If c is an integer and c 0, is c a root of the equation

Question

If c is an integer and c > 0, is c a root of the equation x^3-14x^2+24x=0 ?
 
(1) c is prime.
 
(2) c is odd.

Bunuel · Answer

If c is an integer and c > 0, is c a root of the equation x^3-14x^2+24x=0 ?

Basically we are asked whether \(c^3-14c^2+24c=0\). Is \(c(c^2-14c+24)=0\)? --> factorize \(c^2-14c+24\): is \(c(c-12)(c-2)=0\)? As we see the question boils down to determine whether \(c=12\) or \(c=2\) (c cannot be zero as given that c>0).

(1) c is prime. If \(c=2=prime\), then the answer is YES but if \(c=3=prime\), then the answer is NO. Not sufficient.

(2) c is odd. This statement implies that \(c\) can be neither 12 nor 2. Thus, the answer to the question is NO. Sufficient.

Answer: B.

Solving and Factoring Quadratics:
https://www.purplemath.com/modules/solvquad.htm
https://www.purplemath.com/modules/factquad.htm

Hope it helps.

SOURH7WK · Answer

Bunuel, I need 1 clarification in validating St 1: Here C can have only 2 value either 2 or 12, so why we are checking with prime no 3? is 3 also a root?

Bunuel · Answer

It's the other way around: we are asked to determine whether  c=12  or  c=2 . (1) says that  c  is prime, thus if  c=2=prime , then the answer is YES but if  c=3=prime , then the answer is NO.

Hope it's clear.

Archit143 · Answer

Hi bunuel
When we know that root of the eqn is 12 and 2
than why are we considering 3 as another root...............
Solution to the eqn gives two specific values 12 and 2 than are we considering 3 
bit confusing

Bunuel · Answer

Check here: if-c-is-an-integer-and-c-0-is-c-a-root-of-the-equation-141202.html#p1134914

Archit143 · Answer

The link redirects tot he same page. It doesnt has any other info.

Bunuel · Answer

This post addresses your issue: if-c-is-an-integer-and-c-0-is-c-a-root-of-the-equation-141202.html#p1134914 Again, we are not told that c is either 12 or 2. We are asked to find out whether c is 12 or 2.

noTh1ng · Answer

Tricky tricky, one is so fast directed in the way where one turns the question around and is not asking whether c is a root of the equation but checks if the solutions fit to the statement....

Have seen some of these **** around

EgmatQuantExpert · Answer

This question plays on the properties of the roots of the equation which is what creates confusion among the options.

We know that for c to be a root of the equation it has to take the value of either 2 or 12. The question plays on the prime nature property of 2 which is one of the roots of the equation.

For a statement to be sufficient to give us the answer it should give us a unique solution by eliminating all other possible options i.e. it should tell us for sure if c is a root of the equation or not.

Statement-I tells us that c is prime 
Many test taker would fall for this trap( as is evident from the low accuracy rate of this question) that since c is prime it should take the value of 2. However before finalizing statement-I as sufficient ask yourself this question: Can c take value of only 2? or is 2 the only prime number? You would notice that of all the values which c can take  2 is one of the values  i.e.  2 is one of the prime numbers.

Since c is prime it can take a value of {2,3,5,7,11.......}

Hence c can take values which may be root of the equation (i.e. 2) or may not be a root of the equation(i.e. any other prime number), st-I does not give us a unique answer. So it is not sufficient to answer the question.

Had the statement said that c is an even prime number, it would have been sufficient to tell us that c can only take a value of 2 which is the root of the equation.

Statement-II tells us that c is odd 
St-II tells us that c is odd. This statement also does not give us a unique value of c but it surely tells us that c can't be a root of the equation as all the roots of the equation are even ( i.e. 2 & 12). Hence st-II is sufficient to answer the question.

Hope this helps!

Regards
Harsh

chayma · Answer

Hello @bunnel !
i don't undertand why you replaced x with c

MBAB123 · Answer

Hi  chayma , root of the equation means that if you replace the variable in the value with root, it should give 0. Hence, he/she/they replaced X with C and then solved the equation. He then evaluated the statement to see if C=12 or 2 holds true or not.

That said, it doesn't really matter which variable you solve for as long as you understand the question.

If c is an integer and c > 0, is c a root of the equation

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