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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If positive integer 36y is divisible by 10, which of the
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Jay@ManhattanReview
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Given that 36 is divisible by 10, we have y is divisible by 5.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
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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Scott@TargetTestPrep
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We can create the following expression: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
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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