A Merchant Has 435 Litres, 493 Litres And 551 Litres Of Three Different Kinds Of Milk GMAT Problem-Solving

Answer: B
Solution and Explanation
Approach Solution 1
This is a question about how to solve a problem on the GMAT. The facts given in the questions must be analysed in order to come up with an answer. Some parts of the method may come from other areas of mathematics. The way the choices are laid out is pretty close to the right answer, so guessing can often lead to mistakes. Students must fully understand the question and think about how to answer it in the right way.

Take note that the difference is 58. Since we also know that the GCF must be an odd number and that it must be a factor of 58, we can deduce that the GCF must be 29. Since 435 = 290 + 145 is a multiple of 29, we can deduce that all of the numbers are all multiples of 29.

435/29 = (290 + 135)/29 = 15. When we divide the two additional numbers by 29, we know that we get 17 and 19, respectively. The total would be 17 * 3 = 51.

B is the correct answer.

Approach Solution 2
This is a question about how to solve a problem on the GMAT. The facts given in the questions must be analysed in order to come up with an answer. Some parts of the method may come from other areas of mathematics. The way the choices are laid out is pretty close to the right answer, so guessing can often lead to mistakes. Students must fully understand the question and think about how to answer it in the right way.

To find the least number of casks of equal size required to store all the milk without mixing, we need to find the greatest common divisor (GCD) of the three given numbers: 435, 493, and 551.
Step 1: Find the GCD of the first two numbers (435 and 493).
Prime factorization of 435:
435 = 3 * 5 * 29
Prime factorization of 493:
493 = 17 * 29
The common prime factors of 435 and 493 are 29.
Step 2: Find the GCD of the result from Step 1 (which is 29) and the third number (551).
Prime factorization of 551:
551 = 19 * 29
The common prime factors of 29 (result from Step 1) and 551 are 29.
Step 3: The GCD of the three numbers is 29.
Now, to store the milk without mixing, we need casks of size 29 liters each. To find the least number of casks required, we simply divide the sum of the three given numbers by the GCD:
Total amount of milk = 435 + 493 + 551 = 1479 liters
Number of casks required = Total amount of milk / GCD = 1479 / 29 = 51
The minimum number of casks of equal size required to store all the milk without mixing is 51.
So, the correct answer is B.

Approach Solution 3
This is a question about how to solve a problem on the GMAT. The facts given in the questions must be analyzed in order to come up with an answer. Some parts of the method may come from other areas of mathematics. The way the choices are laid out is pretty close to the right answer, so guessing can often lead to mistakes. Students must fully understand the question and think about how to answer it in the right way.

We must determine the three supplied integers' greatest common divisor (GCD) in order to determine the smallest number of equal-sized casks needed to hold all the milk without mixing. These three numbers are 435, 493, and 551.
Finding the GCD of the first two numbers (435 and 493) is the first step.
435's prime factors are as follows: 3 * 5 * 29
Prime factors of 493 are as follows: 493 = 17 * 29
29 is the shared prime factor between 435 and 493.

Determine the GCD of the third number (551) and the result of Step 1 (29).
551's prime factors are as follows: 551 = 19 * 29
The prime factorization of 551 and 29 (the result of Step 1) is 29.

The three numbers' GCD is 29.
Now, we need 29-liter barrels in order to store the milk separately. Simply divide the sum of the three figures supplied by the GCD to determine the smallest number of barrels necessary:
Total milk volume is 435 + 493 + 551 liters.

The required number of casks is equal to the sum of the milk and the GCD, which is 1479 / 29.
To preserve all the milk without mixing it, 51 equal-sized casks must be present at all times.

So, B is the right response.