Of the following, which one is third greatest?

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Oct 23, 2017 4:27 am

Of the following, which one is third greatest?

$$A.\ 2\sqrt{2}\ -\ 1$$

$$B.\ \sqrt{2}\ +\ 1$$

$$C.\ 1\ -\ \sqrt{2}$$

$$D.\ \sqrt{2}\ -\ 1$$

$$E.\ \sqrt{2}\ $$

How will i start the solution to this problem?

OA E

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Source: Beat The GMAT — Problem Solving | Mon Oct 23, 2017 4:27 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 23, 2017 4:38 am

lheiannie07 wrote:Of the following, which one is third greatest?

$$A.\ 2\sqrt{2}\ -\ 1$$

$$B.\ \sqrt{2}\ +\ 1$$

$$C.\ 1\ -\ \sqrt{2}$$

$$D.\ \sqrt{2}\ -\ 1$$

$$E.\ \sqrt{2}\ $$

How will i start the solution to this problem?

OA E

Everyone should be sure to memorize the following roots for test day:
âˆš2 â‰ˆ 1.4
âˆš3 â‰ˆ 1.7
âˆš5 â‰ˆ 2.2

So, .....
A) 2âˆš2 - 1 â‰ˆ 2(1.4) - 1 â‰ˆ2.8 - 1 â‰ˆ1.8
B) âˆš2 + 1 â‰ˆ1.4 + 1 â‰ˆ2.4
C) 1 - âˆš2 â‰ˆ1 - 1.4 â‰ˆ-0.4
D) âˆš2 - 1 â‰ˆ1.4 - 1 â‰ˆ0.4
E) âˆš2 â‰ˆ 1.4

The third greatest value is âˆš2

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

Of the following, which one is third greatest?

by GMATGuruNY » Mon Oct 23, 2017 4:40 am

lheiannie07 wrote:Of the following, which one is third greatest?

$$A.\ 2\sqrt{2}\ -\ 1$$

$$B.\ \sqrt{2}\ +\ 1$$

$$C.\ 1\ -\ \sqrt{2}$$

$$D.\ \sqrt{2}\ -\ 1$$

$$E.\ \sqrt{2}\ $$

How will i start the solution to this problem?

OA E

âˆš2 â‰ˆ 1.4.

A: 2âˆš2 - 1 â‰ˆ (2)(1.4) - 1 = 1.8.
B: âˆš2 + 1 â‰ˆ 1.4 + 1 = 2.4.
C: 1 - âˆš2 â‰ˆ 1 - 1.4 = -0.4.
D: âˆš2 - 1 â‰ˆ 1.4 - 1 = 0.4
E: âˆš2 â‰ˆ 1.4.

As the results above indicate, the third greatest is the option in green.

The correct answer is E.

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by [email protected] » Mon Oct 23, 2017 1:21 pm

Hi lheiannie07,

We're asked which of the 5 choices is '3rd greatest.' As 'scary' as this question might look, as long as you recognize that âˆš2 is GREATER than 1, you can simply 'compare' answer choices (and avoid doing almost every calculation).

Answer A: 2âˆš2 - 1
Answer B: âˆš2 + 1
Answer C: 1 - âˆš2
Answer D: âˆš2 - 1
Answer E: âˆš2

To start, we can look for patterns and similarities in the answer choices to make some easy deductions:
Answer C is the only NEGATIVE answer, so it's "5th"
Answer B > Answer E > Answer D (because of the "+1" and "-1"

Answer A can be rewritten as âˆš2 + âˆš2 -1. Since âˆš2 is greater than 1, we know that (âˆš2 - 1) would give us a positive result. Thus, Answer A > Answer E.

We now know that two of the Answers are GREATER than E (Answers A and B) and two of the answers are LESS than E (Answers C and D). Thus, the 3rd largest answer is....

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Mon Dec 04, 2017 10:49 am

lheiannie07 wrote:Of the following, which one is third greatest?

$$A.\ 2\sqrt{2}\ -\ 1$$

$$B.\ \sqrt{2}\ +\ 1$$

$$C.\ 1\ -\ \sqrt{2}$$

$$D.\ \sqrt{2}\ -\ 1$$

$$E.\ \sqrt{2}\ $$

Since âˆš2 â‰ˆ 1.4, we can analyze each answer choice:

A) 2 x 1.4 - 1 = 1.8

B) 1.4 + 1 = 2.4

C) 1 - 1.4 = -0.4

D) 1.4 - 1 = 0.4

E) 1.4

So the 3rd greatest is choice E, 1.4.

Answer: E

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