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Operation F means “take the square root,” operation G means “multiply
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04 Dec 2019, 01:44
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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 Are You Up For the Challenge: 700 Level Questions
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Re: Operation F means “take the square root,” operation G means “multiply
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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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Operation F means “take the square root,” operation G means “multiply
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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 QuestionsOnly Option is 0 1 is the answer. Thanks To Ahmed9955As 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. IMOE



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Re: Operation F means “take the square root,” operation G means “multiply
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05 Dec 2019, 09:14
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 QuestionsOnly 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. IMOC 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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Re: Operation F means “take the square root,” operation G means “multiply
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05 Dec 2019, 09:18
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 QuestionsOnly 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. IMOC 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. Will update my answer. It should be 1. IMOE Posted from my mobile device



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Re: Operation F means “take the square root,” operation G means “multiply
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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=1/2: 1/√(xc)=1/√(x/2)=√(2/x)… 1c/(√x)=1/2/(√x)=1/(2√x)…different answers c=1 Ans (E)



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Re: Operation F means “take the square root,” operation G means “multiply
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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 QuestionsWe 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. Answer: E
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Re: Operation F means “take the square root,” operation G means “multiply
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