On the first quiz, Tony's score was $12$...... | Free GMAT Practice Question | GMAT Panda

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Question

On the first quiz, Tony's score was 12 points higher than Lisa's score. On the second quiz, Lisa's score was 8 points higher than Tony's score. If Lisa's average score on the three quizzes was 5 points higher than Tony's average score, then Lisa's score on the third quiz was how many points higher than Tony's score?

Answer Choices

A. $3$
B. $11$
C. $19$
D. $21$
E. $27$

Steps

Explanation	Calculations	Help
$We create variables for Tony's and Lisa's scores on each of the three quizzes.$	$T_{1} = Tony’s first quiz score T_{2} = Tony’s second quiz score T_{3} = Tony’s third quiz score L_{1} = Lisa’s first quiz score L_{2} = Lisa’s second quiz score L_{3} = Lisa’s third quiz score$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "On the first quiz, Tony's score was 12 points higher than Lisa's score." into an equation.$	$T_{1} = L_{1} + 12$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "On the second quiz, Lisa's score was 8 points higher than Tony's score." into an equation.$	$L_{2} = T_{2} + 8$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "Lisa's average score on the three quizzes was 5 points higher than Tony's average score." into an equation.$	$\frac{L _{1} + L _{2} + L _{3}}{3} = \frac{T _{1} + T _{2} + T _{3}}{3} + 5$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We eliminate the denominators by multiplying both sides of the equation by 3.$	$L_{1} + L_{2} + L_{3} = T_{1} + T_{2} + T_{3} + 15$
$We substitute the expressions for T_{1} and L_{2} from earlier steps into the equation.$	$L_{1} + (T_{2} + 8) + L_{3} = (L_{1} + 12) + T_{2} + T_{3} + 15$
$We simplify and cancel common terms to isolate L_{3} .$	$L_{1} + T_{2} + 8 + L_{3} = L_{1} + T_{2} + T_{3} + 27 L_{1} + T_{2} + 8 + L_{3} = L_{1} + T_{2} + T_{3} + 27 8 + L_{3} = T_{3} + 27 L_{3} = T_{3} + 27 - 8 L_{3} = T_{3} + 19$	Theory & Tactics Method Card CALC1-A Click to view full details

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Final Answer

C

Question

On the first quiz, Tony's score was 12 points higher than Lisa's score. On the second quiz, Lisa's score was 8 points higher than Tony's score. If Lisa's average score on the three quizzes was 5 points higher than Tony's average score, then Lisa's score on the third quiz was how many points higher than Tony's score?

Answer Choices

A. $3$
B. $11$
C. $19$
D. $21$
E. $27$

Steps

Explanation	Calculations	Help
$We create variables for Tony's and Lisa's scores on each of the three quizzes.$	$T_{1} = Tony’s first quiz score T_{2} = Tony’s second quiz score T_{3} = Tony’s third quiz score L_{1} = Lisa’s first quiz score L_{2} = Lisa’s second quiz score L_{3} = Lisa’s third quiz score$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "On the first quiz, Tony's score was 12 points higher than Lisa's score." into an equation.$	$T_{1} = L_{1} + 12$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "On the second quiz, Lisa's score was 8 points higher than Tony's score." into an equation.$	$L_{2} = T_{2} + 8$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "Lisa's average score on the three quizzes was 5 points higher than Tony's average score." into an equation.$	$\frac{L _{1} + L _{2} + L _{3}}{3} = \frac{T _{1} + T _{2} + T _{3}}{3} + 5$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We eliminate the denominators by multiplying both sides of the equation by 3.$	$L_{1} + L_{2} + L_{3} = T_{1} + T_{2} + T_{3} + 15$
$We substitute the expressions for T_{1} and L_{2} from earlier steps into the equation.$	$L_{1} + (T_{2} + 8) + L_{3} = (L_{1} + 12) + T_{2} + T_{3} + 15$
$We simplify and cancel common terms to isolate L_{3} .$	$L_{1} + T_{2} + 8 + L_{3} = L_{1} + T_{2} + T_{3} + 27 L_{1} + T_{2} + 8 + L_{3} = L_{1} + T_{2} + T_{3} + 27 8 + L_{3} = T_{3} + 27 L_{3} = T_{3} + 27 - 8 L_{3} = T_{3} + 19$	Theory & Tactics Method Card CALC1-A Click to view full details

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Final Answer

C