Last visit was: 15 Nov 2024, 11:22 It is currently 15 Nov 2024, 11:22

Close

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

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.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29961
Own Kudos [?]: 36232 [41]
Given Kudos: 25906
Send PM
Most Helpful Expert Reply
Verbal Expert
Joined: 18 Apr 2015
Posts: 29961
Own Kudos [?]: 36232 [28]
Given Kudos: 25906
Send PM
Most Helpful Community Reply
avatar
Intern
Intern
Joined: 26 Jan 2019
Posts: 1
Own Kudos [?]: 24 [24]
Given Kudos: 0
Send PM
General Discussion
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12189 [11]
Given Kudos: 136
Send PM
xy < 0 [#permalink]
8
1
2
Bookmarks
Carcass wrote:
\(xy < 0\)

\(\frac{a}{x} < \frac{b}{y}\)


Quantity A
Quantity B
ay
bx



Nice question! (I think it's harder than medium)

If \(xy < 0\), then there are two possible cases: EITHER x is positive and y is negative, OR x is negative and y is positive
Let's consider both possible cases.


case i: x is positive and y is negative

Take: \(\frac{a}{x} < \frac{b}{y}\)

Multiply both sides by x to get: \(a < \frac{bx}{y}\) [since x is POSITIVE, the inequality symbol REMAINS facing the same direction]

Now multiply both sides by y to get: \(ay > bx\) [since y is NEGATIVE, the direction of the inequality symbol is REVERSED]

In this case, we get \(ay > bx\), which means Quantity A is greater


case ii: x is negative and y is positive

Take: \(\frac{a}{x} < \frac{b}{y}\)

Multiply both sides by y to get: \(\frac{ay}{x} < b\) [since y is POSITIVE, the inequality symbol REMAINS facing the same direction]

Now multiply both sides by x to get: \(ay > bx\) [since x is NEGATIVE, the direction of the inequality symbol is REVERSED]

In this case, we get \(ay > bx\), which means Quantity A is greater


In BOTH possible cases, we concluded that Quantity A is greater
So, the correct answer is A

Cheers,
Brent

RELATED VIDEO FROM OUR COURSE
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12189 [0]
Given Kudos: 136
Send PM
Re: xy < 0 [#permalink]
1
CarlosSG wrote:
Carcass wrote:
\(xy < 0\)

\(\frac{a}{x} < \frac{b}{y}\)


Quantity A
Quantity B
ay
bx


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.


First, use a/x < b/y

(a/x) - (b/y) < 0
(ay-bx)/xy < 0

but xy<0, so ay-bx>0
Finally ay>bx

ANSWER (A)


Beautiful solution, Carlos!!
Kudos for you!!!!

Cheers,
Brent
avatar
Manager
Manager
Joined: 18 Jun 2019
Posts: 122
Own Kudos [?]: 42 [0]
Given Kudos: 0
Send PM
Re: xy < 0 [#permalink]
I just cross multiplied the second equation and got:
ay < bx.
Therefore B>A. Is that wrong?
Verbal Expert
Joined: 18 Apr 2015
Posts: 29961
Own Kudos [?]: 36232 [3]
Given Kudos: 25906
Send PM
Re: xy < 0 [#permalink]
2
Expert Reply
1
Bookmarks
Is wrong because the stem says that xy<0

Which means that you cannot cross multiply because you do not know which is positive or negative.

Could x or y but not both.

Hope now is more clear.

Regards
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12189 [3]
Given Kudos: 136
Send PM
Re: xy < 0 [#permalink]
3
bellavarghese wrote:
I just cross multiplied the second equation and got:
ay < bx.
Therefore B>A. Is that wrong?


IMPORTANT CONCEPT: If we multiply both sides of an inequality by a NEGATIVE value, we must REVERSE the direction of the inequality sign.
Your solution assumes that x and y are both positive.

Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12189 [5]
Given Kudos: 136
Send PM
Re: xy < 0 [#permalink]
4
1
Bookmarks
Carcass wrote:
\(xy < 0\)

\(\frac{a}{x} < \frac{b}{y}\)


Quantity A
Quantity B
ay
bx



Here's another (faster) approach that one of my students pointed out.


Take: \(\frac{a}{x} < \frac{b}{y}\)

Multiply both sides by \(xy\) to get: \(ay > bx\) [since we multiplied both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol]

Answer: A

Cheers,
Brent
avatar
Active Member
Active Member
Joined: 27 Aug 2019
Posts: 59
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: xy < 0 [#permalink]
1
Carcass wrote:
\(xy < 0\)

\(\frac{a}{x} < \frac{b}{y}\)


Quantity A
Quantity B
ay
bx


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.


Hi Carcass could you please update the solution? (there is still B as answer)

Thank you! :)
Verbal Expert
Joined: 18 Apr 2015
Posts: 29961
Own Kudos [?]: 36232 [0]
Given Kudos: 25906
Send PM
Re: xy < 0 [#permalink]
Expert Reply
Thank you :)

The book still reports A as far as I could see.
Mah :roll:
avatar
Intern
Intern
Joined: 10 Jun 2020
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: xy < 0 [#permalink]
should we not consider the sign of a & b?
avatar
Intern
Intern
Joined: 13 Mar 2020
Posts: 32
Own Kudos [?]: 7 [0]
Given Kudos: 0
Send PM
Re: xy < 0 [#permalink]
good question
avatar
Intern
Intern
Joined: 22 Sep 2020
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: xy < 0 [#permalink]
GreenlightTestPrep wrote:
Carcass wrote:
\(xy < 0\)

\(\frac{a}{x} < \frac{b}{y}\)


Quantity A
Quantity B
ay
bx



Here's another (faster) approach that one of my students pointed out.


Take: \(\frac{a}{x} < \frac{b}{y}\)

Multiply both sides by \(xy\) to get: \(ay > bx\) [since we multiplied both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol]


Answer: A

Cheers,
Brent


Shouldn’t we consider the signs of a and b?
avatar
Intern
Intern
Joined: 24 Oct 2020
Posts: 15
Own Kudos [?]: 17 [0]
Given Kudos: 0
Send PM
Re: xy < 0 [#permalink]
1
The second condition which is (a/x) < (b/y) is what's governing the signal alternation between a & b.

In other words, if x was -ve then a should be +ve to fulfill the condition above, and y should be positive to fulfill the first condition xy<0.

For example:

Take x = -1 , y = 2

a = 3 , b = -4 (or 4)

it will give us a/x < b/y

-3 < -2 (2) => ay = 6, bx = 4 (-4). And both ways ay > bx

The second condition makes the question solvable i believe
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 170 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: xy < 0 [#permalink]
CarlosSG wrote:
Carcass wrote:
\(xy < 0\)

\(\frac{a}{x} < \frac{b}{y}\)


Quantity A
Quantity B
ay
bx


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.


First, use a/x < b/y

(a/x) - (b/y) < 0
(ay-bx)/xy < 0

but xy<0, so ay-bx>0
Finally ay>bx

ANSWER (A)

BEST APPROACH
avatar
Intern
Intern
Joined: 22 May 2021
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: xy < 0 [#permalink]
Posted from my mobile device
Retired Moderator
Joined: 09 Jan 2021
Posts: 576
Own Kudos [?]: 846 [2]
Given Kudos: 194
GRE 1: Q167 V156
GPA: 4
WE:Analyst (Investment Banking)
Send PM
Re: xy < 0 [#permalink]
2
Hello!

Solution:

Firstly as xy<0

x=+ve; y=-ve
x=-ve; y=+ve

Now, let work on the other given info, using the above
a/x<b/y
This means, x and a carry different signs because if the have the same signs it can be greater than the RHS and y and b carry the same signs.

So, if x=+ve; a--> -ve & y=-ve and b-->-ve
Thus, Qty A: -ve x -ve= +ve
Qty B: +ve x -ve= -ve

Similarly, x=-ve; y=+ve then,
Qty A: +ve x +ve= +ve
Qty B: +ve x -ve= -ve

Thus, in both of the above cases A>B

IMO A

Hope this helps!
Intern
Intern
Joined: 22 Jul 2021
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 411
GRE 1: Q166 V167
Send PM
Re: xy < 0 [#permalink]
Beautifully simple! What an elegant solution.

GreenlightTestPrep wrote:
Carcass wrote:
\(xy < 0\)

\(\frac{a}{x} < \frac{b}{y}\)


Quantity A
Quantity B
ay
bx



Here's another (faster) approach that one of my students pointed out.


Take: \(\frac{a}{x} < \frac{b}{y}\)

Multiply both sides by \(xy\) to get: \(ay > bx\) [since we multiplied both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol]

Answer: A

Cheers,
Brent
avatar
Intern
Intern
Joined: 04 Jan 2023
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 64
Send PM
Re: xy < 0 [#permalink]
Carcass wrote:
Thank you :)

The book still reports A as far as I could see.
Mah :roll:



Can I tell that y is -ve, b is -ve so b/y is +ve and x is +ve a/x is +ve
So, both a/x and b/y are +ve but magnitude of b/y is greater
In this case how will you proceed?
Prep Club for GRE Bot
Re: xy < 0 [#permalink]
 1   2   
Moderators:
GRE Instructor
78 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne