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If x is divisible by 18 and y is divisible by 12, which of t
[#permalink]
12 Aug 2018, 16:07

1

Expert Reply

Question Stats:

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.

_________________

Sandy

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Re: If x is divisible by 18 and y is divisible by 12, which of t
[#permalink]
15 Aug 2018, 04:25

1

I think the answer is A, not B and not C.

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Re: If x is divisible by 18 and y is divisible by 12, which of t
[#permalink]
15 Aug 2018, 08:16

2

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.

_________________

Sandy

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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.

_________________

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Re: If x is divisible by 18 and y is divisible by 12, which of t
[#permalink]
15 Aug 2018, 09:10

So I am right. You've made a mistake posting answer as C.

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Joined: **07 Jun 2014 **

Posts: **4810**

WE:**Business Development (Energy and Utilities)**

Re: If x is divisible by 18 and y is divisible by 12, which of t
[#permalink]
15 Aug 2018, 11:02

Expert Reply

Simon wrote:

So I am right. You've made a mistake posting answer as C.

Yup! sorry about that it is A.

_________________

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Re: If x is divisible by 18 and y is divisible by 12, which of t
[#permalink]
20 Sep 2021, 09:32

2

First number 18a, 2nd 12b

x+y=18a+12b=6*(3a+2b) hence multiple of 6

xy=18a*12b=8*27*ab

Now a and b both could be 1 so min 8*27 is not multiple of 48

x/y=18a/12b=3a/2b

a & b could be 1

So x/y=3/2 not multiple of 6

x+y=18a+12b=6*(3a+2b) hence multiple of 6

xy=18a*12b=8*27*ab

Now a and b both could be 1 so min 8*27 is not multiple of 48

x/y=18a/12b=3a/2b

a & b could be 1

So x/y=3/2 not multiple of 6

If x is divisible by 18 and y is divisible by 12, which of t
[#permalink]
26 Feb 2024, 03:43

1

The prime factors of 18 = 3, 3, 2

The prime factors of 12 = 2, 2, 3

A)

x+y is divisible by 6.

Now x+y should at least contain 18+12=30 which is divisible by 6. Hence x+y is divisible by 6. As all other values of x and y would be multiples of 18 and 12 and would contain at least 30 inside them.

B) xy is divisible by 48

The factors of xy are the factors of x and y taken together = 3, 3, 2, 2, 2, 3

Now you cannot create 48 by multiplying the prime factors of xy listed above

So xy is NOT divisible by 48

C)

\(\frac{x}{y}\) is divisible by \(6\)

\(\frac{x}{y} = \frac{18}{12} = \frac{3}{2}\). Hence it is NOT divisible by \(6\).

The answer is only A

_________________

The prime factors of 12 = 2, 2, 3

A)

x+y is divisible by 6.

Now x+y should at least contain 18+12=30 which is divisible by 6. Hence x+y is divisible by 6. As all other values of x and y would be multiples of 18 and 12 and would contain at least 30 inside them.

B) xy is divisible by 48

The factors of xy are the factors of x and y taken together = 3, 3, 2, 2, 2, 3

Now you cannot create 48 by multiplying the prime factors of xy listed above

So xy is NOT divisible by 48

C)

\(\frac{x}{y}\) is divisible by \(6\)

\(\frac{x}{y} = \frac{18}{12} = \frac{3}{2}\). Hence it is NOT divisible by \(6\).

The answer is only A

_________________

gmatclubot

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