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If x is divisible by 18 and y is divisible by 12, which of t
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12 Aug 2018, 16:07
12 Aug 2018, 16:07
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Question Stats:
68% (01:26) correct
31% (01:46) wrong based on 101 sessions
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If x is divisible by 18 and y is divisible by 12, which of the following statements must be true?
Indicate all such statements.
A. x + y is divisible by 6.
B. xy is divisible by 48.
C. \(\frac{x}{y}\) is divisible by 6.
Indicate all such statements.
A. x + y is divisible by 6.
B. xy is divisible by 48.
C. \(\frac{x}{y}\) is divisible by 6.
Re: If x is divisible by 18 and y is divisible by 12, which of t
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15 Aug 2018, 04:25
15 Aug 2018, 04:25
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I think the answer is A, not B and not C.
Re: If x is divisible by 18 and y is divisible by 12, which of t
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15 Aug 2018, 08:16
15 Aug 2018, 08:16
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Expert Reply
Explanation
To solve this problem with examples, make a short list of possibilities for each of x and y:
x = 18, 36, 54…
y = 12, 24, 36…
Now try to disprove the statements by trying several combinations of x and y above. In the 1st statement, x + y could be 18 + 12 = 30, 54 + 12 = 66, 36 + 24 = 60, or many other combinations.
All of those combinations are multiples of 6. This makes sense, as x and y individually are multiples of 6, so their sum is, too. The first statement is true.
To test the second statement, xy could be 18(12) = 216, which is not divisible by 48. Eliminate the second statement.
As for the third statement, \(\frac{x}{y}\) could be \(\frac{18}{12}\), which is not even an integer (and therefore not divisible by 6), so the third statement is not necessarily true.
To solve this problem with examples, make a short list of possibilities for each of x and y:
x = 18, 36, 54…
y = 12, 24, 36…
Now try to disprove the statements by trying several combinations of x and y above. In the 1st statement, x + y could be 18 + 12 = 30, 54 + 12 = 66, 36 + 24 = 60, or many other combinations.
All of those combinations are multiples of 6. This makes sense, as x and y individually are multiples of 6, so their sum is, too. The first statement is true.
To test the second statement, xy could be 18(12) = 216, which is not divisible by 48. Eliminate the second statement.
As for the third statement, \(\frac{x}{y}\) could be \(\frac{18}{12}\), which is not even an integer (and therefore not divisible by 6), so the third statement is not necessarily true.
