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17 Nov 2014, 20:11
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Can someone help me with the above? This is a question from my Veritas Prep book. It says the answer is -1/17 < x but I'm having a hard time understanding how the 17 got moved to 1/17.
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17 Nov 2014, 23:22
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willowtree2
In this inequality, is the variable \(x\) constrained to be positive. For now, let's assume x is positive.
First multiply both sides by x, because x is positive the sense of the inequality remains the same.
\(-1/x > 17\)
\(-1 > 17x\)
Divide both sides by 17, which is a positive quantity, again the sense of the inequality is preserved:
\(-1/17> x\)
which is also equivalent to
\(x < -1/17\)
If we knew nothing about x, then the only option would be to add and subtract terms and we can about it this way:
\(-1/x > 17\)
add -1/x to both sides
\(1/x+ 17 < 0\)
which is equivalent to
\((17x+1)/x< 0\)
and go from there. Typically GMAT will then add some conditions as part of the statements in data sufficiency.
Cheers,
Dabral
In this inequality, is the variable \(x\) constrained to be positive. For now, let's assume x is positive.
First multiply both sides by x, because x is positive the sense of the inequality remains the same.
\(-1/x > 17\)
\(-1 > 17x\)
Divide both sides by 17, which is a positive quantity, again the sense of the inequality is preserved:
\(-1/17> x\)
which is also equivalent to
\(x < -1/17\)
If we knew nothing about x, then the only option would be to add and subtract terms and we can about it this way:
\(-1/x > 17\)
add -1/x to both sides
\(1/x+ 17 < 0\)
which is equivalent to
\((17x+1)/x< 0\)
and go from there. Typically GMAT will then add some conditions as part of the statements in data sufficiency.
Cheers,
Dabral
19 Nov 2014, 10:32
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Thanks for your input dabral. When you mentioned whether or not we could assume X was positive I looked back over the question and realized they do state that x<0, implying that it's negative and now it makes prefect sense. To be fair the entire problem starts like this:
0>x(which would imply that x is negative)
-1/x > 17
And they want the inequality simplified.
If I start where you mentioned we know X is negative.
-1/x > 17
Add 1/x to both sides
0 > 17 + 1/x
Subtract 17 from both sides
-17 > 1/x
Multiply each side by x
-17x < 1 <---sign changes because we know that X is negative.
Divide by -17
x> -1/17
Thanks again for your help.
0>x(which would imply that x is negative)
-1/x > 17
And they want the inequality simplified.
If I start where you mentioned we know X is negative.
-1/x > 17
Add 1/x to both sides
0 > 17 + 1/x
Subtract 17 from both sides
-17 > 1/x
Multiply each side by x
-17x < 1 <---sign changes because we know that X is negative.
Divide by -17
x> -1/17
Thanks again for your help.
