GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 20:15

### 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

# M70-21

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58445

### Show Tags

03 Sep 2018, 05:16
00:00

Difficulty:

35% (medium)

Question Stats:

80% (02:07) correct 20% (02:15) wrong based on 5 sessions

### HideShow timer Statistics

Which of the following equals $$(1 + \sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}})^2 - (\sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}})^2$$

A. $$\sqrt{5}+\sqrt{3}+1$$
B. $$1-\sqrt{3}-\sqrt{5}$$
C. $$2\sqrt{2}$$
D. $$4$$
E. $$4\sqrt{5}-4\sqrt{3}$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58445

### Show Tags

03 Sep 2018, 05:16
1
Official Solution:

Which of the following equals $$(1 + \sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}})^2 - (\sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}})^2$$

A. $$\sqrt{5}+\sqrt{3}+1$$
B. $$1-\sqrt{3}-\sqrt{5}$$
C. $$2\sqrt{2}$$
D. $$4$$
E. $$4\sqrt{5}-4\sqrt{3}$$

The expression $$(1 + \sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}})^2 - (\sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}})^2$$ is of the form of the identity $$a^2 – b^2$$, that equals $$(a + b)(a – b)$$. We’ll use it for simplification:

$$(1 + \sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}}+\sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}})(1 + \sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}}-\sqrt{\frac{5}{4}} - \sqrt{\frac{3}{4}})=$$

$$=(1 + 2*\sqrt{\frac{5}{4}}+ 2*\sqrt{\frac{3}{4}})(1)$$

Looking at the answers, we see none have fractions, so we’ll simplify:

$$=1 + 2*\sqrt{\frac{5}{4}}+ 2*\sqrt{\frac{3}{4}}$$

$$=1 + 2(\sqrt{\frac{5}{4}}+ \sqrt{\frac{3}{4}})$$

$$=1 + 2(\sqrt{\frac{1}{4}})(\sqrt{5}+ \sqrt{3})$$

$$=1 + 2(\frac{1}{2})(\sqrt{5}+ \sqrt{3})$$

$$=1 + \sqrt{5}+ \sqrt{3}$$

_________________
Re M70-21   [#permalink] 03 Sep 2018, 05:16
Display posts from previous: Sort by

# M70-21

Moderators: chetan2u, Bunuel