Four students, Jackie, Mandy, Bertrand, and Tao, took a science quiz. If Mandy scored 30% higher than Bertrand did, Tao scored 20% lower than Jackie did, and Jackie scored 40% higher than Mandy did, how much lower did Bertrand score than Tao?
Choose the correct choice from the following choices:
A) 50% lower B) 20% lower C) 5% lower D) 40% lower E) 30% lower
In this word problem, the first key is to turn the story into equations:   Mandy scored 30% higher than Bertrand did: M = 0.30 + B   Tao scored 20% lower than Jackie did: T = J - 0.20   Jackie scored 40% higher than Mandy did: J = 0.40 + M   Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and T (how much higher did Bertrand score than Tao did?). This means that your goal is to get the equations in terms of B and T so that you can solve for the expression B - T.   Taking the first equation and solving for B, you have B = M - 0.30.   Taking the second equation and solving for T you have T = J - 0.20, and then with the third equation you can replace J with 0.40 + M so that both B and T are in terms of M: T = (0.40 + M) - 0.20.   So if B = M - 0.30 and T = M + 0.20, then:   B - T = (M - 0.30) - (M + 0.20)   B - T = M - 0.30 - M - 0.20 (remove the parentheses by distributing the multiplication)   B - T = -0.50, so the answer is 50% lower.
<result>A</result>
Four students, Jackie, Mandy, Bertrand, and Tao, took a science quiz. If Mandy scored 30% higher than Bertrand did, Tao scored 20% lower than Jackie did, and Jackie scored 40% higher than Mandy did, how much lower did Bertrand score than Tao?