if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 : GMAT Data Sufficiency (DS)
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# if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2

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if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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18 Jun 2011, 10:32
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85% (hard)

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17% (02:11) correct 83% (02:13) wrong based on 30 sessions

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if a not equal to Zero,
1/a < a/(b^4+3)

1. a^2=b^2
2. a^2 = b^4

PS: Any one who has MGMAT adv Quant book can confirm ,whether the uestion is correct or there is a typo.
I dont agree with the OA . I believe there is a typo. Its page 106

PROPER VERSION OF THIS QUESTION IS HERE: if-a-does-not-0-is-1-a-a-b-120511.html
[Reveal] Spoiler: OA
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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18 Jun 2011, 10:52
sudhir18n wrote:
if a not equal to Zero,
1/a < a/(b^4+3)

1. a^2=b^2
2. a^2 = b^4

PS: Any one who has MGMAT adv Quant book can confirm ,whether the uestion is correct or there is a typo.
I dont agree with the OA . I believe there is a typo. Its page 106

can't be A.

(1)
a^2=b^2 --> is true for both -1 and 1 which give different answers
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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18 Jun 2011, 11:03
is 1/a < a / (b^4) + 3

(1) since a can't be 0, b also can't be 0 because a^2=b^2.......any other number works here though the only problem is the sign....-1 AND 1 can work. Hence this statement by itself is insufficient.

1/(-1) < -1 / (1)^4 + 3 --> -1 < -1/4 << YES!!
1/1 < 1/1^4+3 = 1 < 1/4 << NO!!

(2)
a^2=b^4 runs into the same problem as (1). since both exponents are even, they hide the sign of their base.

Together: Doesent really make a difference. Again sign of base is hidden.

Hence, IMO
[Reveal] Spoiler:
(E)

In a question like this where both statements are giving you the exact same information, the answer is usually (D) or (E)........

(A) doesent make sense to me
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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18 Jun 2011, 11:18
sudhir18n wrote:
if a not equal to Zero,
1/a < a/(b^4+3)

1. a^2=b^2
2. a^2 = b^4

PS: Any one who has MGMAT adv Quant book can confirm ,whether the uestion is correct or there is a typo.
I dont agree with the OA . I believe there is a typo. Its page 106

I don't have the book but the answer should be E.

b=1
a=1 or a="-1"

Not Sufficient combined. Please intimate them.
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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20 Jun 2011, 10:17
Yes, this question was discussed at length at BTG recently. The answer is definitely E; the book is wrong.
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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23 Jun 2011, 03:02
a check for 1,1; 1,-1; -1,1;-1,-1. gives different results. Not sufficient,

b checking for above values and +|-4,2 also give different results.
not sufficient.

a+b the +|- 1 gives the same results as a.

E it is.
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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01 Aug 2011, 04:23
I solve this question mathematically, works better for me than plugging in numbers.

I will share if anyone wants. thanks.
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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01 Aug 2011, 07:00
1. Not Sufficient

a = +- b

b =1 => a = +- 1

a = 1 , LHS > RHS
a= -1, LHS < RHS

2. Not sufficient

a = +- b^2

lets say b=1 => a = +- 1

same as 1.

together

b can be 0 ,-1 ,1

when b =1 , same situation as 1 & 2.

Not sufficient.

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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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09 Dec 2015, 22:07
1/a<a/(b^4+3) may be rewritten as:

Multiplying both sides by a^2
a < a^3/(b^4+3)
further shifting RHS to LHS and taking "a" common

a*(1-a^2/(b^4+3))<0 ....................(1)

For statement 1 Eq (1) reduces to a*(1-some positive no less thn 1)<0 So depends on sign of "a" which is not given
For statement 2 Eq 1again reduces to a*(1-some positive no less thn 1)<0 So depends on sign of "a" which is not given

Combining statement 1 and 2 will give
a^2=b^2
a^2=b^4
b=+/-1 which again doesn't give ne inf abt sign of "a"
so Not sufficient

Hence "E"
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2 [#permalink]

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09 Dec 2015, 22:34
PROPER VERSION OF THIS QUESTION IS HERE: if-a-does-not-0-is-1-a-a-b-120511.html
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Re: if a not equal to Zero, 1/a < a/(b^4+3) 1. a^2=b^2 2. a^2   [#permalink] 09 Dec 2015, 22:34
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