A function f(x) is defined for all real numbers by the expression (x –

Question

https://gmatclub.com/forum/download/file.php?id=47427 A function f(x) is defined for all real numbers by the expression (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5). For which one of the following values of x, represented on the number line, is f(x) negative? (A) Point A (B) Point B (C) Point C (D) Point D (E) Point E 2019-04-17_1053.png

GMATinsight · Answer

For (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) to be Negative, either 3 of these 4 must be positive or 3 of these 4 must be negative

(A) Point A All 4 are Negative hence f(x) is positive
(B) Point B 3 of 4 are positive hence f(x) is Negative CORRECT ANSWER
(C) Point C 2 of 4 are positive and other 2 negative hence result is positive
(D) Point D at this point f(x) is ZERO
(E) Point E All 4 are Positive hence f(x) is positive

Answer: Option B

Archit3110 · Answer

for the function value (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5)
substitute value of x ; 
we observe that at x =2 ; we get a -ve number
IMO B

Kinshook · Answer

Given: A function f(x) is defined for all real numbers by the expression (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5). 
Asked: For which one of the following values of x, represented on the number line, is f(x) negative?

(A) Point A
x = 1: (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) = (1 – 1.5)(1 – 2.5)(1 – 3.5)(1 – 4.5) = (-.5)(-1.5)(-2.5)(-3.5) : Positive
(B) Point B
x = 2: (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) = (2 – 1.5)(2 – 2.5)(2 – 3.5)(2 – 4.5) = .5 (-.5)(-1.5)(-2.5) : Negative
(C) Point C
x = 3: (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) = (3 – 1.5)(3 – 2.5)(3 – 3.5)(3 – 4.5) = 1.5*.5 (-.5)(-1.5) : Positive
(D) Point D
x = 4.5: (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) = (4.5 – 1.5)(4.5 – 2.5)(4.5 – 3.5)(4.5 – 4.5) = 3*2*1*0 = 0 : Zero
(E) Point E
x = 5.5: (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) = (5.5 – 1.5)(5.5 – 2.5)(5.5 – 3.5)(5.5 – 4.5) = 4*3*2*1 : Positive

IMO B

MathRevolution · Answer

f(x) = (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) < 0 when 3 of this 4 must be negative.

For x = 2(Point B), the product will be negative as there is 1 value less than 2 and 3 values higher than 2.

Answer B

BrushMyQuant · Answer

Given that f(x) = (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) and we need to find which of the answer choice is negative

A. f(1) 
To find f(1) we need to substitute x=1 in f(x) = (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5)
=> f(0.5) = (1 – 1.5)(1 – 2.5)(1 – 3.5)(1 – 4.5) = NEGATIVE * NEGATIVE * NEGATIVE * NEGATIVE = POSITIVE * POSITIVE = POSITIVE

B. f(2) 
=> f(2) = (2 – 1.5)(2 – 2.5)(2 – 3.5)(2 – 4.5) = POSITIVE * NEGATIVE * NEGATIVE * NEGATIVE = NEGATIVE * POSITIVE = NEGATIVE
We don't need to proceed further as we already got the answer. But solving remaining options to complete the solution

C. f(3) 
=> f(3) = (3 – 1.5)(3 – 2.5)(3 – 3.5)(3 – 4.5) = POSITIVE * POSITIVE * NEGATIVE * NEGATIVE = POSITIVE * POSITIVE = POSITIVE

D. f(4.5) 
=> f(4.5) = (4.5 – 1.5)(4.5 – 2.5)(4.5 – 3.5)(4.5 – 4.5) = POSITIVE * POSITIVE * POSITIVE * ZERO = ZERO = Neither POSITIVE Nor NEGITIVE

E. f(5.5) 
=> f(5.5) = (5.5 – 1.5)(5.5 – 2.5)(5.5 – 3.5)(5.5 – 4.5) = POSITIVE * POSITIVE * POSITIVE * POSITIVE = POSITIVE * POSITIVE = POSITIVE

So,  Answer will be B 
Hope it helps!

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