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
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
If x>5 and (4x+y)=8, which of the following must be true?
[#permalink]
12 Sep 2022, 20:05
1
1
Bookmarks
00:00
Question Stats:
0% (00:00) correct
100% (00:42) wrong based on 1 sessions
HideShow
timer Statistics
If x>5 and (4x+y)=8, which of the following must be true?
[A] y<-10 [B] y=-12 [C] y>10 [D] y>-12 [E] y<-14
I get to y<-12, so I guessed that since y<-12<-10 then y<-10 must be true. But other classmates say y<-14 is the correct answer because of the domain of the inequality. What do you think is the correct answer?
If x>5 and (4x+y)=8, which of the following must be true?
[#permalink]
14 Sep 2022, 06:36
1
1
Given that x>5 and (4x+y)=8 and we need to find which of the following is correct
4x + y = 8 => 4x = 8 - y => x = \(\frac{8}{4}\) - \(\frac{y}{4}\) = 2 - \(\frac{y}{4}\)
Now, x > 5 => 2 - \(\frac{y}{4}\) > 5 => \(\frac{y}{4}\) < 2 - 5 => y < -3*4 => y < -12
Now, if we look at the answer choices then only two answer choices stand out
y < -10 and y < -14
y < -14 is incorrect because it DOES NOT CONTAIN all the values which are in the range of y < -12 Ex.: y = -13 which is in the range of y < -12 but not in y < -14
y < -10 on the other hand CONTAINS all the solutions in the range of y < -12
See below image to visualize why y < -10 is correct as
Attachment:
-10 to -14.png [ 4.67 KiB | Viewed 1462 times ]
-> Given that y < -12 then it is implied that y < -10 also, as y < -10 contains y < -12 -> Given that y < -12 then it is NOT necessary that y < -14 as y can very well be -13
So, Answer will be A Hope it helps!
Watch the following video to learn the Basics of Inequalities