When X Is Divided By 13, The Answer Is Y With a Remainder of 3. GMAT Problem Solving

Question: When x is divided by 13, the answer is y with a remainder of 3. When x is divided by 7, the answer is z with a remainder of 3. If x, y, and z are all possible integers, what is the remainder of yz/13?

1. 0
2. 3
3. 4
4. 7
5. None of these

“When x is divided by 13, the answer is y with a remainder of 3.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

The given condition is that when x is divided by 13, the answer is y with a remainder 3. Further, when x is divided by 7, the answer is z, with a remainder of 3.

In order to do the find the value of remainder of yz/13, considering that x, y, z are all integers.

Accordingly, it may be identified that the equation could be evaluated as:

x= 13y + 3 (when x is divided by 13 it gives a quotient of y a remainder of 3)

x= 7z + 3 (when x is divided by 7 it gives a quotient of z and it gives a remainder of 3)

Now reversing the equations to find y and z

y=(x-3)/13

z= (x-3)/7

Considering the given situation which states that x, y and z are integers, thus the product YZ is divisible by (13*7)=81 because it's a multiple of it.

But 81 is divisible by 13 thus the remainder is 0.

Correct Answer: A

Approach Solution 2:

The requirement is that the result of dividing x by 13 equals y with a remainder of 3. In addition, the result of dividing x by 7 is z, leaving a remainder of 3.

Given that x, y, and z are all integers, the value of the remainder of yz/13 must be determined.

As a result, it is apparent that the equation may be calculated as:

x= 13y + 3 (when x is divided by 13 it provides a quotient of y a remainder of 3) (when x is divided by 13 it gives a quotient of y a remainder of 3)

x= 7z + 3 (when x is divided by 7 it yields a quotient of z and it gives a residual of 3) (when x is divided by 7 it gives a quotient of z and it gives a remainder of 3)

To find y and z, reverse the equations now.

y=(x-3)/13

z= (x-3)/7

Given that x, y, and z are all integers, the product YZ is divisible by (13*7)=81 since it is a multiple of that number.

But because 81 is divisible by 13, there is no remainder.

Correct Answer: A

Approach Solution 3:

The condition states that x divided by 13 must equal y with a remainder of 3. In addition, when you divide x by 7, you get z, leaving a 3 digit leftover.

It is necessary to figure out the value of the remainder of yz/13 since x, y, and z are all integers.

It follows that the equation may be computed as follows:

x= 13y + 3 (When x is divided by 13, a quotient of y and a residual of 3 are produced) (when x is divided by 13 it gives a quotient of y a remainder of 3)

x= 7z + 3 (When x is divided by 7, the resultant division is z, and the remainder is 3) (When x is divided by 7, the result is z as the quotient and 3 as the remainder.

Reverse the equations to determine y and z.

y=(x-3)/13

z= (x-3)/7

Given that x, y, and z are all integers, the product YZ is a multiple of (13*7)=81 since it is an integer and is thus divisible by that amount.

However, since 81 may be divided by 13, there is no remainder.

Correct Answer: A

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