s111
GMATinsight Can you share an easier explanation to this question?
s111 Here is my way of solving this question
Quote:
If integers p and q are the roots of the equation ax^2 + bx + c = 0, where a, b and c are constants and a > 0, by what percentage is c greater than |b|?
(1) |p+1| = |q – 3|
(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
Question REPHRASED: We need to know the sign and value of c and the absolute value of b to answer the questionStatement 1: |p+1| = |q – 3|multiple solutions are possible hence
NOT SUFFICIENT
Statement 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 12i.e. HCF of |p| and |q| = 2
and LCM of |p| and |q| = 12
Property: Product of two numbers = Product of their LCM and HCF
i.e. |p| * |q| = 2*12 = 24
Product of factors of any quadratic equation ax^2 + bx + c = 0 is given by c/a
i.e. product of roots here = +24 or -24 (as signs of p and q are still unknown)
still no information about b hence
NOT SUFFICIENT
Combining the two statementsWe have |p+1| = |q – 3| and |p| * |q| = 24
24 may be written in following ways (i.e. values of |p| and |q| may be as follows in any order)
1*24 but this pair of values does NOT satisfy |p+1| = |q – 3|
2*12 but this pair of values do NOT satisfy |p+1| = |q – 3|
3*8 but this pair of values do NOT satisfy |p+1| = |q – 3|
4*6 this satisfies if p = 6 and q = -4
i.e. roots of the equation are 6 and -4
i.e. \(ax^2 + bx + c = (x-6)*(x+4)\)
i.e. \(ax^2 + bx + c = x^2 - 2x - 24\)
i.e. a = 1, b = -2 and c = -24
now we can calculate with CERTAINTY the percentage required hence
SUFFICIENT
Answer: Option C