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Senior RC Moderator V
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If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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Question Stats: 47% (01:22) correct 53% (01:14) wrong based on 68 sessions

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If $$a = 4$$, what is the value of $$c$$?

(1) $$(abc)^4 = (ab^2c^3)^2$$

(2) $$b = 5$$

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If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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SajjadAhmad wrote:
If $$a = 4$$, what is the value of $$c$$?

(1) $$(abc)^4 = (ab^2c^3)^2$$

(2) $$b = 5$$

solve for #1
$$(abc)^4 = (ab^2c^3)^2$$
we get
a^2=c^2
c = +/-4
insufficeint
#2
only b given c relation missing
from 1 & 2 we cannot get any info
IMO E
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Originally posted by Archit3110 on 29 Apr 2019, 07:59.
Last edited by Archit3110 on 01 May 2019, 01:46, edited 1 time in total.
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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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i think answer is E,
a2=c2 does not mean a=c, it means c2=16, now c can be +4 and -4, so not enough to give exact value of c, hence E is answer
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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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lifeforhuskar wrote:
i think answer is E,
a2=c2 does not mean a=c, it means c2=16, now c can be +4 and -4, so not enough to give exact value of c, hence E is answer

lifeforhuskar
even i thoight that E., but if you square after a^2=c^2 ; you shall get a=c
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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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a = 4 is given , so c can not be -4 , it will take only +4 .

hope this helps

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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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Archit3110 wrote:
lifeforhuskar wrote:
i think answer is E,
a2=c2 does not mean a=c, it means c2=16, now c can be +4 and -4, so not enough to give exact value of c, hence E is answer

lifeforhuskar
even i thoight that E., but if you square after a^2=c^2 ; you shall get a=c

I dont agree, you can try and put -4 or +4 in the equation, both are giving same results. May be we need ER on this.
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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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solve for #1
(abc)4=(ab2c3)2(abc)4=(ab2c3)2
we get
a^2=c^2

c= √a²
c= √16
c= +/- 4

Hence E
But gmat considers Roots to be +ve and square to have both +/- sign
Hence A.

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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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[quote="mohitranjan05"]solve for #1
(abc)4=(ab2c3)2(abc)4=(ab2c3)2
we get
a^2=c^2

c= √a²
c= √16
c= +/- 4

But gmat considers Roots to be +ve and square to have both +/- sign

Can someone explain this...thanks
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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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1
The Answer is (E)

Given A=4, c=?

1) (abc)^4= (ab^2c^3)^2
a^4b^4c^4 - a^2b^4c^6 = 0
a^2b^4c^2(a^2 - c^2) = 0
This implies that either of a,b,c take a zero value or a^2=c^2.
Since we know that a=4, but if b=0, then c can take any value. Hence N.S

2) b=5
NS on its own

Combining both we get either c=0 or c^2=a^2 which means c can have two possible values c=0 and c=a=4. Hence NS

Answer (E)
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If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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Also, in this problem when a^2=c^2, this means that |a| = |c| and since its already given that a=4, we do not need to consider the -ve case.
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SajjadAhmad wrote:
If $$a = 4$$, what is the value of $$c$$?

(1) $$(abc)^4 = (ab^2c^3)^2$$

(2) $$b = 5$$

by (1) we get a^4b^4c^4-a^2b^4c^6=0 and a^2b^4c^4(a^2-c^2) = 0 and a^2b^4c^4(a+c)(a-c) = 0. Since we can factor out (a+c)(a-c) = 0 we see that a=+-c, thus c=+-4 are two solutions. Since we get AT LEAST 2 solutions for C we can mark NS

(2) b =5? So what. Nothing related to c

NS

(1) and (2) --- Copy from (1), and plug in b = 5 ---> a^2(5)^4(4+c)(4-c) = 0. Even after plugging in b = 5 we still get at least two solutions for c thus NS E
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If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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m1033512 wrote:
a = 4 is given , so c can not be -4 , it will take only +4 .

hope this helps

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I don't quite get, how you reached to this conclusion that c can not be -4. Can you explain this a bit further?
IMO,
St(1) does not provide us with any of the values, but a = 4. We know nothing about b and c.
So, b and c can have ANY of the THREE signs : Positive, Negative, and Zero.

B and C can have a range of values. If b = 0 then C can have any value on the number line and vice versa. Not Sufficient.

St(2) is clearly insufficient.

St(1) + St(2) :
After combining both the statements, we sill get C^2 = 16 and thus, C can be +4 or -4. Two values. Not Sufficient.
The problem is with the square, we don't know whether it is +4 or - 4, but if we had something like c^odd number = Some positive number, then surely C would have been a positive number.

I hope this helps. I don't mind Kudos!
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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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|a|=|c| so two cases c=a or c=-a
Archit3110 wrote:
SajjadAhmad wrote:
If $$a = 4$$, what is the value of $$c$$?

(1) $$(abc)^4 = (ab^2c^3)^2$$

(2) $$b = 5$$

solve for #1
$$(abc)^4 = (ab^2c^3)^2$$
we get
a^2=c^2
square both sides
a=c
sufficeint
#2
only b given c relation missing
IMO A

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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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(stat.1).... (a^4•b^4•c^4)=(a^2•b^4•c^6) —> (a^4•b^4)/(a^2•b^4)=c^6/c^4 —> a^2•b^0=c^2 —> c^2=a^2
Haha forgot the absolute value though credit to Skyline393 who reminded me so |c|=|a| —> c=-/+a
c=+/-4
But why you guys doing some complicated calc. with the statement (1) though I am an advocate of not dividing by an unknown value. Lolx

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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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m1033512 wrote:
a = 4 is given , so c can not be -4 , it will take only +4 .

hope this helps

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Hi

a^2 = c^2 is given and a=4
16= c^2

c can be 4 or -4 to have square 16.
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Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5  [#permalink]

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1
Ans. is E
after solving the equation in A, we get c^2=16 => c=4 or-4 Re: If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5   [#permalink] 05 Aug 2019, 07:37
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# If a = 4, what is the value of c? (1) (abc)^4 = (ab^2c^3)^2 (2) b = 5

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