BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Need Help

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 126
Joined: Sat Jun 07, 2014 5:26 am
Thanked: 3 times

Need Help

by sandipgumtya » Sun Mar 22, 2015 8:26 pm
Hi,
Got stuck by this.Pl help:

Q-Given that 2^x = 4^y = 8^z and xyz=288,what is the value of (1/2x)+(1/4y)+(1/8z).

A) 18/74
B) 18/96
C) 11/74
D) 11/96


OA is D.
Top
Source: — Data Sufficiency |
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Sun Mar 22, 2015 10:02 pm
Let's start by simplifying the exponents.

2ˣ = 4ʸ = 8ᶻ

is really

2ˣ = (2²)ʸ = (2³)ᶻ

so

x = 2y = 3z

we also have

xyz = 288

Now just do substitution. Since x = 2y and z = (2/3)y, we have

xyz = 2y*y*(2/3)y = 288

That gives y = 6

From this, x = 12 and z = 4.

The sum at the end is 1/24 + 1/24 + 1/32, or 11/96.
Top
Master | Next Rank: 500 Posts
Posts: 126
Joined: Sat Jun 07, 2014 5:26 am
Thanked: 3 times

by sandipgumtya » Sun Mar 22, 2015 11:12 pm
Thanks for quick repl.Is this GMAT relevant?
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Mar 23, 2015 3:39 am
The problem should read as follows:
If 2ˣ = 4ʸ = 8ᶻ and xyz=288, what is the value of 1/(2x) + 1/(4y) + 1/(8z)?

A) 18/74
B) 18/96
C) 11/74
D) 11/96
Let 2ˣ = 4ʸ = 8ᶻ = 64.
In this case, x=6, y=3 and z=2.
Implication:
x:y:z = 6:3:2.

Test multiples of this ratio until a product of 288 is yielded:
6*3*2 = 36.
12*6*4 = 288.
The option in red works.

Since x=12, y=6, and z=4, we get:
1/(2x) + 1/(4y) + 1/(8z) = 1/24 + 1/24 + 1/32 = 4/96 + 4/96 + 3/96 = 11/96.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1