If (x-11)(x-3)

Question

If (x-11)(x-3) < 0, which of the following must be true? A. x^2 + 5x + 6 < 0 B. x^2 + 5x + 6 > 0 C. 5 - x < 0 D. x - 5 < 0 E. 11 - x > 0

stonecold · Answer

As X lies between (3,11)
hence x is always less than 11
so => Hence E

Vinayprajapati · Answer

If (x-11)(x-3) < 0, which of the following must be true?

A. x^2 + 5x + 6 < 0
B. x^2 + 5x + 6 > 0
C. 5 - x < 0
D. x - 5 < 0
E. 11 - x > 0

Show Answer

Official Answer

E

ajdse22 · Answer

Clearly if the expression is true, then x must be between 3 and 11. 
If I look at expression E, it says x< 11. I am not sure why this must be true as the questions asks. What if x< 3. Take x= 2. 
Then expression equals (-9)*(-1) = +9. This means that we cant say that x must be less than 11. 
What is going on. Someone please help with the question

ajdse22 · Answer

Clearly if the expression is true, then x must be between 3 and 11. 
If I look at expression E, it says x< 11. I am not sure why this must be true as the questions asks. What if x< 3. Take x= 2. 
Then expression equals (-9)*(-1) = +9. This means that we cant say that x must be less than 11. 
What is going on. Someone please help with the question

chetan2u · Answer

Hi, the reason is - we are not saying that - x can be ANY value < 11..... But WHATEVER be the value of x, it will be <11.... and 30, this also would be true, as the range 30..

adiagr · Answer

(x-11)(x-3) < 0; 3 Given condition If we review options, E is always true. Let us review others: x^2 + 5x + 6 = (x+3)(x+2) (x+3)(x+2)<0, then -3 This will not be true with the given conditions (30, then x> -2 and x < -3 --> This will not be true with the given conditions (3 5. But if x = 12 , then given condition is not satisfied. So C is also out. D. x - 5 < 0 x<5 But if x = 1, (which is less than 3) then given condition is not satisfied. E is the answer.

sudhirmadaan · Answer

x lies between 3 and 11 
3<x<11
so x-11<0 === 11-x>0 (E)

AbdurRakib · Answer

(x-11)(x-3)<0 can be written as (11-x)(x-3)>0 So,to inequality hold true multiple of (11-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 30 or x<11,which must be true (I started to look from E to A for making easy decision first) Correct Answer E

TheUltimateWinner · Answer

<----(-1)----0---1---2---3---4---5---6---7---8---9---10---  11---12--->
Actually, the question stem says the green part only.
E says: 
11-x>0
---> 11>x
---> for the value of x in the green part 11 always must be greater than that green value.
So, the correct choice is E to me.

bumpbot · Answer

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If (x-11)(x-3) < 0, which of the following must be true?

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