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(1) 5n is a positive integer. (2) n/5 is a positive integer.
Kudos for a correct solution.
1) 5n is a positive int, so n could be any values above 0.. insuff 2) n/5 is positive int, so n has to be 5,10... always greateer than or equal to 5.. so uff as ans would be NO
(1) 5n is a positive integer. (2) n/5 is a positive integer.
Kudos for a correct solution.
Solution -
Stmt1 - 5n is a positive integer. -> n is a positive integer greater than or equal to 0. n can be decimal(1/5) or integer(>1). Not Sufficient. Stmt2 - n/5 is a positive integer. ->n is a multiple of 5. This stmt clearly says that n>=5. Sufficient.
(1) 5n is a positive integer. (2) n/5 is a positive integer.
Kudos for a correct solution.
Question : Is n < 5?
Statement 1: 5n is a positive integer. This statement doesn't limit the value of n in positive range and for any value of n, 5n will be an Integer as Given that n is an Integer. Hence, NOT SUFFICIENT
Statement 2: n/5 is a positive integer. i.e. n must be a multiple of 5 and greater than 0 for being positive i.e. Possible values of n = 5, 10, 15, 20, 25, ----- etc. But n may be equal to 5 or may be Greater than 5 but Never less than 5 hence SUFFICIENT
Answer: option B
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Question Type: Yes/No Is n an integer less than 5? Notice that the question requires two components to provide the answer “yes”: n must be an integer and n must be less than 5.
Statement 1: 5n is a positive integer. This statement is not sufficient. If you Play Devil’s Advocate you can get both integers and non-integers for n. For example, n could equal 1, which is an integer less than 5. Or n could = 1/5 and 5n = 1. This would give you a “no” since 1/5 is not an integer.
You could also manipulate the “algebra” on this one. If 5n = positive integer, then n = (positive integer)/5 That allows n to equal something like 5/5 (which is 1) or 1/5 (which is not an integer). This statement is not sufficient. Eliminate choices A and D.
Statement 2: n/5 is a positive integer. In order for n/5 to be a positive integer, n must be at least equal to 5 and must be a multiple of 5. For example, 5/5 = 1 and 10/5 = 2, etc. So this statement is sufficient because the answer is “no.” n is an integer but is not less than 5.
Again, you could also perform the “algebra” by saying that n/5 = (positive integer). This means that n = 5(positive integer). And since the lowest positive integer is 1, then n at a minimum is 5(1). Accordingly, n cannot be less than 5. Because you can answer definitively “no” to this question then this statement is sufficient and the answer is B.
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(1) 5n is a positive integer. (2) n/5 is a positive integer.
Kudos for a correct solution.
Target question:Is n an integer less than 5?
Statement 1: 5n is a positive integer Let's TEST some values. There are several values of n that satisfy statement 1. Here are two: Case a: n = 1. Here, 5n = (5)(1) = 5, and 5 IS a positive integer. In this case, n IS an integer less than 5 Case b: n = 6. Here, 5n = (5)(6) = 30, and 30 IS a positive integer. In this case, n is NOT an integer less than 5 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n/5 is a positive integer If n/5 is positive then n is positive Also, if n/5 is an integer, then we can conclude that n is divisible by 5 If n is a positive number that's divisible by 5, then some possible values of n are: 5, 10, 15, 20, 25, 30,..... NOTICE that all of the possible values of n are greater than or equal to 5. In other words, it is NOT POSSIBLE for n to be an integer less than 5 So, the answer to the target question is "No, n is definitely NOT an integer less than 5" Since we can answer the target question with certainty, statement 2 is SUFFICIENT
This is a fairly easy question on integer properties. In such a question, a smart approach would be to prove that the smallest value of n is equal to 5, so that we can answer the question with a NO.
From statement 1, 5n is a positive integer. This does not tell us anything about n, conclusively. For example, if n = \(\frac{1}{5}\), 5n = 1 satisfies statement 1. But, n is not even an integer.
If n = 10, 5n = 50 also satisfies statement 1. Here, n is an integer greater than 5. Statement 1 is insufficient. Possible answer options are B, C or E. Answer options A and D can be eliminated.
From statement 2, \(\frac{n}{5}\) is a positive integer. We can therefore rewrite the equation as, n = 5*positive integer.
Now, we know that the smallest positive integer is 1. Therefore, the smallest value for n will be 5*1 = 5. Since the smallest value of n is 5, it’s clear that n is NOT an integer less than 5. This is sufficient to answer the question with a definite NO.
Statement 2 is sufficient. Answer options C and E can be eliminated, the correct answer option is B.