Which of the following is greatest?
A. 10√3
B. 9√4
C. 8√5
D. 7√6
E. 6√7
B
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OG Which of the following is greatest
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AbeNeedsAnswers
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Jay@ManhattanReview
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We see that we have to handle square roots here. Let's get rid of them.AbeNeedsAnswers wrote:Which of the following is greatest?
A. 10√3
B. 9√4
C. 8√5
D. 7√6
E. 6√7
B
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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Matt@VeritasPrep
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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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Matt@VeritasPrep
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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. 
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Scott@TargetTestPrep
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Let's estimate √3, √5, √6, and √7.AbeNeedsAnswers wrote:Which of the following is greatest?
A. 10√3
B. 9√4
C. 8√5
D. 7√6
E. 6√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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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
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
