Question about Number properties

[gargarjun]

I came across this question on one of the GMAT Club test.

Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. X^2 is a multiple of 30


I selected B as the answer as i thought if x^2 has 2,3,5 prime factors then certainlly x will have the same factors as factors come in pair.
So I selected as B the answer. However, the Answer is C. Can you please help me to understand why ? The explanation says that
x can be sqrt(30). I had the assumption in these kind of problems GMAT don't expect you to think about negative and sqare root kind of things.
I remember reading that in MHGMAT number properties book.

Please help..

[gargarjun]

Similarly this question

Is 4Q/11 a positive integer?

1. Q is a prime number
2. 2Qis divisible by 11

The statement 2 by itself is not sufficient to answer the Question as Q can be -ve or + positive. ( As per the GMAT club explanation)

I am little confused now on these kind of questions..

[atul.prasad]

Hey Arjun,

The First question does not say that X is an integer. so sqrt is a valid value for X. You mustn't assume that unless explicitly mentioned. Watch out for such things :)

And about the 2nd question, since it is specifically asked if 4q/11 is positive, you must try out some negative values also.

I guess as a rule of thumb, a) never assume that a given no is integer unless specified b) while searching for answers on a trial an error basis, be sure to include some negative numbers as well..

[jnelson0612]

I came across this question on one of the GMAT Club test.

Is X divisible by 15?

1. When X is divided by 10, the result is an integer
2. X^2 is a multiple of 30


I selected B as the answer as i thought if x^2 has 2,3,5 prime factors then certainlly x will have the same factors as factors come in pair.
So I selected as B the answer. However, the Answer is C. Can you please help me to understand why ? The explanation says that
x can be sqrt(30). I had the assumption in these kind of problems GMAT don't expect you to think about negative and sqare root kind of things.
I remember reading that in MHGMAT number properties book.

Please help..

gargarjun, the GMAT absolutely can have you consider that the square root of 30 is a possible value for x. You will never have a negative square root of 30 as a possible x, but the positive square root of 30 is absolutely fair game.

[jnelson0612]

Similarly this question

Is 4Q/11 a positive integer?

1. Q is a prime number
2. 2Qis divisible by 11

The statement 2 by itself is not sufficient to answer the Question as Q can be -ve or + positive. ( As per the GMAT club explanation)

I am little confused now on these kind of questions..

gargarjun,
You should always abide by what the GMAT tells you about the variables in question, but beyond that try different types of numbers to obtain different results.

For example, on statement #2, I can choose Q=11. That makes the statement true, as 2(11) is divisible by 11. I must always choose numbers to make the statement true. Then take Q=11 and answer the question "Is 4Q/11 a positive integer?". Using Q=11, my answer would be YES.

Now, I should try to choose a number that would result in an answer of NO. I should choose Q=-11. Statement #2 is still true using -11--2(-11), or -22, is divisible by 11. However, when I plug Q=-11 into the main question, I now receive an answer of NO.

I now have obtained a YES and a NO using different numbers--insufficient.

Thank you,

[agha79]

I also got the answer B. if x^2 is a multiple of 30 then it must be divisible by 15. Why are we talking about the negative or positive square root of 30? Can some one please shed more light on the explanation of the answer?

[jnelson0612]

I also got the answer B. if x^2 is a multiple of 30 then it must be divisible by 15. Why are we talking about the negative or positive square root of 30? Can some one please shed more light on the explanation of the answer?

Agha, be careful with what you are saying in the bolded statement above.

The question is whether x is divisible by 15.

Statement 2 says that x^2 is a multiple of 30. Thus, what could x be?

x could be 30 itself. 30 squared is 900 which is obviously a multiple of 30. If x is 30, then x is divisible by 15. We answer the question with a YES.

However, x could also be the square root of 30. Two square roots of 30 multiplied together give us 30. That fits statement 2. However, if x is the square root of 30 it is NOT divisible by 15. We answer the question with a NO. Since we have a YES and a NO, not sufficient.

The takeaway is to be careful not to confuse x with x^2.

[agha79]

Thanks a lot Nelson. The explanation that 30 and sqrt 30 could be the possible values x made it very easy to conclude the insufficiency of statement 2 to answer th question!

[jnelson0612]

Great, very glad that was helpful. :-)