A certain adhesive is formed by mixing 2 components, a resin and a har

Question

A certain adhesive is formed by mixing 2 components, a resin and a hardener, and allowing the mixture to dry. For example, 2 grams of resin mixed with 2 grams of hardener will result in 4 grams of adhesive.

A worker has 6 grams of resin and 8 grams of hardener and wishes to form adhesive using one of the following mixture formulas:

Mixture A has a ratio of 3 parts resin to 2 parts hardener.

Mixture B has a ratio of 2 parts resin to 4 parts hardener.

Select for Mixture A the maximum amount, in grams, that the worker can make of Mixture A, and select for Mixture B the maximum amount, in grams, the worker can make of Mixture B, according to the information provided. Make only two selections, one in each column.

Bismuth83 · Accepted Answer

1. The problem asks us to find the   maximum   amount of adhesive that can be made as   mixture A   and   mixture B  , separately.

2. To get the maximum amount of a mixture, either resin or hardener must be fully used up (could be both). Then, we have to consider two cases for each mixture.

3. Let's denote the ratio   R   :   H   as the ratio of  resin  to  hardener  (both in grams).

4. For mixture A we have  3 : 2 .

Case#1  : All resin is used up. Then, the ratio is 6 : 4 and 4   \leq   8. It  works  and the total mass is 6 + 4 =  10 grams .

Case#2  : All hardener is used up. Then, the ratio is 12 : 8 and 12   \geq   6. It  doesn't work  since we use more resin than we have.

5. For mixture B we have  2 : 4 .

Case#1  : All resin is used up. Then, the ratio is 6 : 12 and 12   \geq   8. It  doesn't work  since we use more hardener than we have.

Case#2  : All hardener is used up. Then, the ratio is 4 : 8 and 4   \leq   6. It  works  and the total mass is 4 + 8 =  12 grams .

6. The answer is  10 grams of mixture A  and  12 grams of mixture B .

---------------------------------------

There is a faster way by noticing that if the ratio of a mixture is less than 6 : 8, then the hardener will be used all the way without overusing the resin. Similarly, if the ratio of a mixture is more than 6 : 8, then the resin will be used all the way without overusing the hardener. This allows to only have 1 case for each mixture.

sayan640 · Answer

Simple Question ...

For Mixture A ,

Lets say , 6 gms of raisins are used.
3/2 = 6 / H
H = 4 gms of hardener needs to be used . And this is the maximum = (6 + 4) gms = 10 gms of Mixture A .

If we take the hardener as 8 gms , we will need 12 gms of raisins . We dont have that much amount.

For the second mixture,

2/4 = R/8
R= 4

Hence total (8+4)= 12 gms maximum is possible for the second mixture.

10 , 12 ==> Answer  GMATinsight

Spectre26 · Answer

In this question, as per the answer
We are supposed to find - Max A "OR" B that can be made.
But from reading the question, it seemed, Max A "AND" B that can be made.
How to avoid these mistakes?

SatvikVedala · Answer

Hi  Spectre26

It is given in the question "wishes to form adhesive using  one  of the following mixture formulas"

-it's Satvik-
I was here, I was solving & I was learning

SergejK · Answer

the 3:2 (r:h) mixture will be a multiple of 5. As we are looking for the max, we can use 10 grams as the answer as we have r=6 and h=8 as total and our answer would only require r=6 and h=4

the 2:4 (r:h) mixture will be a multiple of 6. As we are looking for the max, we can use 12 grams as the answer as we have r=6 and h=8 as total and our answer would only require r=4 and h=8

Hitesh0701 · Answer

Easiest way: 
We have Resins 6 grams and Hardener 8 grams

Ratio:
A: 3:2 
B:2:4

If ratio is multiplied by 2
A: 6:4 Total : 10
B: 4:8 Total : 12

If ratio is multiplied by 3
A: 9:6 Not possible As we have resins 6 grams only
B: 6:12 Again not possible as we have hardener maximum of 6 grams only

Hence correct answers are  10 and 12  respectively

Armaan209 · Answer

The main thing to notice is both these events are independent

when we crease maximum Mix A we donot need to calculate anything for Mix B
and vice-Versa

napolean92728 · Answer

One way to approach such question is to divide the given grams material by the parts of the material for each material and then the take the minimum number of parts of each material, also note while taking the minimum number of parts pls multiple it with the weight of that part.

For e.g. here 6g R and 8g H are available, so for mixture A 6/3 = 2 and 8/2=4 , so minimum is two parts of each , so 2 * 3 + 2 * 2 = 10 is the answer and similarly we can find the answer for mixture B

egmat · Answer

Let me walk you through this step by step.

You have  6  grams of resin and  8  grams of hardener. Each mixture is evaluated independently — you're finding the max of each one separately (not making both at the same time).

MIXTURE A (ratio 3 resin : 2 hardener)

Every  5  grams of Mixture A requires  3 g resin +  2 g hardener.

Now check which ingredient runs out first:
- Resin: You have  6 g. At  3 g per batch of  5 g → you can make  6 / 3  =  2  batches →  2  ×  5  =  10  grams total.
- Hardener: You have  8 g. At  2 g per batch of  5 g → you can make  8 / 2  =  4  batches →  4  ×  5  =  20  grams total.

Resin is the limiting factor.  Maximum Mixture A =  10  grams   (Row 3)  .

To verify:  10 g of Mixture A uses  6 g resin (all of it) and  4 g hardener (within the  8 g available). Works!

MIXTURE B (ratio 2 resin : 4 hardener)

Every  6  grams of Mixture B requires  2 g resin +  4 g hardener.

Check which ingredient runs out first:
- Resin: You have  6 g. At  2 g per batch of  6 g →  6 / 2  =  3  batches →  3  ×  6  =  18  grams total.
- Hardener: You have  8 g. At  4 g per batch of  6 g →  8 / 4  =  2  batches →  2  ×  6  =  12  grams total.

Hardener is the limiting factor.  Maximum Mixture B =  12  grams   (Row 4)  .

To verify:  12 g of Mixture B uses  4 g resin (within  6 g available) and  8 g hardener (all of it). Works!

Key Insight:  For ratio problems with limited supplies, always check BOTH ingredients separately and let the scarcer one (the bottleneck) determine your maximum.

Answer: Mixture A = Row 3, Mixture B = Row 4

A certain adhesive is formed by mixing 2 components, a resin and a har

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