Ada and Paul received their scores on three tests.... | Free GMAT Practice Question | GMAT Panda

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Question

Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?

Answer Choices

A. $9$
B. $14$
C. $17$
D. $23$
E. $25$

Steps

Explanation	Calculations	Help
$We create variables for Ada's and Paul's scores on each of the three tests.$	$A_{1} = Ada’s first test score A_{2} = Ada’s second test score A_{3} = Ada’s third test score P_{1} = Paul’s first test score P_{2} = Paul’s second test score P_{3} = Paul’s third test score$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "On the first test, Ada’s score was 10 points higher than Paul’s score." into an equation.$	$A_{1} = P_{1} + 10$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "On the second test, Ada’s score was 4 points higher than Paul’s score." into an equation.$	$A_{2} = P_{2} + 4$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "Paul’s average (arithmetic mean) score on the three tests was 3 points higher than Ada’s average score on the three tests." into an equation.$	$\frac{P _{1} + P _{2} + P _{3}}{3} = \frac{A _{1} + A _{2} + A _{3}}{3} + 3$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We eliminate the denominators by multiplying both sides of the equation by 3.$	$P_{1} + P_{2} + P_{3} = A_{1} + A_{2} + A_{3} + 9$
$We substitute the expressions for A_{1} and A_{2} from earlier steps into the equation.$	$P_{1} + P_{2} + P_{3} = (P_{1} + 10) + (P_{2} + 4) + A_{3} + 9$
$We simplify and cancel common terms to isolate P_{3} .$	$P_{1} + P_{2} + P_{3} = P_{1} + P_{2} + A_{3} + 10 + 4 + 9 P_{1} + P_{2} + P_{3} = P_{1} + P_{2} + A_{3} + 23 P_{3} = A_{3} + 23$

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Final Answer

23 (Choice D)

Question

Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?

Answer Choices

A. $9$
B. $14$
C. $17$
D. $23$
E. $25$

Steps

Explanation	Calculations	Help
$We create variables for Ada's and Paul's scores on each of the three tests.$	$A_{1} = Ada’s first test score A_{2} = Ada’s second test score A_{3} = Ada’s third test score P_{1} = Paul’s first test score P_{2} = Paul’s second test score P_{3} = Paul’s third test score$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "On the first test, Ada’s score was 10 points higher than Paul’s score." into an equation.$	$A_{1} = P_{1} + 10$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "On the second test, Ada’s score was 4 points higher than Paul’s score." into an equation.$	$A_{2} = P_{2} + 4$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "Paul’s average (arithmetic mean) score on the three tests was 3 points higher than Ada’s average score on the three tests." into an equation.$	$\frac{P _{1} + P _{2} + P _{3}}{3} = \frac{A _{1} + A _{2} + A _{3}}{3} + 3$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-C Click to view full details
$We eliminate the denominators by multiplying both sides of the equation by 3.$	$P_{1} + P_{2} + P_{3} = A_{1} + A_{2} + A_{3} + 9$
$We substitute the expressions for A_{1} and A_{2} from earlier steps into the equation.$	$P_{1} + P_{2} + P_{3} = (P_{1} + 10) + (P_{2} + 4) + A_{3} + 9$
$We simplify and cancel common terms to isolate P_{3} .$	$P_{1} + P_{2} + P_{3} = P_{1} + P_{2} + A_{3} + 10 + 4 + 9 P_{1} + P_{2} + P_{3} = P_{1} + P_{2} + A_{3} + 23 P_{3} = A_{3} + 23$

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Final Answer

23 (Choice D)