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OG Which of the following is greatest

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by Jay@ManhattanReview » Thu Aug 17, 2017 9:11 pm
AbeNeedsAnswers wrote:Which of the following is greatest?

A. 10√3

B. 9√4

C. 8√5

D. 7√6

E. 6√7

B
We see that we have to handle square roots here. Let's get rid of them.

One of the ways is to square all the numbers and then compare them.

A. 10√3 => (10√3)^2 = 100 x 3 = 300

B. 9√4 => (9√4)^2 = 81 x 4 = 324

C. 8√5 => (8√5)^2 = 64 x 5 = 320

D. 7√6 => (7√6)^2 = 49 x 6 = 276

E. 6√7=> (6√7)^2 = 36 x 7 = 252

Since 324 is the greatest, option [spoiler]B = 9√4[/spoiler] is the greatest.

The correct answer: B

Hope this helps!

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by Matt@VeritasPrep » Fri Aug 18, 2017 1:40 pm
Since all of these are > 1, we know that if x > y, x² > x² and vice versa. With that in mind, we can square each answer and take the biggest one, which is B.
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by Matt@VeritasPrep » Fri Aug 18, 2017 1:42 pm
Also, a follow up question for all those browsing the forum: if 13 > x > 0, for what positive value of x is x * √(13 - x) the greatest? Your answers will be scored by how elementary they are, the simpler (no calculus!) the better. :D
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by Scott@TargetTestPrep » Wed Nov 15, 2017 3:59 pm
AbeNeedsAnswers wrote:Which of the following is greatest?

A. 10√3

B. 9√4

C. 8√5

D. 7√6

E. 6√7
Let's estimate √3, √5, √6, and √7.

√3 ≈ 1.7

√5 ≈ 2.2

√6 ≈ 2.4

√7 ≈ 2.7

Thus:

A) 10 x 1.7 = 17

B) 9 x 2 = 18

C) 8 x 2.2 = 17.6

D) 7 x 2.4 = 16.8

E) 6 x 2.7 = 16.2

Alternate Solution:

Another way to get rid of the roots to compare each answer is to square each answer choice:

A) (10√3)^2 = 100 x 3 = 300

B) (9√4)^2 = 81 x 4 = 324

C) (8√5)^2 = 64 x 5 = 320

D) (7√6)^2 = 49 x 6 = 294

E) (6√7)^2 = 36 x 7 = 252

Answer: B

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Re: OG Which of the following is greatest

by [email protected] » Mon Apr 19, 2021 8:26 pm
Hi All,

We’re asked which of the 5 answer choices is GREATEST. Calculating all of those square roots would be tedious; thankfully, we can modify all 5 answer choices in the same way so that we can AVOID doing those specific calculations.

From the wording of the prompt, we know that one of the 5 answers is clearly largest, so if we multiplied all the answers by 2, then the largest answer would still be largest. If we added 1 to each answer, then the largest answer would still be greatest. Etc.

So what can we do to eliminate those square root signs? SQUARE each answer…

Answer A becomes (10)(10)(3) = 300
Answer B becomes (9)(9)(4) = 324
Answer C becomes (8)(8)(5) = 320
Answer D becomes (7)(7)(6) = 294
Answer E becomes (6)(6)(7) = 252

Final Answer: B

GMAT Assassins aren’t born, they’re made,
Rich
Contact Rich at [email protected]
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