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Roman Numeral questions on the GMAT are usually designed in such a way that you can use the answer choices to avoid doing some of the work. Without those answer choices, we're forced to work through all 3 Roman Numerals. Thus, it would help if you include the 5 answer choices.

Although the prompt doesn't state it, I think that it is supposed to state that "Y is an INTEGER."

Given that, we can use Prime Factorization to deal with this prompt.

Again, assuming that Y is an integer, we're told that 36Y is divisible by 10. This means that 36Y must have a "2" and a "5" among its prime factors.

36 = (2)(2)(3)(3), so it has the '2' that we're looking for, but it doesn't have the '5.' This means that the Y must contain at least a "5" (although it could have other prime factors also, including additional 5s). This is all meant to say that Y MUST be a multiple of 5. Since the prompt asks for what MUST be true, we can use Y=5 to assess the Roman Numerals.

I. Y^2 is divisible by 25

Y=5 Y^2 = 25, which IS divisible by 25 Any larger multiple of 5 will also be divisible by 25. Roman Numeral 1 is always true. Eliminate Answers B and C.

II. Y^2 is divisible by 100

With the work that we did in Roman Numeral 1, we've proven that this is NOT always true. Eliminate Answer D.

III. 3Y/15 is an integer

Even before we consider the value of Y, we can simplify this fraction.... 3Y/ 15 = Y/5

So, is Y/5 always an integer? We already proved that Y had to be a multiple of 5, so this Roman Numeral is also always true. Eliminate Answer A. If we had dealt with this Roman Numeral immediately after dealing with Roman Numeral 1, then we wouldn't even have had to deal with Roman Numeral 2. There's only one answer that includes Roman Numerals 1 and 3...

Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

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13 Sep 2015, 11:15

EMPOWERgmatRichC wrote:

Although the prompt doesn't state it, I think that it is supposed to state that "Y is an INTEGER."

hi

hecked once again - i fully restated the question, the stimulus does not say y is an integer. if this were a DS variation of the question it would be E. thanks
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Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

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24 Sep 2017, 06:08

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If positive integer 36y is divisible by 10, which of the following must be true?

I. y^2 is divisible by 25.

II. y^2 is divisible by 100.

III. \(\frac{3Y}{15}\) is an integer.

A. I only B. II only C. III only D. I and II only E. I and III only

We can create the following expression:

36y/10 = integer

18y/5 = integer

So we see that y must be a multiple of 5.

Thus, Roman numerals I and III must be true.

Roman numeral II, on the other hand, does not have to be true. For instance, we see that y = 5 satisfies the hypothesis that 36y is divisible by 10; but y^2 = 25 is not divisible by 100.

Answer: E
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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

If positive integer 36y is divisible by 10, which of the following must be true?

I. y^2 is divisible by 25.

II. y^2 is divisible by 100.

III. \(\frac{3y}{15}\) is an integer.

A. I only B. II only C. III only D. I and II only E. I and III only

Sorry Bunuel, I still don't get the explanation you provide. Can you please help?

The question is basically asking whether Y contains any 5.

If y^2 is divisible by 100, then y^2 must contains at least multiple of 2 and 5. When we apply Y(2*2*5*5) back, 36Y can be divided by 10.

What am I getting wrong here?

It seems that you don't understand the question.

We are told that 36y is divisible by 10, and asked to find which of the options MUST be true. For 36y to be divisible by 10, y (assuming it's an integer) must be a positive multiple of 5, so y could be 5, 10, 15, 20, ...

Is the second option (y^2 is divisible by 100) always true? NO. If y = 5, then y^2 =25, and it's NOT divisible by 100. So, it's not always true.