GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Sep 2019, 17:55

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In the formula above, a, b, c, and d are positive numbers.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Board of Directors
User avatar
D
Joined: 01 Sep 2010
Posts: 3402
In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post Updated on: 12 Sep 2013, 09:37
1
1
15
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

54% (02:30) correct 46% (02:44) wrong based on 201 sessions

HideShow timer Statistics

x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21

_________________

Originally posted by carcass on 12 Sep 2013, 09:32.
Last edited by Bunuel on 12 Sep 2013, 09:37, edited 1 time in total.
Moved to PS forum.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58098
Re: In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 12 Sep 2013, 09:44
3
7
carcass wrote:
x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21


\(\frac{8a}{c} + \frac{16b}{c}=\frac{8a+16b}{c}=\frac{8a+16b}{a+b}\).

You can notice that it's a weighted average formula for \(a+b\) items, where the weight of each of the items of \(a\) is 8 and the weight of each of the items of \(b\) is 16. Now, since b > a, then the average must be closer to 16, then to 8. Only D fits.

Answer: D.
_________________
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58098
Re: In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 12 Sep 2013, 09:45
2
Bunuel wrote:
carcass wrote:
x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21


\(\frac{8a}{c} + \frac{16b}{c}=\frac{8a+16b}{c}=\frac{8a+16b}{a+b}\).

You can notice that it's a weighted average formula for \(a+b\) items, where the weight of each of the items of \(a\) is 8 and the weight of each of the items of \(b\) is 16. Now, since b > a, then the average must be closer to 16, then to 8. Only D fits.

Answer: D.


Similar question to practice from OG:
Quote:
If x, y, and k are positive numbers such that (x/(x+y))(10) + (y/(x+y))(20) = k and if x < y, which of the following could be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30


Discussed here: if-x-y-and-k-are-positive-numbers-such-that-x-x-y-128231.html
_________________
Intern
Intern
avatar
Joined: 15 Sep 2013
Posts: 32
Concentration: Strategy, Entrepreneurship
GMAT 1: 680 Q47 V36
GMAT 2: 740 Q50 V40
GPA: 3.65
GMAT ToolKit User Reviews Badge
Re: In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 08 Sep 2014, 03:50
1
1
carcass wrote:
x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21


x = 8a/c + 16b/c
x= 8(a+b)/c + 8b/c
now substituting c = a + b in the above equation
x = 8 + 8b/(a+b)
The ratio b/(a+b) is smaller than 1 thus answer choice E is eliminated... and as a < b ... thus the ratio b/(a+b) is larger than 1/2 or 0.5... thus
8*b/(a+b) is larger than 4... thus the only answer choice left is D
_________________
Please +1 KUDOS if my post helped you in any way
Intern
Intern
avatar
Joined: 02 Jul 2013
Posts: 12
Concentration: General Management, Finance
GMAT Date: 11-08-2013
WE: Programming (Computer Software)
In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 13 Sep 2014, 01:09
Can anyone explain this in detail?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58098
Re: In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 13 Sep 2014, 07:18
Director
Director
User avatar
G
Joined: 20 Feb 2015
Posts: 778
Concentration: Strategy, General Management
In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 15 Sep 2015, 13:30
x = 8(a/c) + 16(b/c)

just by looking at the options .. we should be able to understand that 8 or its multiple i.e 16 should be divisible by C..why ? Because none of the options are in p/q form.

let us say c =4 which gives us a=1 and b=3

the equation thus becomes x=8(1/4) + 16(3/4) =2+12=14 --close enough :)
the other value c can take is 8
which gives us possible values for (a,b) as (1,7) (2,6) (3,5)

take 1,7

x=8(1/8)+16(7/8)=15

That's how I managed to do.
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2523
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 11 Jan 2016, 19:17
oh man..I did the long way..
8a+8b/a+b = 8
now, 8b/a+b =??
we can eliminate A right away..
tried several numbers..then got to:
a=1
b=7
a+b=8
8b=56.
56/8=7.
7+8=15.

D
_________________
Image
Intern
Intern
avatar
B
Joined: 20 Mar 2019
Posts: 44
Location: India
GMAT ToolKit User
Re: In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 27 May 2019, 14:45
CounterSniper wrote:
x = 8(a/c) + 16(b/c)

just by looking at the options .. we should be able to understand that 8 or its multiple i.e 16 should be divisible by C..why ? Because none of the options are in p/q form.

let us say c =4 which gives us a=1 and b=3

the equation thus becomes x=8(1/4) + 16(3/4) =2+12=14 --close enough :)
the other value c can take is 8
which gives us possible values for (a,b) as (1,7) (2,6) (3,5)

take 1,7

x=8(1/8)+16(7/8)=15

That's how I managed to do.


I did exactly the same way! Can someone clarify if this method is OK to use for future such questions? Feels like guess work and lucked out with this one.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7771
Location: United States (CA)
Re: In the formula above, a, b, c, and d are positive numbers.  [#permalink]

Show Tags

New post 28 May 2019, 18:06
carcass wrote:
x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21



Simplifying, we have:

x = (8a + 16b)/c

x = (8a + 16b)/(a + b)

We see that we have a weighted average, and since b is greater than a, then x must be closer to 16 and also between 8 and 16, so x could be 15.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: In the formula above, a, b, c, and d are positive numbers.   [#permalink] 28 May 2019, 18:06
Display posts from previous: Sort by

In the formula above, a, b, c, and d are positive numbers.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne