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

It is currently 15 Dec 2018, 08:48

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

A shopkeeper mixes three varieties of rice costing $10, $12, $17 per

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

Hide Tags

Intern
Intern
avatar
B
Joined: 28 Oct 2017
Posts: 7
A shopkeeper mixes three varieties of rice costing $10, $12, $17 per  [#permalink]

Show Tags

New post 30 Sep 2018, 05:34
9
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

56% (01:43) correct 44% (02:06) wrong based on 101 sessions

HideShow timer Statistics

A shopkeeper mixes three varieties of rice costing $10, $12, $17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at $15.60 per kg?

(A) 9:14:36
(B) 11:14:25
(C) 14:36:43
(D) 2:6:3
(E) None of these
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7107
A shopkeeper mixes three varieties of rice costing $10, $12, $17 per  [#permalink]

Show Tags

New post 30 Sep 2018, 06:55
1
Sriharsh wrote:
A shopkeeper mixes three varieties of rice costing $10, $12, $17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at $15.60 per kg?

(A) 9:14:36
(B) 11:14:25
(C) 14:36:43
(D) 2:6:3
(E) None of these



Now the profit is 20%, so let us find the average price the price at which there is no profit and no loss...
15.60=120x/100......x=15.6×100/120=13

So prices are 10:12:17 and average 13..
Let us how far the numbers are from average price..
(13-10):(13-12):(17-13).....3:1:6...
So the ratio *the difference of the price on either side of average price should be equal..
So let us check the choices..
(A) 9:14:36..........so \(9*(13-10)+14*(13-12)=36*(17-13)...9*3+14*1=36*4\).....no
(B) 11:14:25......so \(11*(13-10)+14*(13-12)=25*(17-13)...11*3+14*1=25*4\).....no
(C) 14:36:43......so \(14*(13-10)+36*(13-12)=43*(17-13)...14*3+36*1=43*4\).....no
(D) 2:6:3......so \(2*(13-10)+6*(13-12)=3*(17-13)...2*3+6*1=3*4.....12=12\)...yes
(E) None of these

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
User avatar
B
Joined: 05 Oct 2017
Posts: 61
Location: India
Schools: GWU '21, Isenberg'21
CAT Tests
Re: A shopkeeper mixes three varieties of rice costing $10, $12, $17 per  [#permalink]

Show Tags

New post 30 Sep 2018, 06:56
1
1
Sriharsh wrote:
A shopkeeper mixes three varieties of rice costing $10, $12, $17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at $15.60 per kg?

(A) 9:14:36
(B) 11:14:25
(C) 14:36:43
(D) 2:6:3
(E) None of these


(10x + 12y + 17z)/ x+y+z = CP ........ (A)

profit % = (SP-CP)/CP

From above formula CP = 13
Putting the value of 13 in equation A , we get
4z =3x+y

Only option D satisfy this equation, Hence correct answer is Option D
_________________

The Path is the Goal

Quant Mega Thread by Bunnel
WTF is “that” doing in my sentence? By VerbalNinja

Intern
Intern
avatar
B
Joined: 21 Nov 2016
Posts: 36
CAT Tests
Re: A shopkeeper mixes three varieties of rice costing $10, $12, $17 per  [#permalink]

Show Tags

New post 30 Sep 2018, 17:52
1
1
We have 3 varieties of rice each costing $10, $12, and $17.
The shopkeeper mixes these three varieties and sells the mixture at $15.6 which gets him a profit of 20%.

Now, CP +CP(20/100) = 15.6
Implies, CP = $13.0

So we have x grams of $10 rice, + y grams of $12 rice + z grams of $17 rice, all mixed together to form 1 kg of rice with a cost price of $13.0
Implies , 10x+12y+17z = 13(x+y+z)
Implies, 4z = 3x + y

The above equation shows us that z has to me minimum of all three.
By seeing the options only D has z being minimum.
So lets check for D.
4z = 3x + y
Implies, 4(3) = 3(2)+6
Implies , 12 = 12

So option D is the correct answer.
Manager
Manager
User avatar
G
Joined: 07 Aug 2018
Posts: 109
Location: United States (MA)
GMAT 1: 560 Q39 V28
CAT Tests
Re: A shopkeeper mixes three varieties of rice costing $10, $12, $17 per  [#permalink]

Show Tags

New post 05 Oct 2018, 02:42
chetan2u wrote:
Sriharsh wrote:
A shopkeeper mixes three varieties of rice costing $10, $12, $17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at $15.60 per kg?

(A) 9:14:36
(B) 11:14:25
(C) 14:36:43
(D) 2:6:3
(E) None of these



Now the profit is 20%, so let us find the average price the price at which there is no profit and no loss...
15.60=120x/100......x=15.6×100/120=13

So prices are 10:12:17 and average 13..
Let us how far the numbers are from average price..
(13-10):(13-12):(17-13).....3:1:6...
So the ratio *the difference of the price on either side of average price should be equal..
So let us check the choices..
(A) 9:14:36..........so \(9*(13-10)+14*(13-12)=36*(17-13)...9*3+14*1=36*4\).....no
(B) 11:14:25......so \(11*(13-10)+14*(13-12)=25*(17-13)...11*3+14*1=25*4\).....no
(C) 14:36:43......so \(14*(13-10)+36*(13-12)=43*(17-13)...14*3+36*1=43*4\).....no
(D) 2:6:3......so \(2*(13-10)+6*(13-12)=3*(17-13)...2*3+6*1=3*4.....12=12\)...yes
(E) None of these

D


Hi chetan2u!

I think you made a small mistake with the marked ratio! Shouldn't it be 3:1:4?

Cheers
_________________

Quantitative Megathread:https://gmatclub.com/forum/ultimate-gmat-quantitative-megathread-244512.html
Verbal Megathread:https://gmatclub.com/forum/all-you-need-for-gmat-verbal-164070.html
Flashcards Quant + Verbal:https://gmatclub.com/forum/gmat-flashcards-108651.html
Thursdays with Ron:https://gmatclub.com/forum/manhattan-s-thursdays-with-ron-consolidated-video-index-223612.html#p2138753

Senior Manager
Senior Manager
User avatar
P
Joined: 18 Jun 2018
Posts: 252
Premium Member CAT Tests
A shopkeeper mixes three varieties of rice costing $10, $12, $17 per  [#permalink]

Show Tags

New post 28 Oct 2018, 22:41
Sriharsh wrote:
A shopkeeper mixes three varieties of rice costing $10, $12, $17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at $15.60 per kg?

(A) 9:14:36
(B) 11:14:25
(C) 14:36:43
(D) 2:6:3
(E) None of these


OA:D

Let the weight of each variety in the mixture be \(x,y,\) and \(z\) kg
Weight of the total mixture \(=x+y+z\)
Cost price + Profit = Selling price
Cost price \(= 10x+12y+17z\)
Profit \(=\frac{20}{100}\) Cost price \(= 0.2\) Cost price
Selling price \(= 15.6(x+y+z)\)

\(10x+12y+17z +0.2(10x+12y+17z)= 15.6(x+y+z)\)
\(1.2(10x+12y+17z)=15.6(x+y+z)\)
\(10x+12y+17z = 13(x+y+z)\)
\(3x+y-4z=0\)

Only Option D satisfies \(3x+y-4z=0\)
As per option D, \(x=2m,y=6m\) and \(z=3m\)
L.H.S : \(3x+y-4z = 3*2m+6m-4*3m = 6m+6m-12m=0\)
R.H.S : \(0\)
\(L.H.S=R.H.S\)
GMAT Club Bot
A shopkeeper mixes three varieties of rice costing $10, $12, $17 per &nbs [#permalink] 28 Oct 2018, 22:41
Display posts from previous: Sort by

A shopkeeper mixes three varieties of rice costing $10, $12, $17 per

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.