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

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Manager
Joined: 09 Feb 2013
Posts: 114
Operation F means “take the square root,” operation G means  [#permalink]

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19 Apr 2013, 23:56
6
9
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:54) correct 37% (01:40) wrong based on 299 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) –½

(C) 0

(D) ½

(E) 1

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Intern
Joined: 03 Mar 2013
Posts: 40
Location: India
Concentration: Technology, Strategy
GMAT 1: 730 Q49 V41
GPA: 3
WE: Information Technology (Telecommunications)
Re: Operation F means “take the square root,” operation G means  [#permalink]

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20 Apr 2013, 00:10
2
The contention is between 0 and 1

for zero you get two values 0 and \frac{1}{0}

for one you get only one answer \frac{1}{\sqrt{x}}

Hence the answer is E i.e 1
Intern
Joined: 05 Apr 2010
Posts: 12
Re: Operation F means “take the square root,” operation G means  [#permalink]

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20 Apr 2013, 00:14
1
Well...for this Q...I would look at values of C which change when a particular operation is applied.
All except E change the value. Hence, E.

Following are a few combinations FCH, CHF, CFH:
FCH
x becomes sqrt[x] -> c * sqrt[x] -> 1/c * sqrt[x]
If c = -1, result = -1/c * sqrt[x]

CHF
x becomes cx -> 1/cx -> sqrt[1/cx]

Value gets changed for FCH and CHF. Hence A is eliminated.

Only E stands because no matter any operation, the value remains same...be it multiplying or dividing.
Manager
Joined: 27 Feb 2012
Posts: 119
Re: Operation F means “take the square root,” operation G means  [#permalink]

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20 Apr 2013, 00:16
1
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

Express appreciation by pressing KUDOS.

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.
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Intern
Joined: 20 Apr 2013
Posts: 20
Concentration: Finance, Finance
GMAT Date: 06-03-2013
GPA: 3.3
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Re: Operation F means “take the square root,” operation G means  [#permalink]

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04 May 2013, 09:10
1
Operation G means “multiply by constant C
Intern
Joined: 31 Mar 2013
Posts: 6
Re: Operation F means “take the square root,” operation G means  [#permalink]

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06 May 2013, 22:25
2
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
Intern
Joined: 05 Apr 2013
Posts: 1
Re: Operation F means “take the square root,” operation G means  [#permalink]

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06 May 2013, 23:36
1
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.

KUDOS
Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 29
Location: United States
GMAT 1: 550 Q47 V23
GPA: 3.7
WE: Analyst (Consulting)
Re: Operation F means “take the square root,” operation G means  [#permalink]

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07 May 2013, 01:22
2
1
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 $$c = 1$$.

Hope that helped.
Intern
Joined: 24 Apr 2013
Posts: 48
Schools: Duke '16
Re: Operation F means “take the square root,” operation G means  [#permalink]

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07 May 2013, 15:58
Man i got a half D I was sooo close. it was a guestimate though hehe
Retired Moderator
Joined: 05 Jul 2006
Posts: 1713
Re: Operation F means “take the square root,” operation G means  [#permalink]

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07 May 2013, 16:43
1
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
Senior Manager
Joined: 15 Jan 2017
Posts: 353
Re: Operation F means “take the square root,” operation G means  [#permalink]

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17 Aug 2017, 22:25
Clearly it asks us if we select a value of C would we get a mirror value which is the same - I did this by substituting quickly:
- -1 and -1/2 and 0 out because sq root won't work on it; plus qx stem says it needs a positive value
- 1/2 is also out becz sq root won't give us 1/2

leaves us with 1 only --> if C = 1; then root 1= 1/ 1*1 = 1/ reciprocal 1 = 1
Ans E
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Posts: 9893
Re: Operation F means “take the square root,” operation G means  [#permalink]

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15 Oct 2018, 05:53
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Re: Operation F means “take the square root,” operation G means   [#permalink] 15 Oct 2018, 05:53
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