If x

Question

If x < 0 and y ≠ 0, which of the following must be true?

I. x^7 < 0
II. x^3 * y^4 < 0
III. |x| = -x

A. I only
B. II only
C. III only
D. II & III only
E. I, II & III

Bunuel · Answer

I. x^7 < 0

Since x is negative, then the above is true.

II. x^3 * y^4 < 0

Since x is negative and y ≠ 0, then the above is true.

III. |x| = -x

Since x is negative, then the above is true.

Answer: E.

BrushMyQuant · Answer

Given that x < 0 and y ≠ 0 and we need to find which of the following must be true?

I. x^7 < 0
Odd power of any negative number will be < 0
( Watch this video to MASTER Positive and Negative Numbers)
=> TRUE

II. x^3 * y^4 < 0
Odd power of a negative number will be negative
=> x^3 < 0
Even power of any non-zero number will be positive
=> y^4 > 0
Negative * Positive = Negative
=> TRUE

III. |x| = -x
Absolute value of a negative number = Negative of that number
=> |x| = -x
=> TRUE

So, Answer will be E
Hope it helps!

Watch the following video to MASTER Absolute Values

Smkv612 · Answer

Hi Bunel,

Could you please explain the third condition in detail. Couldn't get it?

III. |x| = -x

|x| can be x or -x. How can it be equal to -x, given its a must be true condition?

Thanks in advance

Bunuel · Answer

The third condition should be the easy one. We are told that x is negative, so if x is negative, then |x| = -x (and if x were positive, then |x| = x).

BrushMyQuant · Answer

When x is negative then |x| = -x

Example: x = -3
Then, |x| = |-3| = -(-3) = 3 = -x, as modulus of a number is the non-negative value of the number.
Hope it helps!

Watch the following video to MASTER Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

vasu1104 · Answer

x<0. so x must be negative.
y is not equal to zero. so can be both positive or negative.

option 1. it will be always negative. because negative number raised to odd power will be always negative.
option 2. x^3 will be always negative. now y can be positive or negative. but it doesnt matter as x is negative and when multiple anything to negative value, result will be always negative. sot this must be true as well.
option 3, it is also true. say x= -1
|x| = 1
-x = -(-1) = 1
so LHS = RHS

all 3 are true.

If x < 0 and y 0, which of the following must be true?

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­If x < 0 and y 0, which of the following must be true?