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Operation F means “take the square root,” operation G means “multiply
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04 Dec 2019, 01:44
4
00:00
A
B
C
D
E
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?
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?
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?
Re: Operation F means “take the square root,” operation G means “multiply
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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?
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
Re: Operation F means “take the square root,” operation G means “multiply
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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?
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
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?
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
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?
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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63% (01:36) correct 
