GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Aug 2020, 02:33

### 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

# In the figure above a > b. Is the area of the shaded region greater th

Author Message
TAGS:

### Hide Tags

Manager
Joined: 31 May 2020
Posts: 204
In the figure above a > b. Is the area of the shaded region greater th  [#permalink]

### Show Tags

11 Jul 2020, 10:14
2
00:00

Difficulty:

75% (hard)

Question Stats:

50% (03:04) correct 50% (02:44) wrong based on 22 sessions

### HideShow timer Statistics

Attachment:

a.JPG [ 12.48 KiB | Viewed 227 times ]
In the figure above a > b. Is the area of the shaded region greater than half the area of square WXYZ?

(1) $$a^2 + b^2 > 6ab$$

(2) $$a > 6b$$
Manager
Joined: 31 May 2020
Posts: 204
Re: In the figure above a > b. Is the area of the shaded region greater th  [#permalink]

### Show Tags

11 Jul 2020, 10:22
Area of square WXYZ = $$(a+b)^2$$
Area of shaded regiion = $$(a-b)^2$$

To find: $$(a-b)^2>\frac{1}{2}*(a+b)^2?= a^2+b^2>6ab?$$

Statement 1: Tells us that a^2+b^2 is greater than 6ab. Sufficient.

Statement 2: a>6b.. Assume a=7b.
Thus, $$(7b-b)^2>\frac{1}{2}(7b+b)^2? --> 72b^2>64b^2--> b^2>0?$$
Since, b>0 in the square given, b^2>0.... Sufficient.

Option (D)
Re: In the figure above a > b. Is the area of the shaded region greater th   [#permalink] 11 Jul 2020, 10:22