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

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20 Apr 2013, 00:56

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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?

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

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20 Apr 2013, 01:16

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emmak 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) –½

(C) 0

(D) ½

(E) 1

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Ok. Looking at options will give you what we are looking at. A and B are out because square root will always be positive. So, we are not dealing with negative numbers. C is out because of 1/0 --> infinity. We can check D and E. E satisfy in first shot. _________________

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

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06 May 2013, 23:25

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assume that all the operations give a constant answer "k". take 1st order for eg. HGF which gives sqroot{c/x} = k 2nd order eg. HFG which gives c*sqroot{1/x} = k

Therefore, sqr{c/x} = c*sqr{1/x} this gives, c = sqr{c} => sqr{c} = 1 => c = 1

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

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07 May 2013, 00:36

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I approached this question by going through the answers. The value of C changes with values in the option A,B,C,D when different combination is applied. The value of E stands out in any operation, the value remains same whether it is multiplication or division. E is the answer strainght away.

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

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07 May 2013, 02:22

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In such a problem, we should consider an example. For instance, x = 2.

Considering the operations we have :

- F : square root ; - G : multiply by a constant c ; - H : reciprocal ;

We want to know which value of the constant "c" that would allow us to get the same result no matter the order of operations applied. Since we have three operations, we get to have 6 possibilities (to be even more accurate 3! = 6) :

F - G - H : \(\frac{1}{c*\sqrt{2}}\) F - H - G : \(\frac{c}{\sqrt{2}}\) G - F - H : \(\frac{1}{\sqrt{2*c}}\) G - H - F : \(\sqrt{\frac{1}{2*c}}\) H - F - G : \(c*\sqrt{\frac{1}{2}}\) H - G - F : \(\sqrt{\frac{c}{2}}\)

As you can see, there are instances where the constant c is within a square root, or in the denominator of a fraction. Which means that zero and non-zero negative values can't be considered, therefore answers A, B and C are excluded.

Answer choice D is a fraction and seeing as the constant c can be either in the numerator or the denominator of the resulting fraction, c can either become \(\frac{1}{2}\) or 2. Which means we get different values everytime we change the order of the operations. Therefore, answer choice D is excluded as well.

Finally, we're left with one possible answer, E, which gives us \(c = 1\).

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

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07 May 2013, 17:43

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) –½

(C) 0

(D) ½

(E) 1

it is simple if we work our way from answer choices

A) if we multiplied c=-1 by x in one of the operations .. there exist no real square root...out b) same with the -ve sign like above ..........out c) there is no reciprocal for x when multiplied by zero i ..out d) just try 2 orders (c : x/2 ,f: sqrt x/2 , h: sqrt x/2) (sqrtx , 2sqrtx 1/2 sqrt x)...out E) ... the only one left intact ... bingo

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

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22 Aug 2015, 19:16

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