What is the value of | (x+5)/(x+7) |? (1) x2 + 7x – 18 = 0 (2) 3x2 + 4

Question

What is the value of |  \frac{(x+5)}{(x+7)}  |?

(1)  x^2 + 7x – 18 = 0

(2)  3x^2 + 46x + 171 = 0

IanStewart · Accepted Answer

Each statement will give us two solutions for x. We can then plug these two values of x in to the expression in the question, and if we get the same answer both times, the statement is sufficient, and if we get two different answers, the statement is not sufficient.

x^2 + 7x - 18 = 0
(x + 9)(x - 2) = 0
x = -9 or x = 2

If you plug these two values of x in to the question, you get two different answers, so Statement 1 is not sufficient.

Looking at Statement 2:

3x^2 + 46x + 171 = 0
(3x + something)(x + something else) = 0

Here the two "something" numbers must multiply to 171. Ordinarily we'd need to work out the divisors of 171, and possibly try out a few divisors until we found the pair that "works" (i.e. that gives "+46x" as the middle term if you multiply the two factors back together), which takes a long time and is the reason you never need to do this kind of factoring on the real GMAT. But we know the two Statements in a GMAT DS question must be consistent. There must be at least one value of x that works in both statements. Since x+9 and x-2 were the only factors in Statement 1, and since we want a factor that includes a number which is a divisor of 171, it must be that x+9 is a factor of the quadratic in Statement 2. So our factorization is

3x^2 + 46x + 171 = (3x + 19) (x + 9)

and just to be sure, we can multiply the right side back out to confirm this is correct. If we do that, we do get "46x" in the middle, so this is the correct factorization. So the two solutions for x are x = -9 and x = -19/3, and if you plug those back in to the question, you get an answer of 2 either way, so Statement 2 is sufficient alone.

srikanth9502 · Answer

Stmnt 1) x=-9,2

Substituting these two values in the given expression gives us two different values

Stmnt 2) x=-9,-19/3

Both these values result in the one solution i.e 2, when substitued in the given expression. Hence suff

chesstitans · Answer

so, there is no way to test whether both values of x in st2 will cause the ABS to have the same value?

NamVu1990 · Answer

It took me almost 4 mins to solve for all the value of x and to plug them back in for testing. 
Is there any faster way to do 700+ level algebra DS like this one? Is it worth to spend that much time on such a question, if you know you can get it right but you have to spend twice as much time as you are allowed?

adityaganjoo · Answer

My approach is a bit time consuming, but it works!

Statement 1: it is easy: (x+9)(x-2)=0;
x = -9, 2
Substituting -9 and 2 one by one, we get 2 & 7/9 respectively.

Statement 1 is insufficient

Statement 2
We know GMAT! Generally there is some sync between the results of both the statements. Since all the coefficients are positive, x=2 cannot be a solution.
Thus, we need to substitute x=-9
x=-9 solves the equation.
x1 + x2 = -(b/a)
i.e. -9 + x = -(46/3)
or, x = -(46/3) + 27/3
or, x = -19/3

Solving the expression for x = -19/3, we get 2
We had already solved the expression for x=-9 in Statement 1. So we know that x=-9 gives 2 as well

Therefore, for either values, expression results in 2
Statement (2) is sufficient

What is the value of | (x+5)/(x+7) |? (1) x2 + 7x – 18 = 0 (2) 3x2 + 4

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GMAT Data Sufficiency (DS) Questions

What is the value of | (x+5)/(x+7) |? (1) x2 + 7x – 18 = 0 (2) 3x2 + 4

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