∛(328 - 800 - 48) is
A) Between -4 and -5
B) Between -5 and -6
C) Between -6 and -7
D) Between -7 and -8
E) Less than -8
There are a few different ways to solve this one.
OA: E
∛(328 - 800 - 48)
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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,
For anyone looking for a hint as to how to solve this quickly...
[spoiler]The GMAT will never expect you to do a super-complex calculation to get to the correct answer, so you should look at how the entire prompt is designed - there will almost certainly be a way to avoid that complex calculation. Here, it's the answer choices. Notice how they're all RANGES - you can use that to your advantage. Can you calculate (-4)^3 and (-5)^3? Then you have the range for Answer A. Does the prompt fit in that range? If not, then you have to keep working until you find the range that it does fit into. And you don't necessarily have to define all of the ranges to get the correct answer...[/spoiler]
GMAT assassins aren't born, they're made,
Rich
For anyone looking for a hint as to how to solve this quickly...
[spoiler]The GMAT will never expect you to do a super-complex calculation to get to the correct answer, so you should look at how the entire prompt is designed - there will almost certainly be a way to avoid that complex calculation. Here, it's the answer choices. Notice how they're all RANGES - you can use that to your advantage. Can you calculate (-4)^3 and (-5)^3? Then you have the range for Answer A. Does the prompt fit in that range? If not, then you have to keep working until you find the range that it does fit into. And you don't necessarily have to define all of the ranges to get the correct answer...[/spoiler]
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Another approach is to use a nice rule that says ∛(ab) = (∛a)(∛b)Brent@GMATPrepNow wrote:∛(328 - 800 - 48) is
A) Between -4 and -5
B) Between -5 and -6
C) Between -6 and -7
D) Between -7 and -8
E) Less than -8
OA: E
We'll also recognize that we can factor out an 8 (and we happens to know that ∛8 = 2)
We get: ∛(328 - 800 - 48) = ∛[8(41 - 100 - 6)
= ∛[(8)(-65)]
= (∛8)(∛-65) [once we apply the above rule]
= (2)(∛-65)
Hmmm, what about (∛-65)?
Well we know that (∛-64) = -4
And we know that (∛-125) = -5
Since -65 lies BETWEEN -64 and -125, we know that (∛-65) lies between -4 and -5
So, let's say that (∛-65) = -4.something
This means that (2)(∛-65) = (2)(-4.something) = some number that's LESS THAN -8
Answer: E
RELATED VIDEO
- Properties of roots: https://www.gmatprepnow.com/module/gmat ... video/1037
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
We can start by combining the values in the parenthesis:Brent@GMATPrepNow wrote:∛(328 - 800 - 48) is
A) Between -4 and -5
B) Between -5 and -6
C) Between -6 and -7
D) Between -7 and -8
E) Less than -8
OA: E
∛(328 - 800 - 48) = ∛-520
Since 8^3 = 512 and 9^3 = 729, (-8)^3 = -512 and (-9)^3 = -729. Since -520 is between -729 and -512, ∛-520 is between -9 and -8, and thus ∛-520 is less than -8.
Answer: E
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
-
- 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
This is ∛-520, so we should look for a cube in the vicinity of 520.
8 * 8 * 8 = 512, so in the positive world, the cube root is slightly greater than 8.
We're in the negative world, so our answer is slightly less than -8, or E.
8 * 8 * 8 = 512, so in the positive world, the cube root is slightly greater than 8.
We're in the negative world, so our answer is slightly less than -8, or E.
-
- 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
Factoring out also seems like a good plan:
∛(-8*(41 - 100 - 6))
∛(-8) * ∛(-41 + 100 + 6)
∛(-8) * ∛65
which is slightly less than -2 * ∛64, or -2 * 4.
∛(-8*(41 - 100 - 6))
∛(-8) * ∛(-41 + 100 + 6)
∛(-8) * ∛65
which is slightly less than -2 * ∛64, or -2 * 4.