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Is x/5 an integer?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Nov 29, 2016 6:20 am
sofiasol wrote:Is x/5 an integer?

1) x/12.35 is an integer.
2) x/6360 is an integer.
Target question: Is x/5 an integer?

Statement 1: x/12.35 is an integer
This statement doesn't FEEL sufficient, so let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 12.35, in which case x/12.35 = 12.35/12.35 = 1, which is an integer. In this case, x/5 = 12.35/5 = 2.47, which is NOT an integer
Case b: x = 1235, in which case x/12.35 = 1235/12.35 = 100, which is an integer. In this case, x/5 = 1235/5 = 247, which IS an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x/6360 is an integer
This tells us that x is a multiple of 6360
In other words, x = 6360k for some integer k
So, x/5 = 6360k/5 = 1272k. Since k is some integer, we can be certain that 1272k is an integer.
In other words, x/5 IS an integer
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

RELATED VIDEO
- Introduction to Divisibility: https://www.gmatprepnow.com/module/gmat ... /video/820
Brent Hanneson - Creator of GMATPrepNow.com
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by crackverbal » Wed Nov 30, 2016 9:11 pm
Hi Sofiasol,

Question is: Is x/5 an integer ?

That is whether "x" is a multiple of 5 ?

Statement I not sufficient:

Given , x/ 12.35 is an integer, it says x is a multiple of 12.35.

x is multiple of 12.35 doesn't mean that "x" is a multiple of 5.

For an example x = 12. 35 , then answer to the question is NO.

But if x = 1235, then answer to the question is YES.

Statement II is sufficient:

x/ 6360 is an integer, so again similarly it says "x" is a multiple of 6360

that is x = 6360*k

then, definitely this is divisible by 5. (6360 - definitely will have minimum one "5" )

So answer to the question is always YES.

So sufficient.

So the answer is B.

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by Jeff@TargetTestPrep » Fri Dec 02, 2016 9:41 am
sofiasol wrote:Is x/5 an integer?

1) x/12.35 is an integer.
2) x/6,360 is an integer.
We need to determine whether x/5 is an integer.

Statement One Alone:

x/12.35 is an integer.

We can multiply our expression by 100/100 and we have:

100x/1235 = integer

100x/1235 = integer

20x/247 = integer

We see that x is a multiple of 247; however, we cannot say for sure whether x is a multiple of 5. For instance if x = 247, it is not a multiple of 5 and if x = 247 x 5, it is a multiple of 5. Thus, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

x/6,360 is an integer.

Using the information in statement two, we see that x is a multiple of 6,360, which means that x is also a multiple of 5, and thus x/5 must be an integer. Statement two alone is sufficient to answer the question.

Answer: B

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by Matt@VeritasPrep » Thu Dec 08, 2016 9:30 pm
Another way to do it:

S1:

Let's say n = an integer.

We're told that x/12.35 = n, or x = 12.35n.

From here, we want x/5. We can find this by dividing both sides by 5: x/5 = 2.47n.

So the question becomes "Is 2.47n an integer?" Who knows! We'd need to know n, and we don't: INSUFFICIENT.

S2:

Let's say m = an integer.

x/6360 = m

x = 6360m

Dividing both sides by 5, as before:

x/5 = 1272m

So x/5 = (integer) * (integer), making it an integer!
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by Jay@ManhattanReview » Thu Feb 02, 2017 10:04 pm
sofiasol wrote:Is x/5 an integer?

1) x/12.35 is an integer.
2) x/6,360 is an integer.

The solution says 2) alone is sufficient, but 1) alone is not sufficient.

I got the opposite... Could someone explain why? Please.
The following we can draw if x/5 is an integer.

1. x = 0
2. x = a positive mutiple of 5: 5, 10, 15, 20, ...
3. x = a negative mutiple of 5: -5, -10, -15, -20, ...

If we are able to establish that x ALWAYS falls in at least one of the three, the answer is YES; however, we are able to establish that x DOES NOT fall in any of the three, the answer is NO. In both the case, the question is answerable.

The question is inconclusive or unanswerable if x sometimes falls in at least one of the three, but also sometimes does not fall in them.

Let us take each statement one by one.

S1: x/12.35 is an integer.

Whenever you see a fraction asking to be tested whether it is an integer, always first test two values: 0 and the given number (here 12.35).

We see that if x = 0 or 12.35, x/12.35 is an integer.

At x=0, the fraction x/5 is an integer; however, at x=12.35, the fraction x/5 is not an integer. No unique answer. Insufficient.

S2: x/6,360 is an integer.

We see that if x = 0 or 6,360, x/6,360 is an integer.

At x=0, the fraction x/5 is an integer; moreover, at x=6360, the fraction x/5 is also an integer.

Should we try more? Well, there is no need, but let's try to understand better.

Since x/6,360 is an integer, x must be a multiple of 6360. Or, x belongs to set: {0, +/-6360, +/-6360*2, +/-6360*3,+/-6360*4,+/-6360*4...}

We if plug-in any of the values given in the set in x/5, x is always divisible by 5, making x/5 an integer. A unique answer. Sufficient.

Correct answer: B

Hope this works.

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