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# If 5a > 6b, is a greater than zero?

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Math Expert
Joined: 02 Sep 2009
Posts: 60646
If 5a > 6b, is a greater than zero?  [#permalink]

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29 Apr 2016, 03:51
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75% (hard)

Question Stats:

44% (02:09) correct 56% (02:25) wrong based on 39 sessions

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If 5a > 6b, is a greater than zero?

(1) a > b
(2) 4b – 5a = 24

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Re: If 5a > 6b, is a greater than zero?  [#permalink]

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30 Apr 2016, 04:42
Bunuel wrote:
If 5a > 6b, is a greater than zero?

(1) a > b
(2) 4b – 5a = 24

It was tough for me...got confused in the middle ...can u pls explain?
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Math Expert
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Posts: 8336
If 5a > 6b, is a greater than zero?  [#permalink]

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30 Apr 2016, 04:53
1
Balajikarthick1990 wrote:
Bunuel wrote:
If 5a > 6b, is a greater than zero?

(1) a > b
(2) 4b – 5a = 24

It was tough for me...got confused in the middle ...can u pls explain?

Hi,
it is slightly tough

Bunuel wrote:
If 5a > 6b, is a greater than zero?

(1) a > b
(2) 4b – 5a = 24

5a>6b...
(1) a > b
a=8, and b=4.. satisfies both equation and a>0
a=-2, and b=-3.. again satisfies both equation and a<0..
Insuff

(2) 4b – 5a = 24
now 5a>6b or 6b-5a<0.. OR 2b+4b-5a <0..
we know from this statement that 4b-5a = 24,
substitute this value in 2b+4b-5a<0.
SO 2b+24<0..or 2b<-24 and b<-12..
Now initial equation is 4b-5a=24 ,
5a = 4b-24...lets take max value as b=-12 although it is even <-12
5a= 4*-12 -24 =-48-24=-72 so a<0
Suff

B
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Re: If 5a > 6b, is a greater than zero?  [#permalink]

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30 Apr 2016, 05:40
chetan2u wrote:
Balajikarthick1990 wrote:
Bunuel wrote:
If 5a > 6b, is a greater than zero?

(1) a > b
(2) 4b – 5a = 24

It was tough for me...got confused in the middle ...can u pls explain?

Hi,
it is slightly tough

Bunuel wrote:
If 5a > 6b, is a greater than zero?

(1) a > b
(2) 4b – 5a = 24

5a>6b...
(1) a > b
a=8, and b=4.. satisfies both equation and a>0
a=-2, and b=-3.. again satisfies both equation and a<0..
Insuff

(2) 4b – 5a = 24
now 5a>6b or 6b-5a<0.. OR 2b+4b-5a <0..
we know from this statement that 4b-5a = 24,
substitute this value in 2b+4b-5a<0.
SO 2b+24<0..or 2b<-24 and a<-48..
so a<0
Suff

B

Hi,

I do not understand how a<-48

if, for example, a=-50 & b=-15 which invalidates the condition that 5a>6b

If 2b<-24...... b<-12, if substitute in 5a>6b.........5a> 6 (-12) then a can take any value -ve or 0 or+ve

Do I miss something?
Math Expert
Joined: 02 Aug 2009
Posts: 8336
Re: If 5a > 6b, is a greater than zero?  [#permalink]

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30 Apr 2016, 06:03
1
Mo2men wrote:
Hi,

I do not understand how a<-48

if, for example, a=-50 & b=-15 which invalidates the condition that 5a>6b

If 2b<-24...... b<-12, if substitute in 5a>6b.........5a> 6 (-12) then a can take any value -ve or 0 or+ve

Do I miss something?

Hi,
there was a typo in solution..
now b<-12..
statement II says 4b-5a = 24..
so 5a = 4b-24..
if b <-12, 4b will also be -ive and it is added to another -ive number -24 so 5a will be -ive and hence a<0..
try with max value, although slightly more than -12, so b=-12..
5a = 4*-12-24=-72. ... so MAX value of a is -72 HENCE a<0..
suff

Hope it helps
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Re: If 5a > 6b, is a greater than zero?  [#permalink]

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14 Jan 2020, 19:21
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Re: If 5a > 6b, is a greater than zero?   [#permalink] 14 Jan 2020, 19:21
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