If x = 3y = 4z, which of the following must equal 6x ?

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

If x = 3y = 4z, which of the following must equal 6x ?

by VJesus12 » Mon May 21, 2018 8:06 am

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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

The OA is the option D.

How can I prove that the correct option is the option D? Could anyone clarify this question to me? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Mon May 21, 2018 8:06 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon May 21, 2018 8:47 am

VJesus12 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

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

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Mon May 21, 2018 6:39 pm

Hi VJesus12,

We're told that X = 3Y = 4Z. We're asked which of the following must equal 6X. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF....
X=12, Y=4, Z=3.....then we're looking for values that equal 6(12) = 72.

I. 18Y

18(4) = 72, so Roman Numeral 1 equals 6X. Eliminate Answers B and C.

II. 3Y + 20Z

3(4) + 20(3) = 12+60 = 72, so Roman Numeral 2 equals 6X. Eliminate Answers A and E. We can technically stop here (since there's only one Answer left). However, we can still disprove Roman Numeral 3....

III. (4Y + 10Z)/3

[4(4) + 10(3)]/3 = 46/3 so Roman Numeral 3 does NOT equal 6X.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue May 22, 2018 5:20 pm

VJesus12 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

Let's analyze each Roman numeral choices.

I. 18y

18y = 6(3y) = 6x

Yes, I is true.

II. 3y + 20z

3y + 20z = 3y + 5(4z) = x + 5x = 6x

Yes, II is true.

At this point, since there is only one answer choice which includes I and II, we know the answer is D. However, let's also analyze Roman numeral III as an exercise:

III. (4y + 10z)/3

Since x = 3y, y = x/3. Likewise, since x = 4z, z = x/4. Thus we have:

(4y + 10z)/3 = (4(x/3) + 10(x/4))/3 = (4x/3 + 5x/2)/3 = 4x/9 + 5x/6 = 8x/18 + 15x/18 = 23x/18

We see that III is not true.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
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