Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Aug 2016, 22:29

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# One kilogram of a certain coffee blend consists of x

Author Message
TAGS:

### Hide Tags

Intern
Joined: 30 Nov 2011
Posts: 31
Location: United States
GMAT 1: 700 Q47 V38
GPA: 3.54
Followers: 1

Kudos [?]: 43 [2] , given: 23

One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

25 Mar 2012, 11:23
2
KUDOS
33
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

42% (02:45) correct 58% (01:50) wrong based on 928 sessions

### HideShow timer Statistics

One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?

(1) y > 0.15

(2) C >= 7.30
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6252

Kudos [?]: 79420 [14] , given: 10016

### Show Tags

25 Mar 2012, 11:28
14
KUDOS
Expert's post
14
This post was
BOOKMARKED
One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?

"One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee"

So, $$x+y=1$$. Question: is $$x<0.8$$.

(1) y > 0.15 --> $$1-x>0.15$$ --> $$x<0.85$$. Not sufficient.

(2) C >=7.30 --> $$C=6.5x + 8.5y\geq{7.3}$$ --> $$C=6.5x + 8.5(1-x)\geq{7.3}$$ --> $$2x\leq{1.2}$$ --> $$x\leq{0.6}$$. Sufficient.

_________________
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 170

Kudos [?]: 1174 [3] , given: 62

### Show Tags

05 Feb 2013, 02:17
3
KUDOS
I tried doing this via using the concept of weighted average.
Its given in statement 2 that 6.5x + 8.5y>=7.3.
Now, when x=.5 and y=.5, then the c would be 7.5. (GIVEN FACT IS THAT X+Y=1.)
Total distance in terms of parts is 2 units and in terms of numerical distance is 1. For every 2 part change, there is a 0.1 deviation in the numerical separation.
Since c>=7.3( note the 0.2 deviation), the numerical deviation is 0.1. Hence x must be <=0.6.
Regards.
_________________
Manager
Joined: 07 May 2012
Posts: 76
Location: United States
Followers: 3

Kudos [?]: 121 [1] , given: 23

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

01 May 2013, 16:39
1
KUDOS
x+y=1
c= 6.5x + 8.5y
Question ---- is x<0.8 ?

As seen from above equations , for a given sum of x and y ( =1) , the value of C increases as x decreases and Y increases ( since y is multipled by greater number than x)

If x=0.8 , then y=0.2
and C= (6.5*0.8) + (8.5*0.2) = 6.9 .

Now if we increase value of x above 0.8 , the value of C decreases below 6.9 ( consider x=0.9 , then y would be 0.1 , which pulls down the value of C below 6.9--- as per the highlighted text above).
And if we decrease the value of x below 0.8 , the value of c increases from 6.9 ( cos y is increased when x is reduced).

Statement 1 - y>0.15 , Y could be 0.2 , in which case x=0.8 ( No to the answer)
or Y = 0.3 , in which case x=0.7 ( yes to the answer)
Insufficient

Statement 2 C>=7.5 , as seen from above , for any c > 6.9 demands a x <0.8 . Hence sufficient.

Hope that helps
Jyothi
_________________

Jyothi hosamani

Intern
Joined: 03 May 2013
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

03 May 2013, 21:29
It is really nice to find this place as it is full of fun. Looking forward for new friends. Hope I'll definitely enjoy my stay here.
ood question and quite a learning...

Out of curiousity, can this sum be solved in less than 2mins that too under "GMAT exam" conditions that too at first sight??
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6252

Kudos [?]: 79420 [0], given: 10016

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

13 Jun 2013, 02:15
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Mixture Problems to practice: search.php?search_id=tag&tag_id=43
All PS Mixture Problems to practice: search.php?search_id=tag&tag_id=114

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6829
Location: Pune, India
Followers: 1917

Kudos [?]: 11922 [4] , given: 221

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

16 Sep 2013, 03:15
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?

(1) y > 0.15

(2) C >= 7.30

Responding to a pm:
Quote:
I could solve most of the problems using the scale method, though I was finding it difficult to solve this particular question using it.

C = Avg cost of the mix = Cost of the blend = 6.5x + 8.5y

If you remember your weighted average formula, Avg = (C1*w1 + C2*w2)/(w1 + w2) =
Avg Cost = (C1*x + C2*y)/(x + y)
(x+y) is 1 kg since the weight of the blend is 1 kg.
Avg Cost = C = (C1*x + C2*y) = (6.5x + 8.5y)
So cost of type I coffee is $6.5/kg and cost of type II coffee is$8.5/kg.

So everything is set for you. All you have to do is plug in the values of x and y now.
Question: Is x > 0.8?

(1) y > 0.15
If y is 0.16, x is 0.84
If y is 0.5, x is 0.5
This statement alone is not sufficient.

(2) C >= 7.30
Let's say C = 7.3
x/y = (8.5 - 7.3)/(7.3 - 6.5) = 12/8 = 3/2 (The Scale Method)
x = 3/5 = 0.6
If C is greater than 7.3, x/y will get smaller and hence the value of x will keep getting smaller too. Say if C = 7.5,
x/y = 1/1
x = 0.5
and so on...

So x can be at most 0.6. Hence it must be less than 0.8.
Statement II alone is sufficient.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 28 Mar 2012
Posts: 6
Location: Yugoslavia
Concentration: Accounting, Finance
GMAT 1: 650 Q V
GPA: 3.75
Followers: 0

Kudos [?]: 8 [1] , given: 21

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

16 Sep 2013, 04:15
1
KUDOS
Idk, in my opinion after you figure out that x+y=1 and that C=6.5x+8.5y (knowing that C can be 7.30), we have two equations and we can solve for X.
Please correct me if I'm wrong but this was my line of reasoning and I've chosen B after 1min.
Intern
Joined: 09 Jul 2012
Posts: 11
Followers: 0

Kudos [?]: 3 [1] , given: 6

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

18 Sep 2013, 12:15
1
KUDOS
one kilogram of a certain coffee blend consists of X kilogram of type I and Y kilogram of type II" means that X+Y=1
Combined C=6.5X+8.5Y,

we get:
X=(8.5-C)/2, Y=(C-6.5)/2
Combined C>=7.3, X=(8.5-C)/2<1.2/2=0.6

Manager
Joined: 22 Aug 2013
Posts: 113
Schools: ISB '15
Followers: 2

Kudos [?]: 26 [0], given: 60

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

28 Nov 2013, 09:10
@Bunuel,
You are just great!!!
_________________

Veritas Prep - 650
MGMAT 1 590
MGMAT 2 640 (V48/Q31)

Current Student
Joined: 14 Jul 2013
Posts: 32
Followers: 0

Kudos [?]: 8 [0], given: 39

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

21 Apr 2014, 01:09
Initially I got the answer wrong but there was a calculation mistake. I am posting my approach anyway :D,

Question Says,
One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?

(1) y > 0.15

(2) C >= 7.30

Sol. x + y = 1 (from question statement)
now, cost C = 6.5x + 8.5y = 6.5 (x + y) + 2y = 6.5 +2y------(eq. 1)
we need to check whether x < 0.8
or y > 0.2 (since x + y = 1)

option 1). y > 0.15
clearly not sufficient alone.

option 2). C >= 7.30
from eq.1, 6.5 + 2y >= 7.30
=> 2y => 0.80
=> y>= 0.40 or x =< 0.60
Hence, sufficient.
Intern
Joined: 12 Jan 2015
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 0

One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

12 Jan 2015, 05:22
One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?

(1) y > 0.15

(2) C >= 7.30
Manager
Joined: 22 Oct 2014
Posts: 88
Concentration: General Management, Sustainability
GMAT 1: 770 Q50 V45
GPA: 3.8
WE: General Management (Consulting)
Followers: 1

Kudos [?]: 57 [1] , given: 4

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

12 Jan 2015, 05:43
1
KUDOS
With x+y = 1, we can simplify the equation for C:

C = 6.5 + 2y

Statement 1: Not sufficient. x can still be anywhere between 0 and 0.85

Statement 2: Sufficient:
7.3 = 6.5 + 2y. This leads to y = 0.4 and x smaller than 0.8. If C is greater than 7.3, this will only increase y and therefore decrease x, which will therefore be smaller than 0.8 in any case.

_________________

$$\sqrt{-1}$$ $$2^3$$ $$\Sigma$$ $$\pi$$ ... and it was delicious!

Please consider giving +1 Kudos if deserved!

Intern
Joined: 12 Jan 2015
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

12 Jan 2015, 05:48
Hi littlewarthog
Manager
Joined: 31 Jul 2014
Posts: 152
GMAT 1: 630 Q48 V29
Followers: 0

Kudos [?]: 41 [0], given: 373

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

12 Jan 2015, 06:21
superjohn5566 wrote:
One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?

(1) y > 0.15

(2) C >= 7.30

Hi
Can someone please explain the solution?

Thanks
Anupama
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6252

Kudos [?]: 79420 [0], given: 10016

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

12 Jan 2015, 07:00
superjohn5566 wrote:
One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?

(1) y > 0.15

(2) C >= 7.30

Merging similar topics. Please refer to the solutions above.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11042
Followers: 509

Kudos [?]: 133 [0], given: 0

Re: One kilogram of a certain coffee blend consists of x [#permalink]

### Show Tags

04 Apr 2016, 01:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: One kilogram of a certain coffee blend consists of x   [#permalink] 04 Apr 2016, 01:53
Similar topics Replies Last post
Similar
Topics:
1 At a certain coffee shop, all of the customers drink either coffee or 2 29 Oct 2015, 01:30
2 A certain 5-liter solution of floor cleaner consists of x liters of co 3 02 Oct 2015, 01:50
3 A certain one-day seminar consisted of a morning session and 4 09 Jul 2012, 03:31
9 One kilogram of a certain coffee blend consists of x 5 29 Sep 2010, 03:25
33 A certain one-day seminar consisted of a morning session and 18 12 Nov 2009, 08:59
Display posts from previous: Sort by