Product of LCM and HCF of two numbers is equal to the product of the numbers

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There is a mistake in a question, it shouldn't be by what percent c is greater than |b|, I suppose it should be just a different or something like that, if so, the answer is C

Before moving to the statements I would like to mention that -p*-q=c and -p-q = b

Statement 1: Not sufficient. Can be any number. Ex: 12 and -19, |12+1|=|-10-3| or let's say -5 and -1, |-5+1|= |-1-3|

Statement 2: Again not sufficient. From this statement, we can find the value of |p|*|q| which is GCF*LCM= 2*12=24, from here we can have the following combinations of values of P and Q: (12, 2), (-12 , 2), (-12,- 2), (-2 , 12), (4, 6), (-4 ,-6), (-4, 6) and (-6, 4)

Combining this 2 statements together we can say that P and Q must be equal to (-4, 6) as this is the only pair that satisfies the statement 1. |6+1|=|-4-3| 7=7. Now we can calculate the C and b: C=-6*4=-24 b=-6+4=-2 and |b|=2
C is not greater than |b|. However, you cannot find the percent difference between these 2 numbers as one of them is negative, while the other is positive
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We have quadratic equation ax^2 + bx + c = 0(where a, b and c are constants and a>0)
We need to find out what percentage is 'c' greater than |b|(absolute value of b). Also known are the roots of the roots are p and q.

(1) |p+1| = |q–3|
Assume values for p and q which satisfy the equation.
Example 1 : p=+2,q=+5. A quadratic equation can be formed by (x-p)(x-q)
(x-2)(x-5) => x^2 -7x +10 = 0. Here c(10) is around 42.85% greater than |b|, which is 7.
Example 2 : p=+2,q=0. A quadratic equation can be formed by (x-p)(x-q)
(x-2)(x) => x^2 -2x +1 = 0 Here c(1) is around 50% lesser than |b|, which is 2. Clearly insufficient.

(2) The greatest number that divides both |p| and |q| is 2 and the smallest number that is divisible by both |p| and |q| is 12
Example 1 : p=-2,q=-6 A quadratic equation can be formed by (x-p)(x-q)
(x+2)(x+6) => x^2+4x+12 Here c(12) is around 200% greater than |b|, which is 4.
Example 2: p=-4,q=-6 A quadratic equation can be formed by (x-p)(x-q)
(x+4)(x+6) => x^2+10x+24 Here c(24) is around 140% greater than |b|, which is 10.Clearly insufficient.

When we combine both the statements, The only value possible for p & q, is p=-4,q=6

When p=-4,q=6 the conditions in both the statements are satisfied and the quadratic equation x^2 - 2x - 24=0
This has value of c(24) which is 1100% greater than |b|. Hence the combination of these statements is sufficient(Option C)
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GMATinsight Can you share an easier explanation to this question?