kanika123 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 lb

How to solve quickly?

Here's a reasonably fast approach.
First consider what would happen if half sold for a 7% profit, and the other half sold for a 17% profit.
The result would be a profit that's midway between 7% and 17%. In other words, we'd have a 12% profit.
HOWEVER, the question tells us that we get only a 10% profit.
So, we must have sold more than half of the sugar at the lower 7% profit.
We can now ELIMINATE B, C and D.

At this point, we can test either of the two remaining answer choices (A or E). It doesn't matter which one we test. If the one we test works, we're done. If it doesn't work, we're still done, because we know the other answer is correct.

Let's test E (60 lbs sold at a 7% profit)
So, 60 out of 100 lbs sold at 7%, and 40 out of 100 lbs sold at 17%
We'll use the formula:
Weighted average = (group A proportion)(group A average) + (group B proportion)(group B average)
Weighted average = (0.6)(7) + (0.4)(17)
= 4.2 + 6.8
= 11
So, this scenario would result in a 11% profit. We want an 10% profit, so ELIMINATE E.

By the process of elimination, the correct answer is A

If you're interested, we have a free video on weighted averages: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Cheers,
Brent

Looks like my response got posted twice.
Deleted this one.

Cheers,
Brent

kanika123 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 lb

How to solve quickly?

Alternatively, we can recognize that there are 10 percentage points between 7% and 17%
So, if the proportions are 50-50, then the resulting percent profit will be halfway between 7% and 17%. In other words, the result will be a 12% profit.

If the proportions are 60-40 (that is 60 lbs sold at 7%, and 40 lbs sold at 17%, then the resulting percent profit will be 4 percentage points away from 7%, and 6 percentage points away from 17%. In other words, the result will be an 11% profit.

If the proportions are 70-30 (that is 70 lbs sold at 7%, and 30 lbs sold at 17%, then the resulting percent profit will be 3 percentage points away from 7%, and 7 percentage points away from 17%. In other words, the result will be a 10% profit. BINGO!

Cheers,
Brent

Hi kanika123,

Each of the various approaches listed here is valid (I think that TESTing the answers would be fastest for most people), but you could also solve this problem using algebra (it's called "system math").

Since we don't know what sugar costs, I'm going to say that sugar costs $1 per pound. So we have $100 worth of sugar and we want a 10% profit (so we're looking for an increase of $10). Now we can create 2 equations:

X = the number of pounds sold at 7% profit
Y = the number of pounds sold at 17% profit

X + Y = 100
.07X + .17Y = $10

Since the question is asking for X, we should isolate and eliminate the Y...

Y = 100 - X

Now substitute in to the second equation:

.07X + .17(100 - X) = 10
.07X +17 - .17X = 10

Combine like terms:
7 - .1X = 0
7 = .1X
70 = X

Final Answer: A

To earn a 700+ on Test Day, you need to be comfortable with a variety of tactics. Make sure you can do the math (when necessary), but also be open to answering questions using tactics (such as using the answer choices against the question).

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

Hi Dicky John williams,

TESTing THE ANSWERS is a perfect approach for this question - and that's exactly what Brent did (he just used a bit of logic to eliminate a few of the answers first).

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