A merchant has 100 lbs of sugar, part of which he sells at 7 : Problem Solving (PS)

rxs0005

Senior Manager

Joined: 07 Jun 2004

Posts: 438

Location: PA

A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

26 Jul 2010, 08:50

4

Kudos

12

Bookmarks

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

83% (01:46) correct

17% (02:14) wrong

based on 337 sessions

Hide Show timer Statistics

A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?

A. 70 lbs
B. 40 lbs
C. 30 lbs
D. 50 lbs
E. 60 lbs

Show Answer

Official Answer

Official Answer and Stats are available only to registered users. Register/Login.

AndreG

Intern

Joined: 22 Jun 2010

Posts: 29

Re: Mixture with profit problem [#permalink]

26 Jul 2010, 09:14

1

Kudos

rxs0005 wrote:

A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?

A. 70 lbs

B. 40 lbs

C. 30 lbs

D. 50 lbs

E. 60 lbs

Is it A? (70lbs)

7% --> 3% difference to 10%
17% --> 7% difference to 10%

so 7:3 is the required mixture (since we are closer to 7 than to 17), hence 70:30.

Cheers,

André

stanford2012

Manager

Joined: 02 Apr 2010

Posts: 78

Re: Mixture with profit problem [#permalink]

26 Jul 2010, 09:28

1

Kudos

Solution by AndreG is correct IMO. I'd doubt that this is a 700 level question (seems to be a pretty straightforward mixture problem), rather a 600 level question (or even lower).

You can also solve this problem algebraically:

Variable we look for:
x = amount of sugar sold at 7% profit

Equation:
10%*100 lbs = x*7% + (100-x)*17%

Solving for x you get x = 70 lbs

rxs0005

Senior Manager

Joined: 07 Jun 2004

Posts: 438

Location: PA

Re: Mixture with profit problem [#permalink]

26 Jul 2010, 09:43

70 is right

and also its not a 700 level problem i accidentally added that tag i guess

thanks !

jlgdr

VP

Joined: 06 Sep 2013

Posts: 1348

Concentration: Finance

Schools: Wharton '17 (A) HBS '17 (WA$)

Re: Mixture with profit problem [#permalink]

02 Feb 2014, 10:50

1

Kudos

1

Bookmarks

rxs0005 wrote:

A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?

A. 70 lbs

B. 40 lbs

C. 30 lbs

D. 50 lbs

E. 60 lbs

I use differentials for these types of weighted average problems

We have X at 7% and 100 - x at 17% give a weighted average of 10%

Hence -3x + 7(100-x) = 0

Solving x = 70

A

Tripp620

Intern

Joined: 22 Dec 2014

Posts: 4

Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

18 Feb 2015, 09:21

1

Bookmarks

I feel that putting the percentages into fractions makes the problem quicker to solve.

100(x)(7/100)+(100(1-x)) (17/100)=100(10/100)

7x+17-17x=10
-10x=-7
x=7/10

100lbs x (7/10) = 70lbs

Show Spoiler

A

L

EMPOWERgmatRichC

GMAT Club Legend

Joined: 19 Dec 2014

Status:GMAT Assassin/Co-Founder

Affiliations: EMPOWERgmat

Posts: 21849

Location: United States (CA)

GMAT 1: 800 Q51 V49

GRE 1: Q170 V170

Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

18 Feb 2015, 22:37

1

Kudos

1

Bookmarks

Expert Reply

Hi All,

These types of "weighted average" questions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:

A = # of pounds sold at 7% profit
B = # of pounds sold at 17% profit
A+B = 100 pounds

(.07A + .17B)/(A+B) = .10

.07A + .17B = .1A + .1B
.07B = .03A
7B = 3A
7/3 = A/B

So, for every 7 pounds of A, we have 3 pounds of B.
With 100 pounds total, we have 70 pounds of A and 30 pounds of B.

Final Answer:

Show Spoiler

A

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

pacifist85

Senior Manager

Joined: 07 Apr 2014

Status:Math is psycho-logical

Posts: 342

Location: Netherlands

GMAT Date: 02-11-2015

WE:Psychology and Counseling (Other)

A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

24 Feb 2015, 02:22

jlgdr wrote:

rxs0005 wrote:

A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?

A. 70 lbs

B. 40 lbs

C. 30 lbs

D. 50 lbs

E. 60 lbs

I use differentials for these types of weighted average problems

We have X at 7% and 100 - x at 17% give a weighted average of 10%

Hence -3x + 7(100-x) = 0

Solving x = 70

A

Almost always I prefer using algebra for these problems, or else weighted averages (if I manage to notice the connection). However, I did like this solution a lot.

I am not sure I understand what it means to subtract 7% and 17% from 10% though. Could someone please explain the reasoning behing this?
Also, why is it -3x and +7(100-x) and not the opposite, if we are subtracting those from 10?

Thank you!

L

EMPOWERgmatRichC

GMAT Club Legend

Joined: 19 Dec 2014

Status:GMAT Assassin/Co-Founder

Affiliations: EMPOWERgmat

Posts: 21849

Location: United States (CA)

GMAT 1: 800 Q51 V49

GRE 1: Q170 V170

Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

24 Feb 2015, 20:13

2

Kudos

Expert Reply

Hi pacifist85,

Differentials are essentially a sub-set of Calculus, which is a category of math that is NOT tested on the Official GMAT. While a Test Taker might be able to use this type of math to answer certain questions, it's not really worth focusing on (for much the same reason why you don't need to know Trigonometry to answer the Geometry questions that you'll see on Test Day. While that math might be use-able on certain questions, it's not tested).

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

PareshGmat

SVP

Joined: 27 Dec 2012

Status:The Best Or Nothing

Posts: 1563

Location: India

Concentration: General Management, Technology

WE:Information Technology (Computer Software)

Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

25 Feb 2015, 00:27

2

Kudos

Answer = A = 70

Using allegation method

7% ............................ 17%

................. 10% ................

(17-10) = 7 .................. (10-7) = 3

$\frac{7}{7+3} * 100 = 70 Lbs$

G

Madhavi1990

Senior Manager

Joined: 15 Jan 2017

Posts: 259

Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

20 Aug 2017, 06:17

Used the weighted avg formula learnt at a different question:
7 = x amount sold at 7% profit
100 - x = rest sold at 17% interest
10 = (17 - 7)
putting in formula
7 + (100 - x)10/100 (denominator here is 100 pounds) = 10 (overall profit)
x = 70 lbs

G

Madhavi1990

Senior Manager

Joined: 15 Jan 2017

Posts: 259

Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

20 Aug 2017, 06:18

Used the weighted avg formula learnt at a different question:
7 = x amount sold at 7% profit
100 - x = rest sold at 17% interest
10 = (17 - 7)
putting in formula
7 + (100 - x)10/100 (denominator here is 100 pounds) = 10 (overall profit)
x = 70 lbs

bumpbot

Non-Human User

Joined: 09 Sep 2013

Posts: 32491

Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

26 Oct 2023, 09:16

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.
_________________

Signature Read More

gmatclubot

Re: A merchant has 100 lbs of sugar, part of which he sells at 7 [#permalink]

26 Oct 2023, 09:16

GMAT Problem Solving (PS) Questions

A merchant has 100 lbs of sugar, part of which he sells at 7

GMAT Question Banks