Which of the following is greatest?
A. 10√3
B. 9√4
C. 8√5
D. 7√6
E. 6√7
B
OG Which of the following is greatest
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 394
- Joined: Sun Jul 02, 2017 10:59 am
- Thanked: 1 times
- Followed by:5 members
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
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!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Singapore | London | Dubai | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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.
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7244
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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