What is the least possible value of (x + 1)(x + 2)(x + 3)(x + 4) + 201

Question

What is the least possible value of (x + 1)(x + 2)(x + 3)(x + 4) + 2019 ?

(A) 2017
(B) 2018
(C) 2019
(D) 2020
(E) 2021

Archit3110 · Answer

i am not sure of solution
if x = -1 then ; (x + 1)(x + 2)(x + 3)(x + 4) =0
so 0+2019 ; 2019
IMO C

sakshamchhabra · Answer

But this holds true only when it is given that X is an integer ,and if this is so then there will be 4 minima values i.e. -1,-2,-3,-4

AkshdeepS · Answer

If x is other than -1 , -2, -3, -4, then we will always get some number greater than zero and the result will always be greater than 2019.

But if x is any of the four above mentioned digits, the result will be 2019 + 0 = 2019

The result of (x + 1)(x + 2)(x + 3)(x + 4) >= 0 always.

IMO C

Vinit800HBS · Answer

AkshdeepS 
 Archit3110 
 sakshamchhabra

I believe the options are wrong and so is the question.

For all the answers provided above, everyone is assuming INTEGRAL values of X even though it’s not specified.

The answer can very well be less than 2019.

Consider X = -1.5
Now, we have 
(-1.5+1)*(-1.5+2)*(-1.5+3)*(-1.5+) + 2019
= -0.5*0.5*1.5*2.5 + 2019
= -0.9375 + 2019
= 2018.0625

That’s just one possibility. We can check further for other values.

Bunuel , will you please check into this.

Posted from my mobile device

sakshamchhabra · Answer

Yes, I did realise this at the very beginning and did mention in my post that 2019 will be possible only if we assume X is an integer.

I checked with Wolfram and the two minima for the answer to be 2018 will be x ≈ -3.618 and x ≈ -1.382

Archit3110 · Answer

I think you are right with your logic , even in my post for this question mentioned that I am not sure of the solution as value of X could be both integer or fraction 
 Vinit800HBS

AkshdeepS · Answer

I am not sure whether 2018.xxx can be considered 2018, or it is 2019 in this case.

In such cases, values can be in the for of ranges such as 2018 < x < 2019 etc.

But to find specific value of X if we are using all real numbers is tricky.

Vinit800HBS · Answer

It’s a polynomial. The maxima or minimal of a polynomial depends on several ranges where it inverts from positive range to negative and vice versa.

The precise answer, as  sakshamchhabra  pointed out through WolframAlpha, is 2018.

Kudos for the efforts to solve these question.

Archit3110 · Answer

I just googled the question ; AkshdeepS Vinit800HBS https://artofproblemsolving.com/wiki/in ... Problem_19 its from american Mathematics Competitions ; not sure whether practicing such question types is really a boon or bane for gmat quant..

Bunuel ; is there any reason why question from american Mathematics Competitions have been posted ? I have noticed that since last Friday you been posting questions mostly from american mathematics competition source , do we really need to practice such high level questions which are not gmat type and which cant be solved under 2 mins...

Vinit800HBS · Answer

the-dimensions-of-a-ream-of-paper-are-8-1-2-inches-by-11-inches-by-294408.html?style=12#p2266249 This is a 700-level question from Official Guide 2020. In respect to this, the question that we solved is way more tough. Definitely not a boon for GMAT prep. Posted from my mobile device

What is the least possible value of (x + 1)(x + 2)(x + 3)(x + 4) + 201

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