GRE Prep 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.
Sep 28Live Online Class with Top GRE Expert Mike Butville
08:00 PM EDT
-10:00 PM EDT
Top scores are possible when you enroll in a powerful GRE course, taught live online + 6 months access to TTP GRE OnDemand video courses included! Class starts Mon/Wed Sept. 28, 2026 - Dec. 9, 2026, 8:00pm-10:00pm EST
0 < x < y
[#permalink]
02 Apr 2019, 09:31
02 Apr 2019, 09:31
Expert Reply
00:00
Question Stats:
52% (01:05) correct
47% (00:45) wrong based on 36 sessions
Hide Show timer Statistics
\(0 < x < y\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(x+\frac{1}{x}\) |
\(y + \frac{1}{y}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: 0 < x < y
[#permalink]
03 Apr 2019, 02:37
03 Apr 2019, 02:37
Expert Reply
This is a good one for picking numbers. Particularly, the range of possible values is so large, especially for y, that I'm sure we can get a D answer.
So first, the low hanging fruit. If y = 999, and x = \(\frac{1}{2}\), then quantity A is somewhere around 2, and quantity B is somewhere close to 1000. So clearly quantity B can be greater.
But now let's go to the opposite extreme. Let's say x = 0.001 and y = \(\frac{1}{2}\). In this case, quantity A is somewhere around 1000, while quantity B is stuck around 2. Quantity A, then, can also be greater.
The range of possible values here is far too great, so choice D is our answer.
So first, the low hanging fruit. If y = 999, and x = \(\frac{1}{2}\), then quantity A is somewhere around 2, and quantity B is somewhere close to 1000. So clearly quantity B can be greater.
But now let's go to the opposite extreme. Let's say x = 0.001 and y = \(\frac{1}{2}\). In this case, quantity A is somewhere around 1000, while quantity B is stuck around 2. Quantity A, then, can also be greater.
The range of possible values here is far too great, so choice D is our answer.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
0 < x < y
[#permalink]
03 Apr 2019, 07:24
03 Apr 2019, 07:24
1
Carcass wrote:
\(0 < x < y\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(x+\frac{1}{x}\) |
\(y + \frac{1}{y}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Notice that x and 1/x are reciprocals of each other.
Likewise, y and 1/y are reciprocals of each other.
This helps is choose some numbers to test.
Case i: x = 1/2 and y = 2 (notice that I chose two values that are reciprocals of each other)
We get:
QUANTITY A: x + 1/x = 1/2 + 1/(1/2) = 1/2 + 2 = 2.5
QUANTITY B: y + 1/y = 2 + 1/2 = 2.5
In this cases, the two quantities are equal
For the next case, choose ANY two values that satisfy the given condition 0 < x < y
Case ii: x = 1 and y = 2
We get:
QUANTITY A: x + 1/x = 1/1 + 1/1 = 1 + 1 = 2
QUANTITY B: y + 1/y = 2 + 1/2 = 2.5
In this cases, Quantity B is greater
Answer: D
RELATED VIDEO
