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If x = 3y = 4z, which of the following must equal 6x ? I. 18y II. 3y
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01 Mar 2021, 10:24
01 Mar 2021, 10:24
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Question Stats:
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If x = 3y = 4z, which of the following must equal 6x ?
eq1: x=3y
eq2: x = 4z
I. 18y
II. 3y + 20z
III. (4y + 10z)/3
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
eq1: x=3y
eq2: x = 4z
I. 18y
II. 3y + 20z
III. (4y + 10z)/3
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: If x = 3y = 4z, which of the following must equal 6x ? I. 18y II. 3y
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01 Mar 2021, 10:25
01 Mar 2021, 10:25
1
I think answer is D)
I. yes
x = 3y , so 6 *x = 3*6*y = 18y
II. 3y + 20z : yes
x = 3y , so 3y + 20 z = x + 20z
x = 4z, so 20z = 4z * 5 = 5*x
With above 2 equations, 3y + 20 z = 6x
III. (4y + 10z)/3 : No
4y + 10 z = x * (4/3) + x * ( (10/4)/3)
= (4*x + 5/2*x ) /3
= (13/2)*x / 3 is not equal to 6x
So only , I and II are correct, hence the answer is D)
Best,
Gocha
Quote:
If x = 3y = 4z, which of the following must equal 6x ?
eq1: x=3y
eq2: x = 4z
I. 18y
II. 3y + 20z
III. (4y + 10z)/3
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
eq1: x=3y
eq2: x = 4z
I. 18y
II. 3y + 20z
III. (4y + 10z)/3
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
I. yes
x = 3y , so 6 *x = 3*6*y = 18y
II. 3y + 20z : yes
x = 3y , so 3y + 20 z = x + 20z
x = 4z, so 20z = 4z * 5 = 5*x
With above 2 equations, 3y + 20 z = 6x
III. (4y + 10z)/3 : No
4y + 10 z = x * (4/3) + x * ( (10/4)/3)
= (4*x + 5/2*x ) /3
= (13/2)*x / 3 is not equal to 6x
So only , I and II are correct, hence the answer is D)
Best,
Gocha
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x = 3y = 4z, which of the following must equal 6x ? I. 18y II. 3y
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01 Mar 2021, 10:26
01 Mar 2021, 10:26
1
Carcass wrote:
If x = 3y = 4z, which of the following must equal 6x ?
I. 18y
II. 3y + 20z
III. (4y + 10z)/3
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
I. 18y
II. 3y + 20z
III. (4y + 10z)/3
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Let's examine each statement
I. 18y
Given: x = 3y
Multiply both sides by 6 to get: 6x = 18y
Perfect!
Statement I is TRUE
Check the answer choices.....ELIMINATE B and C since they state that statement I is not true.
II. 3y + 20z
Given: x = 3y
Also, since x = 4z, we can multiply both sides by 5 to get: 5x = 20z
Now notice that 6x = x + 5x
= 3y + 20z
Perfect!
Statement II is TRUE
Check the answer choices.....ELIMINATE A and E since they state that statement II is not true.
By the process of elimination, the correct answer is D
Cheers,
Brent
