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QOTD#25 If the value of the expression above is to be double
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13 Nov 2016, 08:30
5
Expert Reply
sandy wrote:
\(\frac{u}{v} * \frac{x}{(y+z)}\)
If the value of the expression above is to be doubled by halving exactly one of the five variables, which variable should be halved?
A. u B. v C. x D. y E. z
Combine the two fractions to get ux/(v)(y+z) First notice that, if we make the numerator smaller, the value of the entire fraction will become smaller. (we want to DOUBLE the value of the entire fraction). So, we can ELIMINATE u (A) and x (C) since halving these values in the numerator would make the entire fraction smaller
IMPORTANT: We have 3 answer choices remaining: v, y and z. Since there can be only one correct answer, I can ELIMINATE y and z. Why? Notice that y and z play the same role in the expression ux/(v)(y+z). y and z are each part of the sum y+z. So, it makes not sense that one would be the correct choice and the other would be incorrect. That is, it's impossible that halving one of those variables would end up doubling the entire fraction BUT halving the other variable would not have the same effect. So, we can ELIMINATE y (D) and z (E)
Answer: B
ASIDE: notice what happens when we take ux/(v)(y+z) and replace v with v/2[i.e., halving v] we get: ux/(v/2)(y+z) Simplify to get: 2ux/(v)(y+z) [we've doubled the original value!] _________________
Re: QOTD#25 If the value of the expression above is to be double
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08 Oct 2016, 05:34
Expert Reply
Explanation
Plug in values for the variables, such as u = 2, v = 4, x = 6, y = 8, and z = 10. With these values, the expression equals \(\frac{1}{6}\). . Try halving each of the values to find which one would change the value of the expression to \(\frac{1}{3}\). Halving v to 2 works; the answer is choice B.
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Re: QOTD#25 If the value of the expression above is to be double
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Updated on: 19 Aug 2019, 14:03
GreenlightTestPrep wrote:
sandy wrote:
\(\frac{u}{v} * \frac{x}{(y+z)}\)
If the value of the expression above is to be doubled by halving exactly one of the five variables, which variable should be halved?
A. u B. v C. x D. y E. z
Combine the two fractions to get ux/(v)(y+z) First notice that, if we make the numerator smaller, the value of the entire fraction will become smaller. (we want to DOUBLE the value of the entire fraction). So, we can ELIMINATE u (A) and x (C) since halving these values in the numerator would make the entire fraction smaller
IMPORTANT: We have 3 answer choices remaining: v, y and z. Since there can be only one correct answer, I can ELIMINATE y and z. Why? Notice that y and z play the same role in the expression ux/(v)(y+z). y and z are each part of the sum y+z. So, it makes not sense that one would be the correct choice and the other would be incorrect. That is, it's impossible that halving one of those variables would end up doubling the entire fraction BUT halving the other variable would not have the same effect. So, we can ELIMINATE y (D) and z (E)
ASIDE: notice what happens when we take ux/(v)(y+z) and replace v with v/2[i.e., halving v] we get: ux/(v/2)(y+z) Simplify to get: 2ux/(v)(y+z) [we've doubled the original value!]
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Originally posted by JNeen on 16 Aug 2019, 13:48.
Last edited by JNeen on 19 Aug 2019, 14:03, edited 1 time in total.
Re: QOTD#25 If the value of the expression above is to be double
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16 Aug 2021, 11:38
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