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.
Is x/5 an integer?
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Target question: Is x/5 an integer?sofiasol wrote:Is x/5 an integer?
1) x/12.35 is an integer.
2) x/6360 is 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
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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.
Hope this helps �
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.
Hope this helps �
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We need to determine whether x/5 is an integer.sofiasol wrote:Is x/5 an integer?
1) x/12.35 is an integer.
2) x/6,360 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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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!
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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The following we can draw if x/5 is an integer.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.
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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