Last visit was: 18 May 2024, 11:31 It is currently 18 May 2024, 11:31
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624745 [10]
Given Kudos: 81900
Send PM
CAT Tests Forum Quiz Mode
If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3 [#permalink] If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3   09 Dec 2019, 01:32
10
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

45% (01:54) correct 55% (02:10) wrong based on 278 sessions
Hide Show timer Statistics
If k is a non zero integer, is \(k > 0\)?

(1) \(|k - 4| = |k| + 4\)

(2) \(k > k^3\)


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
D
User avatar
G
TestPrepUnlimited
Tutor
Joined: 17 Sep 2014
Posts: 1251
Own Kudos [?]: 950 [4]
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Send PM
Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3 [#permalink] If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3   09 Dec 2019, 09:33
3
Kudos
Expert Reply
Bunuel wrote:
If k is a non zero integer, is \(k > 0\)?

(1) \(|k - 4| = |k| + 4\)

(2) \(k > k^3\)


Are You Up For the Challenge: 700 Level Questions


Statement 1:
The absolute values give us the regions we should check. There are three cases, k > 4, 0 < k < 4, and k < 0. If k > 4, the equation is k - 4 = k + 4 which has no solution. If 0 < k < 4, we get 4 - k = k + 4 and k = 0, which isn't within the region but plugging in k = 0 tells us it's a viable solution. Therefore there are no positive k solutions, k cannot be positive. Sufficient.

Statement 2:
Whenever we are comparing powers of a single variable, we should check the 4 regions: k < -1, -1 < k < 0, 0 < k < 1, and k > 1. We can check the regions by picking a point in the region and if the point satisfies the inequality, the entire region is a solution set. For example, k = 0.5 satisfies this inequality so 0 < k < 1 is a solution set. By plugging in k = -2, we can see the same is true for k < -1. So we can have positive k or negative k, insufficient.

Ans: A
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11266
Own Kudos [?]: 32586 [2]
Given Kudos: 306
Send PM
Reviews Badge Forum Quiz Mode
Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3 [#permalink] If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3   12 Jan 2020, 03:51
2
Kudos
Expert Reply
ShankSouljaBoi If k is a non zero integer, is \(k > 0\)?

(1) \(|k - 4| = |k| + 4\)
Now both sides are positive, so you can square two sides
\(k^2-8k+16=k^2+8|k|+16......|k|=-k\). This will be true ONLY when k is negative.
OR
Logically if you see what is happening to two sides.
The right side is adding two quantities but the left will add only when k and -4 have same sign, so k has to be 0 or <0
Suff

(2) \(k > k^3\)
\(k(1-k^2)>0\)..
If k>0, 1-k^2>0....k^2<1...-1<k<1 but no integer value exists as k is non zero.
When k<0, 1-k^2<0....k^2>1...k<-1
Suff

D
User avatar
S
samarpan.g28
Manager
Manager
Joined: 08 Dec 2023
Posts: 221
Own Kudos [?]: 33 [0]
Given Kudos: 1176
Location: India
Concentration: Strategy, Operations
Schools: HEC Montreal ISB IIM Rotman HEC INSEAD Jan'25 intake
GPA: 4
WE:Engineering (Tech)
Send PM
Forum Quiz Mode
Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3 [#permalink] If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3   29 Apr 2024, 09:03
Bunuel wrote:
If k is a non zero integer, is \(k > 0\)?

(1) \(|k - 4| = |k| + 4\)

(2) \(k > k^3\)


Are You Up For the Challenge: 700 Level Questions

­Hi Bunuel. For statement 1, I later understood that the equation holds only for k<0. But algebraically I could not figure it out therefore I selected B as the correct option. Can you kindly help me understand? Thank you in advance.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624745 [0]
Given Kudos: 81900
Send PM
CAT Tests Forum Quiz Mode
Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3 [#permalink] If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3   30 Apr 2024, 01:03
Expert Reply
samarpan.g28 wrote:
Bunuel wrote:
If k is a non zero integer, is \(k > 0\)?

(1) \(|k - 4| = |k| + 4\)

(2) \(k > k^3\)


Are You Up For the Challenge: 700 Level Questions

­Hi Bunuel. For statement 1, I later understood that the equation holds only for k<0. But algebraically I could not figure it out therefore I selected B as the correct option. Can you kindly help me understand? Thank you in advance.

­Squaring \(|k - 4| = |k| + 4\) gives:

\(k^2 - 8k + 16 = k^2 +8|k| + 18\)

\(|k| = -k\)

The above is only true when \(k \leq 0\). Since given that k is a non zero integer, then we get \(k<0\).

P.S. Note that such type of pure algebraic questions are no longer a part of the syllabus of the GMAT.­
GMAT Club Bot
gmatclubot
Re: If k is a non zero integer, is k > 0? (1) |k - 4| = |k| + 4 (2) k>k^3 [#permalink]
30 Apr 2024, 01:03
Moderator:
Bunuel
Math Expert
93334 posts