Last visit was: 21 May 2024, 12:27 It is currently 21 May 2024, 12:27
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Director
Director
Joined: 21 Feb 2017
Posts: 521
Own Kudos [?]: 1054 [27]
Given Kudos: 1091
Location: India
GMAT 1: 700 Q47 V39
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5986
Own Kudos [?]: 13499 [5]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625602 [1]
Given Kudos: 81918
Send PM
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10152
Own Kudos [?]: 16711 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
Expert Reply
|6 - |x + 2|| = 10

| - 10| = 10 and |10| = 10. So we need 6 - |x + 2| = 10 or -10.

=> 6 - |x + 2| = 10 for this 6 - 10 = -4 = |x + 2| (Not possible)

=> 6 - |x + 2| = -10 for this 6 + 10 = 16 = |x + 2|

=> x + 2 = 16 and x = 14 and x + 2 = -16 and x = -18

'x' is a non-negative and hence x = 14 is the value considered.

Answer B
Director
Director
Joined: 16 Jun 2021
Posts: 992
Own Kudos [?]: 183 [0]
Given Kudos: 309
Send PM
Re: If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
Kritisood wrote:
If x is a non-negative integer and |6 - |x + 2|| = 10, then find the number of values of x that satisfy the given absolute value inequality?

a. 0
b. 1
c. 2
d. 3
e. 4



The question simply asks us to find whether |x+2| = 16

=>which is possible in two scenarios that being at x=14 since it's positive it can take this posiibilities

next we have x=-18 which it cannot be included since we require only positive values

Therefore IMO only value satisfies
Hence B
Intern
Intern
Joined: 09 Aug 2023
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 24
Send PM
If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
When should we be solving it the way described in the explanations vs substituting | x+ 2 | with a and solving based on that? Would that even work? Why or why not?

I tried it and got the right answer.. but I think I stumbled onto it through luck
Manager
Manager
Joined: 17 May 2018
Posts: 169
Own Kudos [?]: 22 [0]
Given Kudos: 111
Location: India
Schools: IIM
Send PM
If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
egmat KarishmaB gmatophobia Can you please check whether my approach is correct ?­
Attachments

IMG_8799.JPG
IMG_8799.JPG [ 1.38 MiB | Viewed 550 times ]

Tutor
Joined: 16 Oct 2010
Posts: 14891
Own Kudos [?]: 65406 [1]
Given Kudos: 431
Location: Pune, India
Send PM
Re: If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
1
Kudos
Expert Reply
Kritisood wrote:
If x is a non-negative integer and |6 - |x + 2|| = 10, then find the number of values of x that satisfy the given absolute value inequality?

a. 0
b. 1
c. 2
d. 3
e. 4

i did as follows: |6-x-2|=10 (x+2 will be +ve since x is a non neg integer) => |4-x|=10 (again 4-x should be +ve since x is a non neg integer) 4-x=10 => -6=x hence there should be zero values that satisfy the inequality as x has to be a non neg integer. could someone help pls?

­|6 - |x + 2|| = 10

Since x is non negative, (x+2) will always be positive. So |x + 2| = (x + 2)
|6 - x - 2| = 10
which is equivalent to:
|x - 4| = 10
x is a point at a distance 10 away from 4. There are only 2 such points: -6 and 14

Answer (C)

Absolute values as distances is discussed here:
https://youtu.be/oqVfKQBcnrs
 
Tutor
Joined: 16 Oct 2010
Posts: 14891
Own Kudos [?]: 65406 [1]
Given Kudos: 431
Location: Pune, India
Send PM
Re: If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
1
Kudos
Expert Reply
Can,Will wrote:
egmat KarishmaB gmatophobia Can you please check whether my approach is correct ?­

­It is correct though too many unnecessary calculations. ­
Manager
Manager
Joined: 17 May 2018
Posts: 169
Own Kudos [?]: 22 [0]
Given Kudos: 111
Location: India
Schools: IIM
Send PM
Re: If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
KarishmaB
If p is a non-positive number, then for what value of p does the expression |77 – 6p| holds the minimum value?

A. 77/12
B. 77/6
C. 12
D. 0
E. -77/6

in this problem can we say that since p is a non positive I77-6pI is negative i.e -77+6p
Tutor
Joined: 16 Oct 2010
Posts: 14891
Own Kudos [?]: 65406 [0]
Given Kudos: 431
Location: Pune, India
Send PM
If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
Expert Reply
 
Can,Will wrote:
KarishmaB
If p is a non-positive number, then for what value of p does the expression |77 – 6p| holds the minimum value?

A. 77/12
B. 77/6
C. 12
D. 0
E. -77/6

in this problem can we say that since p is a non positive I77-6pI is negative i.e -77+6p

|77 - 6p| = |6p - 77| gives two cases:
6p - 77 >= 0 which means p >= 77/6 (Not possible because p is not positive) 
OR
6p - 77 < 0 which means p < 77/6 (which includes 0 and all negative values)
So |6p - 77| = - (6p - 77)

You should check out this post:
https://anaprep.com/algebra-the-why-beh ... questions/

This is how you will arrive at the answer here though:

­p is non positive (though this term isn't really used) means p can be 0 or negative. 
If p = 0,  |77 – 6p| = 77
If p is negative, – 6p becomes positive and when added to 77 is gives us something more than 77.
So the minimum value of |77 – 6p| happens when p = 0.­
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625602 [0]
Given Kudos: 81918
Send PM
Re: If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
Expert Reply
Can,Will wrote:
KarishmaB
If p is a non-positive number, then for what value of p does the expression |77 – 6p| holds the minimum value?

A. 77/12
B. 77/6
C. 12
D. 0
E. -77/6

in this problem can we say that since p is a non positive I77-6pI is negative i.e -77+6p

­This question is discussed here:

https://gmatclub.com/forum/if-x-is-a-no ... l#p3389087
GMAT Club Bot
Re: If x is a non-negative integer and |6 - |x + 2|| = 10, then find the n [#permalink]
Moderator:
Math Expert
93373 posts