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QOTD#25 If the value of the expression above is to be double
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08 Oct 2016, 05:31
08 Oct 2016, 05:31
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\(\frac{u}{v} * \frac{x}{(y+z)}\)
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
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
Drill 1
Question: 10
Page: 284
Question: 10
Page: 284
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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
13 Nov 2016, 08:30
5
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
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!]
General Discussion
Re: QOTD#25 If the value of the expression above is to be double
[#permalink]
08 Oct 2016, 05:34
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.
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.
