If p is a non-positive number, then for what value of p does the

Question

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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himanics · Accepted Answer

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.

Chethan92 · Answer

|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.

Archit3110 · Answer

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..

jfranciscocuencag · Answer

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

D

LeoN88 · Answer

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.

EgmatQuantExpert · Answer

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.

Answer: D

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emonmisra · Answer

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

CEdward · Answer

Bit confused here. So the question is saying p is non-negative yet gives us positive values of p as possible choices. Shouldn't E be the answer? -(-77/6 = ~13) so 77 - 13 < 77 - 0

Makesh89 · Answer

If p is a non negative then we eliminate option AB C then we test for option D and E and at p=0 is where the value of the expression is minimum.

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Fdambro294 · Answer

If you step back for a second and analyze what’s going on, you can get to the answer just by looking at the question. (Worst case scenario, plug the 5 answer choices in)

If p is non-positive, it is either zero or negative.

The output of the absolute value Modulus will always be non-negative. The minimum value you could ever hope to obtain for the output is 0.

If p is any negative number, then inside the absolute value Modulus we would be multiplying:

(-6) * (-negative value) = (+) positive value

And this positive value would be added to 77, thereby increasing the output from the absolute value.

The best we can do is eliminate the -6(p) term and be left with just

This will happen when p = 0

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ueh55406 · Answer

damn it ! fell right into the trap !

P is NON-POSITIVE

sk1999 · Answer

Hey, shouldn’t option B be the correct answer? Can someone clarify?

Krunaal · Answer

Please share your analysis henceforth on how did you end up with an incorrect choice - that helps highlight the fault in your approach.

If p is non-positive then it is less than or equal to 0

|77 - 6p| will always be positive, or 0 as it is inside the mod. You cannot take p as 77/6 because of the above highlighted constraint.  Any negative number for p will increase the value of 77 - p . The only minimum value possible is 77, when p = 0. Hope this helps.

napolean92728 · Answer

It's given p is non-positive how can you say that it should be non-negative, rather you can clearly eliminate A,B and C as they are positive the only feasible options are D and E and on substituting any negative number you are going to get an answer greater than 77 so you are left with only 0 to get the least value i.e. 77, hence option D is the answer.

If p is a non-positive number, then for what value of p does the

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If p is a non-positive number, then for what value of p does the

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