Is y a perfect square, where x and y are natural numbers?

Question

Given, x and y are positive integers. Is y a perfect square?

I. y is divisible by (x + 1) and (x + 2).

II. y < 200

chetan2u · Answer

GMAT does not use the term natural numbers generally and you will find positive integers instead.

So, x and y are positive integers. Is y a perfect square?

1. y is divisible by x+1 and x+2.
So, y is multiple of two consecutive integers.  NOTE that we do not know anything about other factors.  
For example: Let x=2
If y is 3*4, then no. 
If y is 36 or 3*4*3, then answer is yes. 
Insufficient

2. y<200
y can be 12 or 36.
Insufficient

Combined 
y can again be 12 or 36 and many other values. 
Insufficient

E

sritamasia · Answer

I've edited the question to positive integers.

JerryAtDreamScore · Answer

Rephrase the question:

It is harder to find a case for y being a perfect square. So we should be more interested in the extreme case where y is a perfect square, and we automatically assume we will always find a case where y is not a perfect square. Thus we can ask "is y possibly a perfect square?"

Statement 1 Alone:

Let  y = (x + 1)^2*(x + 2)^2 . Then y could be a perfect square. Thus statement 1 alone is insufficient.

Statement 2 Alone:

Insufficient.

Both Statements Combined:

We could still let x = 1 and use the example in statement 1. Then combined it is still insufficient.

Answer: E

kaptainklutz · Answer

Start with statement B- Y being less than 200 tells us nothing about y being a perfect square. This eliminates options b and C.

A gives us a condition that y is divisible by x + 1 and x + 2. However, that leads us to multiple values like 12, 24, 36, etc

Using both together also does not give us a clear answer. Hence both the answer choices together are not sufficient

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Is y a perfect square, where x and y are natural numbers?

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