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

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by VJesus12 » Sun Apr 14, 2019 10:26 am

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B

C

D

E

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Difficulty—

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. 3y/15 is an integer.

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

[spoiler]OA=E[/spoiler]

Source: Veritas Prep
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by Jay@ManhattanReview » Mon Apr 15, 2019 12:33 am
VJesus12 wrote: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. 3y/15 is an integer.

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

[spoiler]OA=E[/spoiler]

Source: Veritas Prep
Given that 36 is divisible by 10, we have y is divisible by 5.

Let's see each option one by one.

I. y^2 is divisible by 25: Since y is divisible by 5, we have y^2 is divisible by 25. Correct

II. y^2 is divisible by 100: From Statement I, we know that y^2 is divisible by 25, but we cannot be sure that y^2 is divisible by 100. Incorrect.

III. 3y/15 is an integer: Since ys is divisible by 5, 3y must be divisible by 15; thus, 3y/15 is an integer. Correct.

The correct answer: E

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Wed Apr 17, 2019 5:47 pm
VJesus12 wrote: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. 3y/15 is an integer.

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

[spoiler]OA=E[/spoiler]

Source: Veritas Prep
We can create the following expression:

36y/10 = integer

18y/5 = integer

Since 18 is not divisible by 5, 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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