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# DS: Integer? (m07q30)

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Retired Moderator
Joined: 18 Jul 2008
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20 Nov 2008, 12:33
Is $$\frac{x}{12}$$ an integer?

1. $$x$$ is a multiple of 60
2. $$x*x*x \gt 0$$

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

My question is - how do you know that if it's a multiple of 12, then it's ALWAYS multiple of 60?
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20 Nov 2008, 12:50
Is x/12 an integer?

1) x is a multiple of 60

2) x*x*x>0

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

My question is - how do you know that if it's a multiple of 12, then it's ALWAYS multiple of 60?

my reason is since 60 is a multiple of 12, so all multiples of 60 will be divisible by 12 because all those multiples will have 60 in them.
suppose x=180, then it can also be written as 60*3/12
you can also do and trial and error method to arrive at the answer.

what is the OA
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20 Nov 2008, 14:58
Factors

x is a factor of y = y/x is an integer
x is a multiple of y =x/y is an interger

Q : x/12 = interger?

1) x/60 is an interger
x = 60, 120, 180, 240 etc...

SUFF

2) x*x*x > 0

x = 1 insuff
x = 6 suff

INSUFF

A
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20 Nov 2008, 23:04
Is x/12 an integer?

1) x is a multiple of 60
2) x*x*x>0

My question is - how do you know that if it's a multiple of 12, then it's ALWAYS multiple of 60?

12 = 3 * 2* 2
60 = 3 * 2 * 2 * 5

any multiple of 60 will have 3 * 2 * 2 as its factor, which, i guess, answers your question (0 is multiple of every number)
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21 Nov 2008, 07:42
Do you mean any multiple of 60 and 12 will have 2*2*3 ?

Thx.

alpha_plus_gamma wrote:
Is x/12 an integer?

1) x is a multiple of 60
2) x*x*x>0

My question is - how do you know that if it's a multiple of 12, then it's ALWAYS multiple of 60?

12 = 3 * 2* 2
60 = 3 * 2 * 2 * 5

any multiple of 60 will have 3 * 2 * 2 as its factor, which, i guess, answers your question (0 is multiple of every number)
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Joined: 08 Aug 2008
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22 Nov 2008, 00:15
yes it will..
$$60=2^2*3^1*5^1$$
$$12=2^2*3^1$$

since the HCF is the second number itself...any number divisible by 60 must be divisible by 12.
Do you mean any multiple of 60 and 12 will have 2*2*3 ?

Thx.

alpha_plus_gamma wrote:
Is x/12 an integer?

1) x is a multiple of 60
2) x*x*x>0

My question is - how do you know that if it's a multiple of 12, then it's ALWAYS multiple of 60?

12 = 3 * 2* 2
60 = 3 * 2 * 2 * 5

any multiple of 60 will have 3 * 2 * 2 as its factor, which, i guess, answers your question (0 is multiple of every number)
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22 Nov 2008, 07:56

1) x is a multiple of 60

2) x*x*x>0

is x = 12a, a is 0 or +ve intiger

from one

x = 60b, b can be 0 or +ve intiger, x = 12*5b, 5b = a..........suff

FROM 2

INSIGNIFICANT , I SAY ANSWER IS A
Intern
Joined: 17 May 2010
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12 Aug 2010, 20:37
@Financier -- even if it is 0, 0/any number is going to be 0 and 0 is an integer. so tht doesn't matter. Answer is A
correct me if i'm wrong
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14 Aug 2010, 08:11
Question in this case, we can't upfront assume that x is an integer. Now when someone says x is a multiple of 60, we mean x=60k. But does k have to be an integer? In other words, can k be fractional with the result that x is a fraction [this thought just occurred to me]. I think multiples mean integer multiples by definition? Of course if you allowed k to be fractional, then A cannot guarantee.
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14 Aug 2010, 09:29
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mainhoon wrote:
Question in this case, we can't upfront assume that x is an integer. Now when someone says x is a multiple of 60, we mean x=60k. But does k have to be an integer? In other words, can k be fractional with the result that x is a fraction [this thought just occurred to me]. I think multiples mean integer multiples by definition? Of course if you allowed k to be fractional, then A cannot guarantee.

Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

On GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

So the terms "divisible", "multiple", "factor" ("divisor") are used only about integers (at least on GMAT).

So "$$x$$ is a multiple of 60" means that $$x$$ is an integer ($$x=60k$$, where $$k$$ is an integer)

Hope it helps.
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17 Aug 2010, 01:25
X is a multiple of 60 => x/60 = I where 'I' is an integer.
X/60 can be written as x/(12*5). x/(12*5) = I => x/12 = 5*I. So, x/12 is an integer.

A is sufficient.
x*x*x>0 is insufficient as x^3 can be integer or a decimal value...

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22 Aug 2010, 06:14
B doesn't tell you anything because x could be 1/2 or even 100

A is right because X = 60,120,180.... which are divisible by 12..
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17 Aug 2011, 10:04
Its mentioned above that in GMAT unless stated otherwise any given x is assumed to be an integer.
Is this assumption correct ?? because this is not the case in CAT or any other mba exam that i have given in the past.
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17 Aug 2011, 10:32
akhil911 wrote:
Its mentioned above that in GMAT unless stated otherwise any given x is assumed to be an integer.
Is this assumption correct ?? because this is not the case in CAT or any other mba exam that i have given in the past.

In GMAT, unless mentioned explicitly, a variable "x" should be considered a Real Number(Rational, Irrational Number).

Imaginary or complex numbers are out of GMAT's domain.
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03 Sep 2011, 02:39
Is $$\frac{x}{12}$$ an integer?

1. $$x$$ is a multiple of 60
2. $$x*x*x \gt 0$$

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

My question is - how do you know that if it's a multiple of 12, then it's ALWAYS multiple of 60?

According to me the answer should be C.

statement 1: 60 * 0 = 0; In other words, 0 is also a multiple of 60; if x=0, then x/12 is not an integer. if x is a multiple of 60 other than 0 then result is an integer. Hence uncertain.

statement 2 : tells us that x is not equal to zero and x is not negative. No clue to answer.

statement 1 & 2 - x is a multiple of 60, and not equal to 0. Implies x is divisible by 12. and the result is an integer. Hence certain, hence "C".
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04 Sep 2011, 03:04
petrifiedbutstanding wrote:

For stmt 2, x*x*x > 0 could be a mixed fraction. Therefore, insufficient.

when x=0, it is a multiple of 60. but x/12 is not an integer. A cannot be the answer. We need statement 2 as well. 1 & 2 together - C is the answer.
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17 Aug 2012, 05:16
REVISED VERSION OF THIS QUESTION IS BELOW:

If $$x$$ is an integer is $$\frac{x}{12}$$ an integer?

(1) $$x$$ is a multiple of both 4 and 6 --> $$x$$ is a multiple of the least common multiple of 4 and 6, so a multiple of 12, hence $$\frac{x}{12}$$ IS an integer. Sufficient.

(2) $$x$$ is a multiple of both 8 and 10 --> $$x$$ is a multiple of the least common multiple of 8 and 10, so a multiple of 40. Now, if $$x=40$$ then the answer is NO but if $$x=120$$ then the answer is YES. Not sufficient.

petrifiedbutstanding wrote:

For stmt 2, x*x*x > 0 could be a mixed fraction. Therefore, insufficient.

when x=0, it is a multiple of 60. but x/12 is not an integer. A cannot be the answer. We need statement 2 as well. 1 & 2 together - C is the answer.

If x=0 then x/12=0=integer (remember: zero is an even integer).
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17 Aug 2012, 05:20
First statement is pretty straightforward. Second Statement is too easy to dismiss.
Normally, the GMAT makes one of the statements a bit more challenging, even on 600-level questions. Nevertheless, not too bad as a practice question for likely-harder GMAT questions.

Cheers,
Der alte Fritz.
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17 Aug 2012, 05:59
Prime factorize 12--> (2)(2)(3)
X is an integer if it contains 12 as a factor

1) X is a multiple of 60, which is a multiple of 12. --> Sufficient.

3) x*x*x>0 All this is telling us is that x is Positive. --> Insufficient

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17 Aug 2012, 07:41
1. sufficient
60=12x5
2.insuff
x is a positive integer and it can be anything 0<x<infinity
(A) wins
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Re: DS: Integer? (m07q30)   [#permalink] 17 Aug 2012, 07:41

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# DS: Integer? (m07q30)

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