Does p^2 = q if p is a prime number?

Forget conventional ways of solving math questions. In DS, Variable approach is

the easiest and quickest way to find the answer without actually solving the

problem. Remember equal number of variables and equations ensures a solution.


Does p^2 = q if p is a prime number?

(1) q^2 - p^2 = 0
(2) p^2 = 49

according to variable approach method, since we have 2 variables (p,q) in the original condition we need 2 more to match the number of variables and equations. we have 1 each in 1) and 2), therefore C is likely the answer. Using both 1) & 2) together we have p=7, q=-7,7 and since no is the answer for p^2=49=7,-7, the condition is sufficient and the answer is C. but since the case if trivial, using common mistake type 4(A) we have 1) p^2=q^2 means q^2=q?, therefore q=0,1?. then we get p^2=0,1? and p=-1,0,1? and thus p is not a prime number, with answer as no. Therefore the condition is sufficient and the answer is A.

(1) \(q^{2}\) – \(p^{2 }\)=0
=> \(q^{2}\) = \(p^{2}\)

If \(p^{2}\)= q is true then
q= \(q^{2}\)
=>q(q-1)=0
=>q= 0 or 1

Now , p can take values -1 , 0 and 1-- none of which is a prime number .
Sufficient.

(2)\(p^{2}\) = 49

No information about q
Not sufficient.
Answer A

Statement 1:

(q-p)(q+p)=0

(q-p)=0 so q=p

OR

(q+p)=0 so q=-p

This means that p^2=q^2

Statement one is sufficient

Statement 2:

No information about q

Statement two is insufficient

Answer is A

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Does p^2 = q if p is a prime number?

(1) q^2 – p^2 =0
(2) p^2 = 49

There are 2 variables (p,q) and 1 equation (p^2=q) in the original condition, 2 equations in the given conditions. This makes (D) our likely answer.
For condition 1, q^2-p^2=q^2-q=0, or q(q-1)=0, or q=0,1 --< p=0,1. They are all not prime numbers, so 'no' and is sufficient.
For condition 2, this answers the question 'yes' for p=7, but 'no' for p=-7, so this is insufficient.
The answer becomes (A).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

If the question stem states that \(p^2=q\) does it not infer that 49=q in 2nd statement?

The stem does not say that p^2 = q, it asks about it: Does p^2 = q if p is a prime number?

That's right.
I guess it is time for me to go to bed

Need to be more accurate at reading the questions.

p is prime. Is p^2 = q?

St1: p^2 - q^2 = 0
(p + q)(p - q) = 0
p + q = 0 or p - q = 0
p = -q or p = q
p is prime --> p can't be negative --> Only valid answer is p = q.
Primes are > 1. So if p = q then \(p^2 \neq {q}\)
Sufficient

St2: p^2 = 49 --> p = 7 --> Clearly insufficient as no information is provided about q

Answer: A

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