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The product of the number 7 and a number x is divided by 4. If the squ
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08 Apr 2023, 10:15
08 Apr 2023, 10:15
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The product of the number 7 and a number x is divided by 4. If the square root of the resulting number is twice of x and x > 0, then what is the value of x ?
0
1/16
1/12
4/15
7/16
0
1/16
1/12
4/15
7/16
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: The product of the number 7 and a number x is divided by 4. If the squ
[#permalink]
15 Apr 2023, 21:00
15 Apr 2023, 21:00
1
Expert Reply
Let's set up the given problem as an equation and solve for x.
The product of the number 7 and a number x is divided by 4:
(7x) / 4
The square root of the resulting number is twice x:
√((7x) / 4) = 2x
We can square both sides of the equation to eliminate the square root:
(√((7x) / 4))^2 = (2x)^2
Simplifying further:
(7x) / 4 = 4x^2
Multiplying both sides of the equation by 4 to eliminate the fraction:
7x = 16x^2
Bringing all terms to one side of the equation:
16x^2 - 7x = 0
Now we can factor out x:
x(16x - 7) = 0
Setting each factor to zero separately:
x = 0 or 16x - 7 = 0
If x = 0, it does not satisfy the condition x > 0 given in the problem.
So we focus on the second factor:
16x - 7 = 0
Adding 7 to both sides:
16x = 7
Dividing both sides by 16:
x = 7/16
So the value of x that satisfies the given conditions (x > 0) is x = 7/16. Therefore, the correct option is "7/16".
The product of the number 7 and a number x is divided by 4:
(7x) / 4
The square root of the resulting number is twice x:
√((7x) / 4) = 2x
We can square both sides of the equation to eliminate the square root:
(√((7x) / 4))^2 = (2x)^2
Simplifying further:
(7x) / 4 = 4x^2
Multiplying both sides of the equation by 4 to eliminate the fraction:
7x = 16x^2
Bringing all terms to one side of the equation:
16x^2 - 7x = 0
Now we can factor out x:
x(16x - 7) = 0
Setting each factor to zero separately:
x = 0 or 16x - 7 = 0
If x = 0, it does not satisfy the condition x > 0 given in the problem.
So we focus on the second factor:
16x - 7 = 0
Adding 7 to both sides:
16x = 7
Dividing both sides by 16:
x = 7/16
So the value of x that satisfies the given conditions (x > 0) is x = 7/16. Therefore, the correct option is "7/16".
gmatclubot
Re: The product of the number 7 and a number x is divided by 4. If the squ [#permalink]
15 Apr 2023, 21:00
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