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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
If p is a non-positive number, then for what value of p does the  [#permalink]

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11 00:00

Difficulty:   75% (hard)

Question Stats: 35% (01:22) correct 65% (01:25) wrong based on 158 sessions

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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

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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1021
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If p is a non-positive number, then for what value of p does the  [#permalink]

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|77-6p| is always positive.
Hence We need a number, which results |77-6p| to zero
Hence P should be 77/6
Then |77-6*77/6| = 0

B should be the answer.

EgmatQuantExpert, I think the P should be a non-negative number.
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Intern  B
Joined: 02 Mar 2019
Posts: 14
Location: India
Schools: HBS '22
Re: If p is a non-positive number, then for what value of p does the  [#permalink]

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if p is a non positive number then it can be either negative or zero. if we take a negative value for p then the expression will increase. if p=0 then we get the minimum value of expression as 77.
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5022
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If p is a non-positive number, then for what value of p does the  [#permalink]

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simply plugin answer options and solve ;
we see at B ; 77/6 we get 0 which is min value..
EgmatQuantExpert
question has mentioned p is a non-+ve number so how come option B is +ve? a non+ve number can be any number from range 0 to -infinity isnt it?
i think it should be non- negative number that way range of p will be from 0 to +ve infinity..

EgmatQuantExpert wrote:
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

Senior Manager  S
Joined: 12 Sep 2017
Posts: 302
Re: If p is a non-positive number, then for what value of p does the  [#permalink]

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If we consider the question just the way it is stated, then it should be D.

D
ISB School Moderator G
Joined: 08 Dec 2013
Posts: 595
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: If p is a non-positive number, then for what value of p does the  [#permalink]

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EgmatQuantExpert wrote:
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

Considering the question is correct, p can have values less than zero. For any non negative p, the answer tends towards maximum value-> (77+6p), hence for p=0 it holds the least value of the expression= l77l=77.
OA D.
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
Re: If p is a non-positive number, then for what value of p does the  [#permalink]

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Solution

Given:
In this question, we are given that
• The number p is a non-positive number.

To find:
We need to determine
• The value of p, for which the expression |77 – 6P| holds the minimum value.

Approach and Working:
As we are trying to minimise the value of the expression |77 – 6p|, our aim should be to minimise the value of 77 – 6p.
• The value of 77 – 6p will be minimum, when 6p will be maximum
• The value of 6p will be maximum, when the value of p will be maximum

Now, we also know that p is a non-positive number.
• Therefore, the maximum value of p = 0

Hence, the correct answer is option D.

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Intern  B
Joined: 14 Jan 2019
Posts: 12
Re: If p is a non-positive number, then for what value of p does the  [#permalink]

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p has to be negative or zero as per question.

Any negative value will add up on top of 77 will give the results which is greater than 77
Only when p = 0 the value of expression becomes 77- 6*0 = 77 which is lowest.

Hence value of p = 0 when the whole expression is minimum = 77 Re: If p is a non-positive number, then for what value of p does the   [#permalink] 25 May 2019, 06:18
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