If n is an integer, then n is divisible by how many positive integers?

Question

1. n is the product of a prime number and a non-prime number

2. n and 20 are each divisible by the same number of positive integers

joshuawang · Answer

For

1) n = p * (some number) therefore it can be anything

2) n and 20 are divisible by the SAME number of positive integers. However 20 = 2*2*5 or 4 * 5 or 10 * 2 or 20. To me, the number can be either 2 or 3, so statement 2 isn't enough to answer this question.

My answer was E. It's wrong though. Am i interpreting this question wrong?

prasun9 · Answer

20 is divisible by the positive integers {1, 2, 4, 5, 10, 20}

Bunuel · Answer

Similar question from OG to practice: if-n-is-an-integer-then-n-is-divisible-by-how-many-positive-164964.html

AverageGuy123 · Answer

Hello ,

As per point 1 , the number n is divisible by prime number and some other non prime number (which may have multiple prime factors). Hence not sufficient.
A per point 2 we can calculate number of factors of 20. The number of factors is not 2 or 3 (20 =1*20(1) or 2*10(2) ).Since as per question number of factors of number n is same ,Hence its sufficient.

kukr007 · Answer

1. there can be many such combinations. 7*4;7*6;.No of divisors vary here.So cant tell. Insufficient

2. n and 20 , each has same number of positive integers as divisors . As 20 can be divided by 6such integers (1, 2, 4, 5, 10, 20) so does n.
Sufficient.

Ans B

Nanobotstv · Answer

If n is an integer, then n is divisible by how many positive integers?
(1) n is the product of a prime number and a non-prime positive integer.
(2) n and 20 are each divisible by the same number of positive integers.

Please assist with above problem.

Bunuel · Answer

Merging topics. Please refer to the discussion above.

abhimahna · Answer

Answer is B.

(1) n is the product of a prime number and a non-prime positive integer. --> We don't know how many factors does a non-prime positive integer has. Hence, insufficient.

(2) n and 20 are each divisible by the same number of positive integers. --> Number of factors of 20 = Number of factors of n. So, we can easily find out the number of factors of 20. Hence, Sufficient.

BrentGMATPrepNow · Answer

Target question : n is divisible by how many positive integers? Statement 1 : n is the product of a prime number and a non-prime positive integer. This statement doesn't FEEL sufficient, so I'll TEST some values. There are several scenarios that satisfy statement 1. Here are two: Case a: n = (3)(1) = 3 . In this case n is divisible by 2 positive integers (1 and 3) Case b: n = (3)(4) = 12. In this case n is divisible by 6 positive integers (1, 2, 3, 4, 6 and 12) Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Aside: For more on this idea of testing values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values Statement 2 : n and 20 are each divisible by the same number of positive integers. 20 is divisible by 6 positive integers (1, 2, 4, 5, 10 and 20), so n must be divisible by 6 positive integers Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer = B RELATED VIDEOS https://www.youtube.com/watch?v=2wzrx4bF8XE https://www.youtube.com/watch?v=mVXwvaxLI20[/you-tube

GMATinsight · Answer

Question REPHRASED : How many factors does n have?

Statement 1 : n is the product of a prime number and a non-prime number 
Case 1: n = 2*4 which has 4 factors
Case 2: n = 2*6 which has 6 factors
NOT SUFFICIENT

Statement 2 : n and 20 are each divisible by the same number of positive integers 
i.e. n and 20 both have equal number of factors
20 has 6 factors and so does n
20 = 2^2*5
No of factors = (2+1)*(1+1) = 6
SUFFICIENT

Answer: option B

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If n is an integer, then n is divisible by how many positive integers?

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GMAT Data Sufficiency (DS) Questions

If n is an integer, then n is divisible by how many positive integers?

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