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# If 3x-1>0 and y is a real number, which of the following is not always

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If 3x-1>0 and y is a real number, which of the following is not always  [#permalink]

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07 Sep 2018, 23:02
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If $$3x-1 > 0$$ and y is a real number, which of the following is NOT always true?

A) $$x(3x-1) > x-\frac{1}{3}$$

B) $$y(3x-1) < y^2(3x-1)$$

C) $$(y+1)(1-3x) < y(1-3x)$$

D) $$(y+1)(3x-1) > y(3x-1)$$

E) $$(2-y)(1-3x) < (1-y)(1-3x)$$

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If 3x-1>0 and y is a real number, which of the following is not always  [#permalink]

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08 Sep 2018, 00:57
If $$3x-1 > 0$$ and y is a real number, which of the following is NOT always true?

A) $$x(3x-1) > x-\frac{1}{3}....................x(3x-1) > \frac{3x-1}{3}.................$$

$$3x(3x-1)>3x-1...............3x(3x-1)-(3x-1)>0.........(3x-1)(3x-1)>0.....(3x-1)^2>0$$.......true

B) $$y(3x-1) < y^2(3x-1).................y(3x-1) - y^2(3x-1)<0..............(y-y^2)(3x-1)<0......y(y-1)(3x-1)<0..$$
not always true. depends on value of y..... If y=0...and is No and if y = 2 ans is yes

C) $$(y+1)(1-3x) < y(1-3x)...................(y+1)(1-3x) - y(1-3x)<0.........(1-3x)<0............3x-1>0.$$..... true

D) $$(y+1)(3x-1) > y(3x-1)...............(y+1)(3x-1) - y(3x-1)>0................3x-1>0$$.........true

E) $$(2-y)(1-3x) < (1-y)(1-3x)...............(2-y)(1-3x) - (1-y)(1-3x)<0............1-3x<0$$....True

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If 3x-1>0 and y is a real number, which of the following is not always  [#permalink]

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08 Sep 2018, 01:23
chetan2u wrote:
If $$3x-1 > 0$$ and y is a real number, which of the following is NOT always true?

A) $$x(3x-1) > x-\frac{1}{3}....................x(3x-1) > \frac{3x-1}{3}.................$$

$$3x(3x-1)>3x-1...............3x(3x-1)-(3x-1)>0.........(3x-1)(3x-1)>0.....(3x-1)^2>0$$.......true

B) $$y(3x-1) < y^2(3x-1).................y(3x-1) - y^2(3x-1)<0..............(y-y^2)(3x-1)<0......y(y-1)(3x-1)<0..$$
not always true. depends on value of y..... If y=0...and is No and if y = 1/2 ans is yes

C) $$(y+1)(1-3x) < y(1-3x)...................(y+1)(1-3x) - y(1-3x)<0.........(1-3x)<0............3x-1>0.$$..... true

D) $$(y+1)(3x-1) > y(3x-1)...............(y+1)(3x-1) - y(3x-1)>0................3x-1>0$$.........true

E) $$(2-y)(1-3x) < (1-y)(1-3x)...............(2-y)(1-3x) - (1-y)(1-3x)<0............1-3x<0$$....True

B

Did you mean y² will be greater than y when it is equal to negative 1/2? Positive 1/2 doesn't result in y² being greater than y

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Re: If 3x-1>0 and y is a real number, which of the following is not always  [#permalink]

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08 Sep 2018, 01:42
rahulkashyap wrote:
chetan2u wrote:
If $$3x-1 > 0$$ and y is a real number, which of the following is NOT always true?

A) $$x(3x-1) > x-\frac{1}{3}....................x(3x-1) > \frac{3x-1}{3}.................$$

$$3x(3x-1)>3x-1...............3x(3x-1)-(3x-1)>0.........(3x-1)(3x-1)>0.....(3x-1)^2>0$$.......true

B) $$y(3x-1) < y^2(3x-1).................y(3x-1) - y^2(3x-1)<0..............(y-y^2)(3x-1)<0......y(y-1)(3x-1)<0..$$
not always true. depends on value of y..... If y=0...and is No and if y = 1/2 ans is yes

C) $$(y+1)(1-3x) < y(1-3x)...................(y+1)(1-3x) - y(1-3x)<0.........(1-3x)<0............3x-1>0.$$..... true

D) $$(y+1)(3x-1) > y(3x-1)...............(y+1)(3x-1) - y(3x-1)>0................3x-1>0$$.........true

E) $$(2-y)(1-3x) < (1-y)(1-3x)...............(2-y)(1-3x) - (1-y)(1-3x)<0............1-3x<0$$....True

B

Did you mean y² will be greater than y when it is equal to negative 1/2? Positive 1/2 doesn't result in y² being greater than y

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Hi..
Typo.. i meant 2 but wrote 1/2..
(y-y^2)(3x-1)<0, 3x-1>0 so y-y^2<0
y^2-y>0......y(y-1)>0 so between 0 and 1 inclusive Ans is NO and for all other values it is YES
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If 3x-1>0 and y is a real number, which of the following is not always &nbs [#permalink] 08 Sep 2018, 01:42
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# If 3x-1>0 and y is a real number, which of the following is not always

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