|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
![If [x^2-16]/[x^2+6x+8]=y and x>-2, which of the following is an expres](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If [x^2-16]/[x^2+6x+8]=y and x>-2, which of the following is an expres"){kind=icon}
27 May 2025, 11:01
Kudos
Bookmarks
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (01:19) correct
0% (00:00) wrong based on 3 sessions
History
Date
Time
Result
Not Attempted Yet
If \(\frac{x^2-16}{x^2+6x+8}=y\) and \(x>-2,\) which of the following is an expression for x in terms of y?
A. \(\frac{1+y}{2-y}\)
B. \(\frac{2y+4}{1-y}\)
C. \(\frac{4y-4}{y+1}\)
D. \(\frac{2y-4}{2+y}\)
E. \(\frac{y+4}{y+1}\)
A. \(\frac{1+y}{2-y}\)
B. \(\frac{2y+4}{1-y}\)
C. \(\frac{4y-4}{y+1}\)
D. \(\frac{2y-4}{2+y}\)
E. \(\frac{y+4}{y+1}\)
31 May 2025, 02:04
Kudos
Bookmarks
OE
Pick a value for x that will simplify your calculations. 4 would work, since 4 is greater than –2, and plugging in 4 for x in the denominator does not cause the denominator to equal 0. When x equals 4, then \(x^2 - 16 = 4^2 - 16 = 0,\) and so the entire fraction on the left side of the equation is equal to zero.
Now, substitute 0 for y in each answer choice in turn. Each choice is an expression for x in terms of y, and since y = 0 when x = 4, the correct answer will have to give a value of 4 when y = 0. Just remember to evaluate all the answer choices, because you might find more than one that gives a result of 4.
Substituting 0 for y in choices (A), (C), and (D) yields \(\frac{1}{2}, \frac{-4}{1,}\) and \(\frac{-4}{2}\) respectively, so none of those choices can be right. But both (B) and (E) give results of 4 when you make the substitution; choosing between them will require picking another number.
Again, pick a number that will make calculations easy. If x = 0, then y=
\(\frac{x^2-16}{x^2+6x+8} = \frac{0-16}{0+0+8} = \frac{-16}{8}= -2\)
Therefore, y = -2 when x = 0. You don’t have to try the new value of y in all the answer choices, just in (B) and (E). When you substitute -2 for y in choice (B), you get 0. That’s what you’re looking for, but again, you have to make sure it doesn’t work in choice (E). Plugging -2 in for y in (E) yields -2 for x, so (B) is correct.
Answer: B
Pick a value for x that will simplify your calculations. 4 would work, since 4 is greater than –2, and plugging in 4 for x in the denominator does not cause the denominator to equal 0. When x equals 4, then \(x^2 - 16 = 4^2 - 16 = 0,\) and so the entire fraction on the left side of the equation is equal to zero.
Now, substitute 0 for y in each answer choice in turn. Each choice is an expression for x in terms of y, and since y = 0 when x = 4, the correct answer will have to give a value of 4 when y = 0. Just remember to evaluate all the answer choices, because you might find more than one that gives a result of 4.
Substituting 0 for y in choices (A), (C), and (D) yields \(\frac{1}{2}, \frac{-4}{1,}\) and \(\frac{-4}{2}\) respectively, so none of those choices can be right. But both (B) and (E) give results of 4 when you make the substitution; choosing between them will require picking another number.
Again, pick a number that will make calculations easy. If x = 0, then y=
\(\frac{x^2-16}{x^2+6x+8} = \frac{0-16}{0+0+8} = \frac{-16}{8}= -2\)
Therefore, y = -2 when x = 0. You don’t have to try the new value of y in all the answer choices, just in (B) and (E). When you substitute -2 for y in choice (B), you get 0. That’s what you’re looking for, but again, you have to make sure it doesn’t work in choice (E). Plugging -2 in for y in (E) yields -2 for x, so (B) is correct.
Answer: B
