Question: x, y, and z are positive integers such that when x is divided by y, the remainder is 3, and when y is divided by z, the remainder is 8. What is the smallest possible value of x + y + z?

1. 12
2. 20
3. 24
4. 29
5. 33

Answer:
Solution with Explanation:
Approach Solution (1):

Given: x = qy + 3, where q is a quotient, an integer \(\geq\) 0. Which means that the least value of x is when q = 0, in that case x = 3. This basically means that x is less than y. for example 3 divided by 4 yields the remainder of 3.
According to above:
x is divided by y, the remainder is 3 means that the minimum value of x is 3;
y divided by z, the remainder is 8 means that the minimum value of y is 8 and the minimum value of z is one more than 8, so 9
So, the smallest possible value of x + y + z = 3 + 8 + 9 = 20

Correct Option: B

Approach Solution (2):

See x has to be atleast 3 for a remainder of 3 when x is divided by y
Then x = 3

y has to be greater than 3 for x/y to get a remainder of 3 and y has to be atleast 8 for y/z to get a remainder of 8
Then y = 8

z has to be greater than 8 for y/z to have a remainder of 8. Lowest possible integer greater than 8 is 9
So going with z = 9
x + y + z = 3 + 8 + 9 = 20

Correct Option: B

“x, y, and z are positive integers such that when x is divided by y, the remainder is 3, and when y is divided by z, the remainder is 8. What is the smallest possible value of x + y + z?”- 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 amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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