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Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 00:28
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Competition Mode Question Which of the following must be true if \(x < y\) and \(\frac{x}{z}\) >\(\frac{y}{z}\)? A. \(z < 0\) B. \(z > 0\) C. \(\frac{x}{y} > 0\) D. \(x > 0\) E. \(y > 0\)
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Re: Which of the following must be true if x/y and x/z > y/z?
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Updated on: 07 Nov 2019, 00:54
\(\frac{x}{z} > \frac{y}{z}\) > \(\frac{(x  y)}{z} > 0\) Since, \(x < y\), > \(x  y < 0\) > \(z\) < 0 ALWAYS (Since for \(\frac{(x  y)}{z} > 0\), ONLY negative/negative > 0)
IMO Option A
Originally posted by Dillesh4096 on 07 Nov 2019, 00:51.
Last edited by Dillesh4096 on 07 Nov 2019, 00:54, edited 1 time in total.



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 00:52
Which of the following must be true if x<y and x/z >y/z?
The eqs. x<y and x/z >y/z will only be valid when z<0.



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 01:10
x<y and x/z > y/z
i.e x/z  y/z > 0 xy/z > 0 Since xy <0, so z has to be < 0 to make the equation > 0 So z must be < 0
OA:A



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Which of the following must be true if x/y and x/z > y/z?
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Updated on: 08 Nov 2019, 02:14
z(xy)>0 given xy<0 therefore Z<0 option A
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Originally posted by sampriya on 07 Nov 2019, 01:31.
Last edited by sampriya on 08 Nov 2019, 02:14, edited 1 time in total.



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 02:48
Which of the following must be true if x < y and \(\frac{x}{z} > \frac{y}{z}\) ? A. z < 0 B. z > 0 C. \(\frac{x}{y}\) > 0 D. x > 0 E. y > 0 Since x < y and inequality \(\frac{x}{z} > \frac{y}{z}\) is with opposite sign, z must be an entity that must be causing the change of sign. Among the choices D and E are straightforward out since both can have both + and  signs. C is also ruled out since x and y can have opposite signs. Only possibility left is A because z > 0 would not lead to change in sign from < to >. Answer A.
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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 07:42
Quote: Which of the following must be true if x<y and x/z >y/z?
A. z<0 B. z>0 C. xy>0 D. x>0 E. y>0 x<y…xy<0 x/z>y/z…x/zy/z>0…xy/z>0 xy<0 so z<0 Ans. (A)



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 08:39
Given x<y, and x/z > y/z, this can only be true if x>0 and y>0 and z<0 or x<0 and y<0 and z<0. In both cases, z<0 must be true.
To illustrate, lets consider the case where x>0 and y>0 and z<0 Let x=2 and y=3, we know x=2 < y=3. if z=1, then x/z=2 and y/z=3. Since 2(x/z) > 3(y/z), then the given condition is satisfied.
In the other case where x<0 and y<0, let x=3 and y=2. 3(x) < 2(y). x/z can only be greater than y/z if z<0, so let z=1. Then x/z=3 and y/z=2. Since 3(x/z) > 2(y/z), then the given condition is satisfied.
In both instances, z<0.
Hence the answer is option A



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 08:44
I cross multiplied, to get zx > zy which would indicate that a sign change has occurred so z < 0
A IMO



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 08:47
the given condition x<y and x/z >y/z can be true if x & z are ve and y is +ve so IMO A ; z<0 should be correct
Which of the following must be true if x<y and x/z >y/z?
A. z<0
B. z>0
C. xy>0
D. x>0
E. y>0



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 14:55
Given x<y but \frac{x}{z}>\frac{y}{z}. Note that the sign is changed when divided by Z.
Theory : Multiplication/division with a negative number can change the inequality sign. Thefore Z has to be negative for this to hold true.
Answer is A.



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 15:21
Which of the following must be true if x < y and \((\frac{x}{z}) > (\frac{y}{z})\)?
\(\frac{(x —y)}{z} > 0\) x—y < 0.
—> in order \(\frac{(x —y)}{z}\) to be positive, z must be less than zero. (z < 0)
The answer is A
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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 15:43
Z should be negative. For example: x=2 and y=3 and z=3 then we have 2<3 so x<y and also 2/3 > 3/3 so x/z > y/z.



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 21:34
A is my answer
Given, (X/z)>(y/z) Here, z can not be zero. So, z must be positive or negative. If z is positive, x>y. If z is negative, x<y
it is also given that x<y. So, Z must be negative.



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Re: Which of the following must be true if x/y and x/z > y/z?
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07 Nov 2019, 22:22
Imo. A
Which of the following must be true if x<y and x/z >y/z?
Let's try from options.
A. z<0, Z is negative, x/z >y/z, If z = 1, x>y, y>x and the same condition x<y is mentioned. Hence, Z must be true to suffice the condition.
B. z>0, Z is positive, x/z >y/z, If z = 1, x>y, which contradicts the give condition x<y. incorrect
C. x/y>0, We don't know the signs of any variables, so there can be multiple options, which could be true, are available.
D. x>0, If x is positive, Y is also positive. But no more information about Z. So multiple values for inequality can be obtained
E. y>0. It implies that y = +ve and x can be +ve/ve. So, again multiple values for inequality can be obtained



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Re: Which of the following must be true if x/y and x/z > y/z?
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12 Nov 2019, 20:37
Bunuel wrote: Competition Mode Question Which of the following must be true if \(x < y\) and \(\frac{x}{z}\) >\(\frac{y}{z}\)? A. \(z < 0\) B. \(z > 0\) C. \(\frac{x}{y} > 0\) D. \(x > 0\) E. \(y > 0\) We see that the inequality sign flips when both x and y are divided by z. This happens when z is negative, i.e., z < 0. Alternate Solution: Using the second inequality, we have: x/z  y/z > 0 (x  y)/z > 0 Since (x  y)/z is positive, (x  y) and z are either both positive or both negative. On the other hand, from the first inequality, we have: x  y < 0 Since (x  y) is negative, it follows that z must also be negative; i.e. z < 0. Answer: A
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Re: Which of the following must be true if x/y and x/z > y/z?
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