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# If ab=8, then is a > b?

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Math Expert
Joined: 02 Sep 2009
Posts: 55274
If ab=8, then is a > b?  [#permalink]

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21 Aug 2017, 05:58
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Difficulty:

45% (medium)

Question Stats:

55% (01:50) correct 45% (01:37) wrong based on 49 sessions

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If ab=8, then is a > b?

(1) -3b >= -18

(2) 2b >= 8

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Re: If ab=8, then is a > b?  [#permalink]

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21 Aug 2017, 06:09
1) -3b >= -18, b<=6, if b =5 then a will be less than b, and if b = 2 then a will be more than b, if b = -4 then a will be -2 then a>b therefore A,D eliminated
2) 2b>=8 , b>=4 , if b =4 then a =2 clearly a <b and if b = 8 a =1 there also a< b, and since b is >4 so we will not consider the negative cases of b which is quite obvious and so for statement 2 we are getting definite NO for what is being asked.

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If ab=8, then is a > b?  [#permalink]

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21 Aug 2017, 23:04
Bunuel wrote:
If ab=8, then is a > b?

(1) -3b >= -18

(2) 2b >= 8

(1) tells us b<=6....(a,b) can take a lot of values (2,4). (-1,-8),(-8,-1) and (4,2) different answers..not sufficient

(2) tells us b>=4...here b will always be 4 or more than 4..sufficient as a will always be less than b for equation to follow since b is greater than $$\sqrt{8}$$ and is non-negative
Sufficient

B
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Luckisnoexcuse
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Re: If ab=8, then is a > b?  [#permalink]

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22 Aug 2017, 00:04
Luckisnoexcuse wrote:
Bunuel wrote:
If ab=8, then is a > b?

(1) -3b >= -18

(2) 2b >= 8

(1) tells us b<=6....(a,b) can take a lot of values (2,4). (-1,-8),(-8,-1) and (4,2) different answers..not sufficient

(2) tells us b>=4...here b will always be 4 or more than 4..sufficient as a will always be less than b for equation to follow since b is greater than $$\sqrt{8}$$ and is non-negative
Sufficient

B

How you got b>√8 kindly elaborate??? or in line 2 may be you wrote by mistake, as by statement 2 i got b>=4 not less than that ??
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Re: If ab=8, then is a > b?  [#permalink]

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22 Aug 2017, 00:08
sahilvijay wrote:
Luckisnoexcuse wrote:
Bunuel wrote:
If ab=8, then is a > b?

(1) -3b >= -18

(2) 2b >= 8

(1) tells us b<=6....(a,b) can take a lot of values (2,4). (-1,-8),(-8,-1) and (4,2) different answers..not sufficient

(2) tells us b>=4...here b will always be 4 or more than 4..sufficient as a will always be less than b for equation to follow since b is greater than $$\sqrt{8}$$ and is non-negative
Sufficient

B

How you got b>√8 kindly elaborate??? or in line 2 may be you wrote by mistake, as by statement 2 i got b>=4 not less than that ??

that was a thought process as b>=4(which is greater than √8 ) since both have to be positive (or both will be negative which we cannot take as b>=4)
the critical point for a=b=√8 and since b is greater than the critical point...automatically it implies that a will be smaller(positive)
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Luckisnoexcuse
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Re: If ab=8, then is a > b?  [#permalink]

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22 Aug 2017, 00:20
okay Luckisnoexcuse
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Re: If ab=8, then is a > b?  [#permalink]

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22 Aug 2017, 03:56
If ab=8, then is a > b?

(1) -3b >= -18

Divide by -3 and flip the sign...then $$x\leq{6}$$

Let b = 6 ......a = 3/4.....Answer is No

Let b = -8......a = -1.......Answer is Yes

Insufficient

(2) 2b >= 8

Divide by 2 (no flip of sign)....then $$x\geq{4}$$

Let Let b = 4 ......a = 2.....Answer is No

Let b = 6 ......a = 3/4.....Answer is No

As b is positive number getting greater, a is positive number getting smaller........Answer is Always NO

Sufficient

Re: If ab=8, then is a > b?   [#permalink] 22 Aug 2017, 03:56
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