It is currently 14 Dec 2017, 11:10

# Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1 | UCLA R1

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is x^2 + xy > 5xy – 4y^2?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4472

Kudos [?]: 3154 [0], given: 0

GPA: 3.82
Is x^2 + xy > 5xy – 4y^2? [#permalink]

### Show Tags

17 Nov 2017, 00:13
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:04) correct 42% (01:04) wrong based on 38 sessions

### HideShow timer Statistics

[GMAT math practice question]

Is $$x^2 + xy > 5xy – 4y^2$$?

1) $$x > 2y$$
2) $$x > y$$
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 3154 [0], given: 0

Math Expert
Joined: 02 Aug 2009
Posts: 5349

Kudos [?]: 6128 [0], given: 121

Re: Is x^2 + xy > 5xy – 4y^2? [#permalink]

### Show Tags

17 Nov 2017, 01:19
MathRevolution wrote:
[GMAT math practice question]

Is $$x^2 + xy > 5xy – 4y^2$$?

1) $$x > 2y$$
2) $$x > y$$

Get the terms to one side to simplify..
$$x^2+xy>5xy-4y^2........x^2-4xy+4y^2>0......(x-2y)^2>0$$
The left side will always be non negative as it is to power of 2..
So ans will be YES other than when x=2y

Let's check the statements..

1) x>2y
So clearly x is NOT EQUAL to 2y... Yes
Sufficient

2) x>y...
If x =2y and is NO
Otherwise YES
Insufficient

A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6128 [0], given: 121

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4472

Kudos [?]: 3154 [0], given: 0

GPA: 3.82
Re: Is x^2 + xy > 5xy – 4y^2? [#permalink]

### Show Tags

19 Nov 2017, 17:22
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the numbers of variables and equations.

Modifying the original condition and question:
$$x^2 + xy > 5xy – 4y^2$$
⇔ $$x^2 - 4xy + 4y^2 > 0$$
⇔$$(x – 2y)^2 > 0$$
⇔ $$x ≠ 2y$$
The question, ‘Is $$x^2 + xy > 5xy – 4y^2$$ ?’, is equivalent to asking if $$x ≠ 2y$$.

Condition 1)
This is sufficient because $$x > 2y$$ implies that $$x ≠ 2y$$.

Condition 2)
If x=3 and y=1, then $$(x-2y)^2=1>0$$, and the answer is ‘yes’.
If x=2 and y=1, then $$(x-2y)^2=0$$, and the answer is ‘no’.
This is NOT sufficient.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 3154 [0], given: 0

Re: Is x^2 + xy > 5xy – 4y^2?   [#permalink] 19 Nov 2017, 17:22
Display posts from previous: Sort by