Is x^2-8x+15 = 0?

Question

Is x^2-8x+15 = 0?

(1) x not equal to 3
(2) x-5 not equal to 0

Bunuel · Answer

Solve  x^2-8x+15=0  for  x  -->  x=3  or  x=5  --> so  x^2-8x+15=0  is true if  x=3  or  x=5 . Basically the question asks: is  x=3  or  x=5 ?

(1)  x
eq{3} .  x  can still be 5. Not sufficient.

(2)  x-5
eq{0}  -->  x
eq{5} .  x  can still be 3. Not sufficient.

(1)+(2)  x
eq{3}  and  x
eq{5} , so the answer to the question is NO. Sufficient.

Answer: C.

HarveyS · Answer

Bunuel,

I did not understand the logic.

Stm1 - X can be 5, so x^2-8x+15 = 0 , Sufficient

Stm 2- X can be 3, So x^2-8x+15 = 0 , Sufficient..

Ans- D

Whats wrong in this.

blueseas · Answer

QUESTION IS whether x^2-8x+15 = 0
statement 1:==>  x
eq{3} .===>means  x  can be  4,5,6,7 ...anthing except  3 
when  x=5 ..the given equation equals to zero but with other numbers let say  4...16-32+15=-1 
so insufficient.

statement 2:similarly here x  cant be  5. ....but at  x=3 ==>equation equals to  0  BUT AT other numbers it is not equal to zero..
hence insufficient.

combining both you are neglecting both the roots of X hence that equation will never be zero .
hence sufficient C

HOPE IT HELPS

Bunuel · Answer

The question asks is x=3 or x=5?

(1) says that x is not 3. If x=5, then we have an YES answer, if x is any other values, then we have a NO answer. Not sufficient.
(2) says that x is not 5. If x=3, then we have an YES answer, if x is any other values, then we have a NO answer. Not sufficient.

(1)+(2) We know that x is neither 3 nor 5, so we have a NO answer to the question. Sufficient.

Answer: E.

Hope it's clear.

HarveyS · Answer

Thanks both of you...... Got it.... :-D

law258 · Answer

C is correct. Here's why:

eqn factors to be (x-3)(x-5) = 0

(1) we know from this that x is not equal to 3, but that's it. We have (x-5) = 0 still to deal with

INSUFFICIENT

(2) from this x is not equal to 5, but we have the problem again of (x-3) = 0 remaining

INSUFFICIENT

Together - (1) + (2) = tells us that x cannot be both 3 and 5, which are the only values that would make the orig eqn equal to zero, thus the eqn cannot equal zero

Rance14 · Answer

x^2-8x+15=0

From a conceptual understanding pov if you solve the above quadratic equation you get

(x-5)(x-3)=0
x=3,x=5

That means the value of the equation x^2-8x+15 can be zero only either x=3 or x=5

We have been asked if x^2-8x+15 = 0 ???

(1) x not equal to 3

Okay, if x is not equal to 3 maybe then x = 2 or 4 or 5 or 11 etc etc etc

Here if we put x=5 then yes the eqn x^2-8x+15 becomes 0 but for any other value of x

The eqn x^2-8x+15 will never be equal to 0

So we ultimately have 2 cases and cannot give a definite answer as to whether x^2-8x+15=0

Hence (1) not sufficient

(2) x not equal to 5

similar reasoning as above for x=3 we will get x^2-8x+15=0 but for any other value of x we will not get x^2-8x+15 = 0

Hence (2) not sufficient

Now combining (1) and (2)

now we know x is not equal to 3 and is not equal to 5

and those are the only values of x which make the eqn x^2-8x+15 = 0

so for every other value of x, the eqn x^2-8x+15 will not be equal to 0 and we can definitely say that, hence, (1) and (2) together sufficient

Is x^2-8x+15 = 0?

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