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If the reciprocal of the negative integer x is greater than
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12 Aug 2018, 10:01
12 Aug 2018, 10:01
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If the reciprocal of the negative integer x is greater than the sum of y and z, then which of the following must be true?
(A) \(x > y + z\)
(B) y and z are positive.
(C) \(1 > x(y + z)\)
(D) \(1 < xy + xz\)
(E) \(\frac{1}{x} > z – y\)
(A) \(x > y + z\)
(B) y and z are positive.
(C) \(1 > x(y + z)\)
(D) \(1 < xy + xz\)
(E) \(\frac{1}{x} > z – y\)
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If the reciprocal of the negative integer x is greater than
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20 Feb 2019, 09:29
20 Feb 2019, 09:29
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Carcass wrote:
If the reciprocal of the negative integer x is greater than the sum of y and z, then which of the following must be true?
(A) \(x > y + z\)
(B) y and z are positive.
(C) \(1 > x(y + z)\)
(D) \(1 < xy + xz\)
(E) \(\frac{1}{x} > z – y\)
(A) \(x > y + z\)
(B) y and z are positive.
(C) \(1 > x(y + z)\)
(D) \(1 < xy + xz\)
(E) \(\frac{1}{x} > z – y\)
GIVEN: The reciprocal of the negative integer x is greater than the sum of y and z
The reciprocal of x is 1/x
So, we can write: 1/x > y + z
Multiply both sides by x to get: 1 < x(y + z) [since x is NEGATIVE, we REVERSE the direction of the inequality symbol]
Expand the right side to get: 1 < xy + xz
Answer: D
Cheers,
Brent
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Re: If the reciprocal of the negative integer x is greater than
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31 Dec 2019, 05:12
31 Dec 2019, 05:12
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Carcass wrote:
If the reciprocal of the negative integer x is greater than the sum of y and z, then which of the following must be true?
(A) \(x > y + z\)
(B) y and z are positive.
(C) \(1 > x(y + z)\)
(D) \(1 < xy + xz\)
(E) \(\frac{1}{x} > z – y\)
(A) \(x > y + z\)
(B) y and z are positive.
(C) \(1 > x(y + z)\)
(D) \(1 < xy + xz\)
(E) \(\frac{1}{x} > z – y\)
Given that \(\frac{1}{x}>(y+z)\), where x<0
Multiplying 'x' both sides, (inequality sign to be flipped since x is negative)
\(x*\frac{1}{x}>x(y+z)\)
Or, \(1 < xy+xz\)
Ans. (D)
QS: can we write the reciprocal as -\(\frac{1}{x}\) and then proceed. please correct me if my thought process is wrong. YES, IT'S WRONG.
Suppose x = -5, reciprocal of x is \(\frac{1}{x}\) = \(\frac{1}{(-5)}\) = -\(\frac{1}{5}\); If you say, reciprocal of x is -\(\frac{1}{x}\), then -\(\frac{1}{x}\) = \(\frac{-1}{-5}\) = \(\frac{ 1}{5}\).
