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If x + y + z + w = 15, then at least k of the numbers x, y, z, w must

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If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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New post Updated on: 06 Jan 2016, 07:42
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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, 07:37.
Last edited by Bunuel on 06 Jan 2016, 07:42, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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New post 06 Jan 2016, 07:45
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.
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Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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New post 06 Jan 2016, 19:40
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
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Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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New post 30 Jul 2016, 18:25
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.
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Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must  [#permalink]

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New post 03 Oct 2018, 09:16
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
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Re: If x + y + z + w = 15, then at least k of the numbers x, y, z, w must   [#permalink] 03 Oct 2018, 09:16
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