Problem Solving

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:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, .....
A) 2√2 - 1 ≈ 2(1.4) - 1 ≈2.8 - 1 ≈1.8
B) √2 + 1 ≈1.4 + 1 ≈2.4
C) 1 - √2 ≈1 - 1.4 ≈-0.4
D) √2 - 1 ≈1.4 - 1 ≈0.4
E) √2 ≈ 1.4

The third greatest value is √2

Answer: E

Cheers,
Brent

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 √2 is GREATER than 1, you can simply 'compare' answer choices (and avoid doing almost every calculation).

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

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 √2 + √2 -1. Since √2 is greater than 1, we know that (√2 - 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

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 √2 ≈ 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