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# If b ≠ 0 and a > b, is a > c? (1) a/b> c/b (2) 5ab > 6bc

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
If b ≠ 0 and a > b, is a > c? (1) a/b> c/b (2) 5ab > 6bc  [#permalink]

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28 Aug 2015, 01:31
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Difficulty:

45% (medium)

Question Stats:

65% (02:04) correct 35% (01:46) wrong based on 93 sessions

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If b ≠ 0 and a > b, is a > c?

(1) a/b> c/b

(2) 5ab > 6bc

Kudos for a correct solution.

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If b ≠ 0 and a > b, is a > c? (1) a/b> c/b (2) 5ab > 6bc  [#permalink]

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28 Aug 2015, 07:08
1
1
Remember b could be positive or negative number.Question is whether or not a>c.

Lets look at the statements

Statement 1 : a/b>c/b,if b=positive number(like 1,0.5,3,4/7,5,6 etc) we can simplify this inequality by multiplying both side b , as a>c
but,if b=negative number(like -1,-0.5,-4/7,5,6 etc) if we want to simplify we must have to alter the inequality as a<c

Statement 1 is not sufficient

Statement 2 : the reasoning of this statement is same as statement 1,like this,

5ab>6bc,if b=positive number (like 1,0.5,3,4/7,5,6 etc) we can simplify this inequality by multiplying both side b, as a>6/5 c (single amount of a is greater more than greater amount of c)
but,b=negative number(like 1,0.5,3,4/7,5,6 etc) we have to reverse the sign of inequality as a<6/5 c

Statement 2 is not sufficient

Since any of this two statement solve the issue whether or not b is positive or negative.My Correct Answer is E
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Re: If b ≠ 0 and a > b, is a > c? (1) a/b> c/b (2) 5ab > 6bc  [#permalink]

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28 Aug 2015, 07:26
Statement 1 - a/b> c/b
If you multiply both sides by b, you get a>c. Thus, sufficient

Statement 2 - 5ab > 6bc
1) Divide both sides by b --> 5a>6c
2) You get a/b > 6/5

Thus sufficient

Answer is D
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Re: If b ≠ 0 and a > b, is a > c? (1) a/b> c/b (2) 5ab > 6bc  [#permalink]

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28 Aug 2015, 07:32
rohankant12 wrote:
Statement 1 - a/b> c/b
If you multiply both sides by b, you get a>c. Thus, sufficient

Statement 2 - 5ab > 6bc
1) Divide both sides by b --> 5a>6c
2) You get a/b > 6/5

Thus sufficient

Answer is D

Be extremely careful with multiplying with variables in inequality questions when you do not know the signs. In this case, you dont know whether b<0 or >0. The sign of inequality changes when you multiply the inequality by a negative number.

Thus, the method to solve it is:

a/b > c/b --> (a-c)/b > 0 ---> 2 cases; either a-c>0 and b>0 or a-c<0 and b<0. Thus you get 2 cases , making statement as NOT SUFFICIENT.

You can even test some numbers.

Per statement 2, 5ab > 6bc, again you can not divide by b as you do not know the sign of 'b'.

5ab > 6bc ---> b(5a-6c) >0 again, 2 cases : either b >0 and 5a-6c>0 or b<0 and 5a-6c <0. NOT SUFFICIENT.

Even when you combine 2 statements, you still can not figure out the sign of b , giving E as the correct answer.
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Re: If b ≠ 0 and a > b, is a > c? (1) a/b> c/b (2) 5ab > 6bc  [#permalink]

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10 Apr 2018, 12:56
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Re: If b ≠ 0 and a > b, is a > c? (1) a/b> c/b (2) 5ab > 6bc   [#permalink] 10 Apr 2018, 12:56
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# If b ≠ 0 and a > b, is a > c? (1) a/b> c/b (2) 5ab > 6bc

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