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18 Feb 2019, 06:54
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GMATH practice exercise (Quant Class 16)
In the second-degree equation x^2-14x+m = 0, the constant m is a positive integer. If A<B are the roots of this equation, what is the value of B-A ?
(1) m=33
(2) A and B are two primes
In the second-degree equation x^2-14x+m = 0, the constant m is a positive integer. If A<B are the roots of this equation, what is the value of B-A ?
(1) m=33
(2) A and B are two primes
18 Feb 2019, 11:24
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Given that A & B are the two roots of quadratic equation X^2-14X+m=0 and B>A.
using 1st statement, we get the equation X^2-14X+33=0, which gives us two roots, B=11 and A=3. So B-A=8, definite answer.
using 2nd statement, we can say that both roots, A&B, are prime numbers. We also know that in a quadratic equation, sum of roots=-b/a, which gives us A+B=14. Hence B=11 and A=3. Again we have definite answer.
Since each of the statements individually gives us definite value of B-A, answer is D.
using 1st statement, we get the equation X^2-14X+33=0, which gives us two roots, B=11 and A=3. So B-A=8, definite answer.
using 2nd statement, we can say that both roots, A&B, are prime numbers. We also know that in a quadratic equation, sum of roots=-b/a, which gives us A+B=14. Hence B=11 and A=3. Again we have definite answer.
Since each of the statements individually gives us definite value of B-A, answer is D.
18 Feb 2019, 18:23
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fskilnik
\({x^2} - 14x + m = 0\,\,,\,\,\,m \ge 1\,\,{\mathop{\rm int}}\)
\(? = B - A\,\,\,\,\left( {A < B\,\,{\rm{roots}}} \right)\,\,\left( * \right)\)
\(\left( 1 \right)\,\,{\rm{equation}}\,\,{\rm{known}}\,\,\,\,\, \Rightarrow \,\,\,{\rm{the}}\,\,2\,\,{\rm{roots}}\,\,A,B\,\,\,{\rm{known}}\,\,\,\,\mathop \Rightarrow \limits^{A\, < \,B} \,\,\,\,\,A\,\,{\rm{unique}}\,,B\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\)
\(\left( 2 \right)\,\,\left\{ \matrix{\\
A + B = 14 \hfill \cr \\
A < B\,\,{\rm{primes}} \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{inspection}}} \,\,\,\,\,\left( {A,B} \right) = \left( {3,11} \right)\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\)
The correct answer is (D).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
