If positive integer 36y is divisible by 10, which of the following mus

Question

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

EMPOWERgmatRichC · Answer

HI shasadou,

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.

GMAT assassins aren't born, they're made,
Rich

EMPOWERgmatRichC · Answer

HI shasadou,

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...

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

shasadou · Answer

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

JeffTargetTestPrep · Answer

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

NNURP · Answer

I have a question of

II. y^2 is divisible by 100.

100 = 2^2 X 5^2, as long as y^2 is divisible by 100 means Y has at least factor 2,2,5,5. Hence 36Y can be divided by 10

Is II wrong because it can not co-exist with I ???

Bunuel · Answer

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

NNURP · Answer

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?

Bunuel · Answer

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.

11. Must or Could be True Questions 
     Theory   
 3 FORMATS FOR GMAT INEQUALITIES QUESTIONS YOU NEED TO KNOW 
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For more check  Ultimate GMAT Quantitative Megathread

NNURP · Answer

Thanks Bunuel!! I finally got it!!! Got confused MUST BE question with DS-style question..

GMATGuruNY · Answer

If  36y = 10 , then  y = \frac{10}{36} = \frac{5}{18} .
Implication:
 y=\frac{5}{18}  satisfies the condition that positive integer  36y  is divisible by 10, since  36*\frac{5}{18} = 10 .
If  y=\frac{5}{18} , then none of the options is true.
The problem is flawed.

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If positive integer 36y is divisible by 10, which of the following mus

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