If $$x=3y=4z$$ Which of the following must equal 6x?
$$I.18y$$
$$II.3y+20z$$
$$III.\frac{(4y+10z)}{3}$$
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
The OA is D.
I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
If x = 3y = 4z, which of the following must equal 6x?
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If x = 3y = 4z, then 6x = 18y = 24zLUANDATO wrote:If $$x=3y=4z$$ Which of the following must equal 6x?
$$I.18y$$
$$II.3y+20z$$
$$III.\frac{(4y+10z)}{3}$$
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
The OA is D.
I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
I. Well, we can see above that 6x = 18y, so this is in.
II. 3y + 20z can be rephrased as 3y + 5* (4z), if 3y = 4z, then we can substitute, and get 3y + 5 *(3y) = 3y + 15y = 18y. So this one is also in.
No need to test III, as we don't have the option of selecting I, II, and III. The answer must be D
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Hi LUANDATO,If $$x=3y=4z$$ Which of the following must equal 6x?
$$I.18y$$
$$II.3y+20z$$
$$III.\frac{(4y+10z)}{3}$$
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
The OA is D.
I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Let's take a look at your question.
$$x=3y=4z$$
We need to check which of the given expressions are equivalent to 6x. Let's evaluate them one by one.
$$I. 18y$$
Let's rewrite y in terms of x.
Since,
$$x\ =\ 3y$$ $$y=\frac{x}{3}$$
Replace value of y in 18y, we get,
$$=18\left(\frac{x}{3}\right)$$
$$=6x$$
$$II.3y+20z$$
From x=3y=4z, we get,
$$y=\frac{x}{3},\ z=\frac{x}{4}$$
Plugin the values in II, we get:
$$=3\left(\frac{x}{3}\right)+20\left(\frac{x}{4}\right)$$
$$=x+5x=6x$$
$$III.\frac{(4y+10z)}{3}$$
Replace values of y and z, we get
$$=\frac{4\left(\frac{x}{3}\right)+10\left(\frac{x}{4}\right)}{3}$$
$$=\frac{\frac{4x}{3}+\frac{5x}{2}}{3}$$
$$=\frac{\frac{8x+15x}{6}}{3}$$
$$=\frac{23x}{6\times3}=\frac{23x}{18}$$
Therefore, only I and II are equal to 6x.
Hence, Option D is correct.
Hope it helps.
I am available if you'd like any follow up.
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We are given that x = 3y = 4z and need to determine what must equal 6x. From the given information, we see that 6x = 18y = 24z. Let's analyze each Roman numeral:LUANDATO wrote:If $$x=3y=4z$$ Which of the following must equal 6x?
$$I.18y$$
$$II.3y+20z$$
$$III.\frac{(4y+10z)}{3}$$
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
I. 18y
Since 6x = 18y, Roman numeral I is true.
II. 3y + 20z
Since 3y = x and 20z = 5(4z) = 5x, 3y + 20z = x + 5x = 6x; Roman numeral II is also true.
III. (4y + 10z)/3
Let's express 4y and 10z in terms of x.
4y = (4/3)3y = (4/3)x
10z = (10/4)4z = (5/2)x
Now, we have:
(4y + 10z)/3 = ((4/3)x + (5/2)x)/3 = [(23/6)x]/3 = (23/18)x.
Clearly, this expression is not equal to 6x.
Thus, only Roman numerals I and II are true.
Answer: D
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