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# Operation F means “take the square root,” operation G means “multiply

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Math Expert
Joined: 02 Sep 2009
Posts: 60727
Operation F means “take the square root,” operation G means “multiply  [#permalink]

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04 Dec 2019, 01:44
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Difficulty:

55% (hard)

Question Stats:

63% (01:36) correct 37% (01:27) wrong based on 91 sessions

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Operation F means “take the square root,” operation G means “multiply by constant c,” and operation H means “take the reciprocal.” For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?

(A) –1

(B) –1/2

(C) 0

(D) 1/2

(E) 1

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Re: Operation F means “take the square root,” operation G means “multiply  [#permalink]

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04 Dec 2019, 01:50
IMO E ; 1
would be correct as all possible given operations are possible with 1 only

Bunuel wrote:
Operation F means “take the square root,” operation G means “multiply by constant c,” and operation H means “take the reciprocal.” For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?

(A) –1

(B) –1/2

(C) 0

(D) 1/2

(E) 1

Are You Up For the Challenge: 700 Level Questions
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Joined: 16 Feb 2015
Posts: 275
Location: United States
Concentration: Finance, Operations
Operation F means “take the square root,” operation G means “multiply  [#permalink]

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Updated on: 05 Dec 2019, 21:53
Bunuel wrote:
Operation F means “take the square root,” operation G means “multiply by constant c,” and operation H means “take the reciprocal.” For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?

(A) –1

(B) –1/2

(C) 0

(D) 1/2

(E) 1

Are You Up For the Challenge: 700 Level Questions

Only Option is 0 1 is the answer. Thanks To Ahmed9955
As anything multiplied with 0 will give same result always. 1/0 is not possilble.

I should have checked all option. As 1 will be remain 1 in either of operations in any order.

IMO-E

Originally posted by rajatchopra1994 on 04 Dec 2019, 02:01.
Last edited by rajatchopra1994 on 05 Dec 2019, 21:53, edited 1 time in total.
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Re: Operation F means “take the square root,” operation G means “multiply  [#permalink]

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05 Dec 2019, 09:14
1
rajatchopra1994 wrote:
Bunuel wrote:
Operation F means “take the square root,” operation G means “multiply by constant c,” and operation H means “take the reciprocal.” For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?

(A) –1

(B) –1/2

(C) 0

(D) 1/2

(E) 1

Are You Up For the Challenge: 700 Level Questions

Only Option is 0
As anything multiplied with 0 will give same result always.
As Doesn't matter the in which operations are applied.
So if C is 0 & multiplied at any operation, result will be same.

IMO-C

Hi rajat,

But 1/ 0 is not defined ;
Therefore
Consider you first apply operation G that is you multiply with zero, the answer will be a Zero
but if you apply operation 'H' first, it is undefined,
now if you multiply with a zero that is applying operation 'G' you'll not get a zero.

Option A and B can be rejected due to Minus sign ;
Option C will not give us the same value;

Therefore only possible solution is 1
that is , Option E
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Joined: 16 Feb 2015
Posts: 275
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Re: Operation F means “take the square root,” operation G means “multiply  [#permalink]

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05 Dec 2019, 09:18
1
Ahmed9955 wrote:
rajatchopra1994 wrote:
Bunuel wrote:
Operation F means “take the square root,” operation G means “multiply by constant c,” and operation H means “take the reciprocal.” For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?

(A) –1

(B) –1/2

(C) 0

(D) 1/2

(E) 1

Are You Up For the Challenge: 700 Level Questions

Only Option is 0
As anything multiplied with 0 will give same result always.
As Doesn't matter the in which operations are applied.
So if C is 0 & multiplied at any operation, result will be same.

IMO-C

Hi rajat,

But 1/ 0 is not defined ;
Therefore
Consider you first apply operation G that is you multiply with zero, the answer will be a Zero
but if you apply operation 'H' first, it is undefined,
now if you multiply with a zero that is applying operation 'G' you'll not get a zero.

Option A and B can be rejected due to Minus sign ;
Option C will not give us the same value;

Therefore only possible solution is 1
that is , Option E

You are right.

It should be 1.
IMO-E

Posted from my mobile device
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Re: Operation F means “take the square root,” operation G means “multiply  [#permalink]

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06 Dec 2019, 09:44
Bunuel wrote:
Operation F means “take the square root,” operation G means “multiply by constant c,” and operation H means “take the reciprocal.” For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?

(A) –1
(B) –1/2
(C) 0
(D) 1/2
(E) 1

F=√x
G=xc
H=1/x

G(x)=xc
F(G(x))=√(xc)
H(F(G(x)))=1/√(xc)
G(H(F(x)))=1c/(√x)

c=0: 1/√(xc)=1/√0=1/0, div by 0 is undefined
c=-1: 1/√(xc)=1/√(-x), root of a negative is undefined; c>0.
c=1

Ans (E)
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Re: Operation F means “take the square root,” operation G means “multiply  [#permalink]

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10 Dec 2019, 20:30
Bunuel wrote:
Operation F means “take the square root,” operation G means “multiply by constant c,” and operation H means “take the reciprocal.” For which value of c is the result of applying the three operations to any positive x the same for all of the possible orders in which the operations are applied?

(A) –1

(B) –1/2

(C) 0

(D) 1/2

(E) 1

Are You Up For the Challenge: 700 Level Questions

We see that the problem is saying, for example, that H(G(F(x)) = H(F(G(x)). Expanding both sides of the equation, we have:

1/(c√x) = 1/√(cx)

c√x = √(cx) = (√c)(√x)

Since √x is positive, we can divide each side by √x:

c = √c

Of the given answer choices, only c = 0 and c = 1 satisfy √c = c. However, c cannot equal 0 because otherwise, the expression 1/(c√x) (and some of the other expressions obtained by applying the operations in different orders) is undefined. Thus, it must be true that c = 1.

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Re: Operation F means “take the square root,” operation G means “multiply   [#permalink] 10 Dec 2019, 20:30
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