Automobile A is traveling at two-thirds the speed that Automobile B

Question

Automobile A is traveling at two-thirds the speed that Automobile B is traveling. How fast is Automobile A traveling?

(1) If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling.

(2) If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling

Stardust Chris · Answer

Let‘s call Automobile A‘s current speed A and Automobile B‘s current speed B. The question stem tells us that  A=\frac{2}{3}B . Statement (1) tells us that  A+10=\frac{3}{4}(B+10) . Thus, between the question stem and Statement (1), we have two non-identical equations, which means we can solve for our two variables. Rule out B, C, and E.

Statement (2) tells us that  A-10=\frac{1}{2}(B-10) . Once again, we have two non-identical equations and two variables. Statement (2) is sufficient, and the correct answer is D.

GMATinsight · Answer

Speed of A = A
Speed of B = B

Then, A=(2/3)B

Question: A = ?

Statement 1: If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling.

(A+10) = (3/4) (B+10)
Substituting B from the previous relationship of A and B
(A+10) = (3/4) (3/2A+10)
8A + 80 = 9A + 60
i.e. A = 20
SUFFICIENT

Statement 2: If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling

(A-10) = (1/2) (B-10)
Substituting B from the previous relationship of A and B
We can find the value of A
i.e. A = 20
SUFFICIENT

Answer: Option  D

BrentGMATPrepNow · Answer

Given : Automobile A is traveling at two-thirds the speed that Automobile B is traveling.   
Let A = Car A's speed
Let B = Car B's speed
So, we can write:  A = (2/3)B

Target question :    What is the value of A?

Statement 1 : If both automobiles increased their speed by 10 miles per hour, Automobile A would be traveling at three-quarters the speed that Automobile B would be traveling.  
Car A's new speed = A + 10
Car B's new speed = B + 10
So, we can write:  A + 10 = (3/4)(B + 10) 
We already know that:  A = (2/3)B 
IMPORTANT: Since we have a system of 2 different linear equations with 2 variables, we COULD solve the system for A and B (but we'd never waste valuable time on test day doing so)
So, we COULD answer the  target question  with certainty. 
Statement 1 is SUFFICIENT

Statement 2 : If both automobiles decreased their speed by 10 miles per hour, Automobile A would be traveling at half the speed that Automobile B would be traveling 
Car A's new speed = A - 10
Car B's new speed = B - 10
So, we can write:  A - 10 = (1/2)(B - 10) 
We already know that:  A = (2/3)B 
Once again, we have a system of 2 different linear equations with 2 variables, which we COULD solve for A and B.
Statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

fskilnik · Answer

Excellent opportunity for  the k technique , one of our powerful tools when dealing with ratios!

A = {2 \over 3}B\,\,\,\,\,\mathop \Rightarrow \limits^{B\,\, 
e \,\,0} \,\,\,\,\,{A \over B} = {2 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
 \,A = 2k \hfill \cr 
 \,B = 3k \hfill \cr} ight.\,\,\,\,\,\left( {k > 0} ight)\,\,\,\,\,\,\,\,\,\left

? = A\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,? = k\,}

\left( 1 ight)\,\,\,2k + 10 = {3 \over 4}\left( {3k + 10} ight)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,k\,\,\,{m{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{m{SUFF}}.

\left( 2 ight)\,\,\,2k - 10 = {1 \over 2}\left( {3k - 10} ight)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,k\,\,\,{m{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{m{SUFF}}.

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

Amestryyz · Answer

its a very tricky..question.

bumpbot · Answer

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Automobile A is traveling at two-thirds the speed that Automobile B

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