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Intern  Joined: 15 Dec 2015
Posts: 34
If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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Difficulty:   15% (low)

Question Stats: 75% (00:49) correct 25% (01:12) wrong based on 117 sessions

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If x + y + z + w = 15, then at least k of the numbers x, y, z, w must be positive, where k is :

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

Originally posted by sara86 on 06 Jan 2016, 08:37.
Last edited by Bunuel on 06 Jan 2016, 08:42, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
CEO  S
Joined: 20 Mar 2014
Posts: 2599
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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sara86 wrote:
If x + y + z + w = 15, then at least k of the numbers x, y, z, w must be positive, where k is :

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

Straightforward question if you realize that 4 negative numbers when added can NEVER give you a positive sum. This directly eliminates A.

As we are given that x+y+z+w=15 and we need to find what is the least number of variables out of the 4 given (x,y,z,w) that need to be positive to adhere to x+y+z+w=15 ,

Consider any large value for x = 45 and -15,-10 and -5 for y,z,w respectively to give you x+y+z+w=15.

Thus k =1 for 'k' value to be the least.

Hope this helps.
SVP  B
Joined: 06 Nov 2014
Posts: 1873
Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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sara86 wrote:
If x + y + z + w = 15, then at least k of the numbers x, y, z, w must be positive, where k is :

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

If we say that none of the numbers are positive, then the sam cannot be positive. (Keep in mind that question is asking positive, not non-negative. 0 is not positive)
Hence Option A is out.

If you want the sum of 4 numbers to be always positive, you can do that by making one number very large and the rest of numbers and small negative numbers.
Ofcourse, more than 1 positive large numbers will also yield the same result.

But since we are asked about the least number of positive numbers, it should be 1.
Option B
Intern  Joined: 29 Aug 2015
Posts: 1
Schools: AGSM '19
Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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Hi!
I don´t understand the concept "at least k of the numbers" what does it mean?
Even though, I´ve got it correct. I thought "k" was multiplying the variables?

Thanks a lot.
Manager  S
Joined: 21 Jul 2017
Posts: 187
Location: India
Concentration: Social Entrepreneurship, Leadership
GMAT 1: 660 Q47 V34 GPA: 4
WE: Project Management (Education)
Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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Bruma14 wrote:
Hi!
I don´t understand the concept "at least k of the numbers" what does it mean?
Even though, I´ve got it correct. I thought "k" was multiplying the variables?

Thanks a lot.

At least K means we are referring to the least value of K. Now for the sum to be positive at least one of these number must be positive. Hence 1 Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must   [#permalink] 03 Oct 2018, 10:16
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