hence, insufficient. Statement 2 doesn't tells anything about the signs of p and z as they could be either positive or negative to get a sum of 14. Hence, insufficient.
Combining both statements, we know that \(p<0\) and \(p+z^4=14\), that only helps us to conclude that \(z^4>14\), which again doesn't helps in confirming the sign of z (i.e. whether it's positive or negative). Hence, insufficient.
The main issue is that even with both the statements, we still don't know the sign of "z". It can be either positive or negative. Hence, we cannot say for sure whether zp <0.
Statement 1: p(z^4) < 0 This statement doesn't FEEL sufficient, so I'll TEST some values. There are several values of p and z that satisfy statement 1. Here are two: Case a: p = -1 and z = 1. In this case, pz = (-1)(1) = -1. So, pz IS negative. Case b: p = -1 and z = -1. In this case, pz = (-1)(-1) = 1. So, pz is NOT negative. Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: p + (z^4) = 14 There are several values of p and z that satisfy statement 1. Here are two: Case a: p = -2 and z = 2. In this case, pz = (-2)(2) = -4. So, pz IS negative. Case b: p = -2 and z = -2. In this case, pz = (-2)(-2) = 4. So, pz is NOT negative. Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined There are still several values of p and z that satisfy BOTH statements. Here are two: Case a: p = -2 and z = 2. In this case, pz = (-2)(2) = -4. So, pz IS negative. Case b: p = -2 and z = -2. In this case, pz = (-2)(-2) = 4. So, pz is NOT negative. Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
will someone confirm whether in statement 1. only p is raised to 4 or zp is raised to 4? it looks ambiguous...i assumed it is only z^4 and got it right
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will someone confirm whether in statement 1. only p is raised to 4 or zp is raised to 4? it looks ambiguous...i assumed it is only z^4 and got it right
If pz were raised to the power it would be written (pz)^4. Since it's written pz^4, then only z is raised to the power.
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The question stem asks: Is either of z or p is negative But here is the catch, even if you know exact sign of p, unless you know the exact sign of z, one cannot decide whether final product will be positive or negative.
If p is negative, a. but z is negative: final product is positive b. but z is positive: final product is negative.
St 1 : p\(z^4\)is negative. Any number raised to even power will always be positive. But are you sure about sign of that number?
\(1^4\) = 1 \((-1)^4\) = 1
Hence z can be 1 or -1. Insuff All we know from this statement is that p is negative since\(z^4\) will always be positive.
Coming to St 2: p + \(z^4\) = 14 Take simple values as below: 13 + \((1)^4\) = 14 13 + \((-1)^4\) = 14 p is positive, z can be positive or negative
You can also take (with same analogy) -2 + \((2)^4\) = 14 -2 + \((-2)^4\)= 14 p is negative, z can be positive or negative
Combining both statements, I am still not sure about sign of z. Bottom line: z raised to even power is the culprit or trap here.
Hope this helps.
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Sinec we know Z^4 will be a positive no ... as Exponent is an even no ... Also if pz^4<0 and we already know Z^4 is positive means = p=-ve . But Z can both be positive or neagative, Since we cant determine the sign of Z . Thiis statment is insufficient.
hence we can not determine pz <0 or not.
Statement 2: p+z^4 = 14 as we already know Z^4 will always be +ve but z can be both +ve as well as -ve and value of p can not be determined
hence we can not determine pz <0 or not.
Both Statements combined we know P is negative but we still donot know the sign of Z hence the ans cant be determined.
close
75% (01:35) correct 
Thanks 
what number Z must be n this case? 
