77) How heavy is the bag

Hi,

Try by plugging in numbers. Start with C.

If the weight of Bag1 is 48 then
B(3/4) = 36 and
A(1/4) = 12

Now in Bag2,
B =36-8 = 28 which is 7/10 th of the total weight
Hence A = 3/10th = (28x3)/7 = 12

The Q says the weight of A is the same as that of the first bag. Hence C is the the correct answer.

Yes correct answer is C.

In first bag total nuts, lets say 4x (why? its easy to calculate), then
B = 3/4 of total (given) == 3x
A = rest of total(given) == x

In second bag total nuts, lets say 10x, then
B = 7/10 of total(given) == 7x
A = will be rest == 3x

Question asked for how much is the weight of nuts in first bag which we can say as they are asking for the weight of 4x nuts.

Just plug-in values and always better to start with C option. C option is 48. So, the weight of 4x nuts == 48gms
x nuts = 48/4 = 12gms. and

From this, we can calculate the weight of A&B nuts in the first bag and A&B nuts in second bag. That is,
In first bag, A= x = 12gms & B = 3x = 3*12 = 36
In second bag, B weight is 8gms less than B weight in first bag (given), then B (second bag) = B (first bag) - 8 = 36-8 = 28. Then we can say,
B nuts 7x=28gms from this, x = 4,
A nuts 3x = 3*4 = 12.

Here you can see A weight (first bag) = A weight (second bag). As it satisfies the given condition, this is answer.

HTH, GOOD LUCK,

Thanks,
Rajesh,
Loves GMAT...!!!!

Hi Was wondering how we could assume that the weight per nut of A and B is 1 gm?

rajeshsources wrote:Yes correct answer is C.

In first bag total nuts, lets say 4x (why? its easy to calculate), then
B = 3/4 of total (given) == 3x
A = rest of total(given) == x

In second bag total nuts, lets say 10x, then
B = 7/10 of total(given) == 7x
A = will be rest == 3x

Question asked for how much is the weight of nuts in first bag which we can say as they are asking for the weight of 4x nuts.

Just plug-in values and always better to start with C option. C option is 48. So, the weight of 4x nuts == 48gms
x nuts = 48/4 = 12gms. and

From this, we can calculate the weight of A&B nuts in the first bag and A&B nuts in second bag. That is,
In first bag, A= x = 12gms & B = 3x = 3*12 = 36
In second bag, B weight is 8gms less than B weight in first bag (given), then B (second bag) = B (first bag) - 8 = 36-8 = 28. Then we can say,
B nuts 7x=28gms from this, x = 4,
A nuts 3x = 3*4 = 12.

Here you can see A weight (first bag) = A weight (second bag). As it satisfies the given condition, this is answer.

HTH, GOOD LUCK,

Thanks,
Rajesh,
Loves GMAT...!!!!

mj78ind ---

Actually, I haven't tried to get the weight of nut A & B. And more over, we have not assumed each nut weight as 1gm. We have calculated weight of bag of nuts having mixture of A&B by taking the fraction of A nuts & fraction of B nuts in the Mixture of A&B.

From the stems of the question "There are two bags with mixed nuts A and B." We can tell the bag has only nuts nothing else.

Generally, let's say your mother asked you to get 1 KG TOMATOES, then the store-keeper given 10 tomatoes(assume). Then, you can calculate how much is the weight of each tomato. i.e.,
1 Kg = 1000gms ---- 10 tomatoes you have got, then
each tomato == 100gms.

I have given an example only for your understanding. So, the weight of whole first bag is 48.

Hope that answers your question, GOOD LUCK,

Thanks,
Rajesh,
Loves GMAT....!!!!

@Rajesh

Thanks, i get it.

So essentially we could also solve this as:
In bag 1, x - A, 3x - B; Bag 2, 3y - A, 7y - B nuts by weight

Eqtn 1 3x - 7y = 8

Eqtn 2 x = 3y

Solving above, we get x = 12 gms. Hence, Bag A = 4x = 4*12 = 48 gms

Algebraic Solution:

x= total weight of nuts in bag 1
y= total weight of nuts in bag 2
A= nut A
B= nut B


Bag 1= (3/4) x B + (1/4) x A
Bag 2= (7/10) y B + (3/10) y A

Given: weight of A in Bag 1 = weight of A in Bag 2
therefore,

(1/4) x A = (3/10) y A
(12/10)y= x
so we know that the weight of bag 1 is 1.2 times the weight of bag 2 and given the above, that difference is in the weight of B nuts
so let's now change x and y as above to reflect this:
Bag 1=1.2 x
Bag 2 =x
Given: weight of B nuts in Bag 1 is 8 g greater than in Bag 2
thus:
fractional weight of B nuts in Bag 1 which is 1.2x bigger than Bag 2= fractional weight of B nuts in Bag 2 +8
(3/4)(1.2x)= (7/10)x + 8
x= 40
According to above then, Bag 1=1.2x= 48

Good Luck