Hello
Please help with the question below
Determine whether the expression can be described as positive, negative or cannot be determined.
-x
------- given that xyz > 0 (Manhattan guide #1 Page 43 Q15)
(-y)(-z)
The answer is negative but how is it possible considering even if x is negative then atleast one other sign has to be negative (considering xyz > 0).
So when doing division the same rule will apply and the result will be always positive.
Please help
Thanks
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Positive / Negatives
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Hi melguy,
Since (X)(Y)(Z) > 0, then there are two possible 'groups' of values:
1) ALL variables are positive, NONE are negative.
2) ONE variable is positive, TWO are negative.
From here, you can either use Number Properties against the prompt or TEST VALUES.
IF... all variables are positive, then we have...
(-1)(pos) / (-1)(pos)(-1)(pos) =
(neg) / (pos) =
neg
IF.... one variable is positive, then we have...
(-1)(pos) / (-1)(neg)(-1)(neg) =
(neg) / (pos) =
neg
or
(-1)(neg) / (-1)(pos)(-1)(neg) =
(pos) / (neg) =
neg
In ALL scenarios, the resulting fraction is NEGATIVE.
GMAT assassins aren't born, they're made,
Rich
Since (X)(Y)(Z) > 0, then there are two possible 'groups' of values:
1) ALL variables are positive, NONE are negative.
2) ONE variable is positive, TWO are negative.
From here, you can either use Number Properties against the prompt or TEST VALUES.
IF... all variables are positive, then we have...
(-1)(pos) / (-1)(pos)(-1)(pos) =
(neg) / (pos) =
neg
IF.... one variable is positive, then we have...
(-1)(pos) / (-1)(neg)(-1)(neg) =
(neg) / (pos) =
neg
or
(-1)(neg) / (-1)(pos)(-1)(neg) =
(pos) / (neg) =
neg
In ALL scenarios, the resulting fraction is NEGATIVE.
GMAT assassins aren't born, they're made,
Rich
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fiza gupta
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-x/(-y)(-z) or we can write : -x/yz
given : xyz>0
so either all are positive or two negative and one positive.
(i) if all positive than -x/yz will be negative
(ii) two negative and one positive
now if that two negative are in division their sign will cancel and will be positive
-a/-b = a/b
and if they are product then will be positive too
-a*-b = ab so from all three if two numbers are negative then they will become positive
-x/yz = will be negative always
given : xyz>0
so either all are positive or two negative and one positive.
(i) if all positive than -x/yz will be negative
(ii) two negative and one positive
now if that two negative are in division their sign will cancel and will be positive
-a/-b = a/b
and if they are product then will be positive too
-a*-b = ab so from all three if two numbers are negative then they will become positive
-x/yz = will be negative always
Fiza Gupta
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vineet.nitd
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Remember as a general thumb rule:
If you know the parity (negative or positive) of the product of any number of variables, then the same will be the parity of any combination of those variables multiplied in numerator or denominator.
Reason is pretty simple the parity of 'a' is always the same as that of its reciprocal '1/a'.
So, essentially if you have ab>0, then this implies that a/b > 0 and vice versa is also true.
Hence, xyz will have the same sign as x/yz and opposite the sign of -x/yz.
We are done here!
If you know the parity (negative or positive) of the product of any number of variables, then the same will be the parity of any combination of those variables multiplied in numerator or denominator.
Reason is pretty simple the parity of 'a' is always the same as that of its reciprocal '1/a'.
So, essentially if you have ab>0, then this implies that a/b > 0 and vice versa is also true.
Hence, xyz will have the same sign as x/yz and opposite the sign of -x/yz.
We are done here!
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Matt@VeritasPrep
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I'd write it as
-x / ((-1) * (-1) * y * z)
or
-x / yz
or
-(x/yz)
Since xyz is positive, x/yz must also be positive, making -(x/yz) negative.
-x / ((-1) * (-1) * y * z)
or
-x / yz
or
-(x/yz)
Since xyz is positive, x/yz must also be positive, making -(x/yz) negative.
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Matt@VeritasPrep
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Another idea would be trying the two scenarios in which xyz > 0.
First scenario: All three are positive
Say we have x = 2, y = 3, z = 4. Then -x/(-y * -z) => -2 / (-3 * -4) => -1/6.
Second scenario: Exactly one is positive
Say we have x = 2, y = -3, z = -4. Then -x/(-y * -z) => -2 / (-(-3) * -(-4)) => -1/6.
So our result is negative in both cases.
First scenario: All three are positive
Say we have x = 2, y = 3, z = 4. Then -x/(-y * -z) => -2 / (-3 * -4) => -1/6.
Second scenario: Exactly one is positive
Say we have x = 2, y = -3, z = -4. Then -x/(-y * -z) => -2 / (-(-3) * -(-4)) => -1/6.
So our result is negative in both cases.
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Matt@VeritasPrep
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One last option: start with the given, and transform it into what you're asked for.
xyz > 0
-xyz < 0
-xyz/(y²z²) < 0
-xyz/((-y)*(-y)*(-z)*(-z)) < 0
-x/(-(-y) * -(-z)) < 0
-x/(-y * -z) < 0
xyz > 0
-xyz < 0
-xyz/(y²z²) < 0
-xyz/((-y)*(-y)*(-z)*(-z)) < 0
-x/(-(-y) * -(-z)) < 0
-x/(-y * -z) < 0
