Is x

Question

Is x < - 20 ?

(1) x^2 + 40x + 391 = 0

(2) x^2 = 529

KarishmaParmar · Accepted Answer

From statement 1
x^2 +23x+17x+391 =0
(x+23) (x+17) = 0
x= -23 , -17

From statement 2
x= +23, -23

From Both
x= -23

Hence C

Was it this simple? Did I miss something? Any reason it is 700 level?

ENGRTOMBA2018 · Answer

Thanks. Updated the tag. Your solution is fine.

iliavko · Answer

What is being tested in this question?

Is there a fast way to realize that 17 times 23 is 391? How can you do it fast? Otherwise I don't see what's the point of this question.

Thanks!

ENGRTOMBA2018 · Answer

Realize that 17*23= (20-3)*(20+3) = 20^2-3^2= 400-9 = 391.

I used the relation that (a-b)(a+b)= a^2-b^2

Posted from my mobile device

iliavko · Answer

Nice one!.. Didn't notice the difference of squares! Good job! thank you

GMATGuruNY · Answer

Statement 2:
Since  20^2=400  and  30^2 = 900 , the positive root must be between 20 and 30.
For the units of  x^2  to be 9, x must have a units digit of 3 or 7.
Since 529 is much closer to 400 than to 900, the positive root must be 23, implying that the negative root is -23.
If x=23, the answer to the question stem is NO.
If x=-23, the answer to the question stem is YES.
INSUFFICIENT.

RULE:
For any DS problem, there must be at least one case that satisfies BOTH statements.

Statement 1:
 x^2 + 40x + 391 = (x+a)(x+b) , where  a+b = 40 .
In accordance with the rule above, one of the roots of this quadratic must be 23 or -23.
Thus, the two factors must look as follows:
 (x+23)(x+b) 
Since 23+b = 40, b=17, with the result that the second factor is (x+17):
 (x+23)(x+17) 
Thus, x=-23 or x=-17.
If x=-17, the answer to the question stem is NO.
If x=-23, the answer to the question stem is YES.
INSUFFICIENT.

Statements combined:
Only x=-23 satisfies both statements.
Thus, the answer to the question stem is YES.
SUFFICIENT.

C

Basshead · Answer

(1)  x^2 + 40x + 391 = 0 
 (x+17)(x+23)

x = -17, -23 ; INSUFFICIENT.

(2)  X^2 = 529 
x can be positive or negative; INSUFFICIENT.

(1&2) Combined,  x = -23 . SUFFICIENT.

Answer is C.

TestPrepUnlimited · Answer

We don't have to factor anything to solve this question logically, we only need to know  x^2 = 400  as a reference.

Statement 1:

There are two negative solutions because all signs are positive. -40 is the sum of the roots, half of that is -20. The solutions are not both -20, thus one of the solutions must be bigger than -20 and one must be less than -20. We would have a "no" and "yes" answer so insufficient.

Statement 2:

The value on the right is greater than 400, so we know the magnitude of x is greater than 20. We get one solution less than -20 and one greater than 20, insufficient.

Combined:

Statement 1 has two negative solutions, statement 2 has one negative one positive, combined there is only one possible value for x which is negative. Sufficient.

Ans: C

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Is x < - 20 ?

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Is x < - 20 ?

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