x/y = 7/9

gives us

9x = 7y

Since these are both positive integers, we now have

x = a multiple of 7
y = a multiple of 9

But 103 isn't a multiple of 7! So x can't be a multiple of 7, and x/y can't be 7/9.

manik11 wrote:Hi Experts! I don't understand how statement 1 could be sufficient, Its been a common pattern in most of the DS problems I've solved so far that when the prompt involves two variables and the statement doesn't say anything about one of the variables, its almost always insufficient.

The pattern you mentioned tends to show up in more basic DS questions, and assuming that it will hold can be risky. For one thing, anyone writing a question knows that people commonly look for equations containing all of the variables. So a good way to write a trick question is to write it in such a way that it's solvable via using something that does not include all of the variables.

Here are a couple of questions that can be answered by using statements that do not include all of the variables.

1) What is the value of (w + x)(y + z)?

(1) 3w + 3x = 51

(2) y² + 2yz + z² = 0


2) An auto dealership has multiple departments. Each of the departments has a manager, each department has multiple employees who work with the manager, and each department has the same number of of people in it. If there are only department managers and other department employees working at the dealership, and if there are fewer than 25 employees at the dealership, how many employees does the dealership have?

(1) The ratio of managers to non manager employees is 1:7.

(2) There are 21 non manager employees at the dealership.


The OA to question 1 is B.

The OA to question 2 is B.

Here's another one.

If x > y, and x, y and x/y are all positive integers, is x/y > 10?

(1) y² < 36

(2) x = 53

The correct answer is B.

Thanks a lot guys!