What is the remainder when integer k is divided by integer j?

Question

(1) j and k each have the same number of unique factors.
(2) 1 < j < k < 10

Kudos for a correct  solution .

GMATinsight · Answer

Question : Remainder (k/j) = ?

Statement 1 : j and k each have the same number of unique factors. 
Case 1: j = k i.e. remainder = 0
Case 2: j = 15 and k=6 i.e. remainder = 3, INCONSISTENT VALUES hence
 NOT SUFFICIENT

Statement 2 : 1 < j < k < 10 
Case 1: j = 2 and k=4 i.e. remainder = 0
Case 2: j = 2 and k=5 i.e. remainder = 1, INCONSISTENT VALUES hence
 NOT SUFFICIENT

Combining the two statements  
j and k must have same no. of Unique factors
Case 1: j = 2 and k=3 i.e. remainder = 1
Case 2: j = 3 and k=5 i.e. remainder = 2, INCONSISTENT VALUES hence
 NOT SUFFICIENT

Answer: option E

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value?  This problem asks you to find the remainder when k is divided by j.

Given information from the question stem: j and k are integers.

Statement 1 : This problem offers a great opportunity to pick numbers/Play Devil’s Advocate.” The easiest numbers to pick are likely prime numbers, since you know that by definition all primes have the same number of factors (two). 5 divided by 3 leaves a remainder of 2, so now you want to find an answer that gives you something other than 2. You want to Play Devil’s Advocate to arrive at an alternative answer to show that the statement is not sufficient. Typically the best way to do that is to try numbers with different properties, and 2—the only even prime—gives you just that opportunity. 3 divided by 2 leaves a remainder of 1, and since we’ve found two different answers (2 and 1) to this specific-value question, we can prove that this statement is not sufficient.

Statement 2 : Notice this: The numbers we chose for Statement 1 are also possibilities given Statement 2. So we can use the same numbers to show that Statement 2 alone is not sufficient, and that even taken together the statements are not sufficient. Accordingly,  the correct answer is E .

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the remainder when integer k is divided by integer j?

(1) j and k each have the same number of unique factors.
(2) 1 < j < k < 10

There are 2 variables (j,k) in the original condition, and we need 2 equations in order to match the number of variables. As 2 equations are provided from the 2 conditions, there is high chance that (C) is going to be the answer. 
However, when looking at the conditions together, 
The remainder becomes 1 when j=2, k=3, and
the remainder becomes 2 when j=3 and k=5. Hence, the conditions are insufficient giving no unique answer, and the answer becomes (E).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

hdwnkr · Answer

Same number of factors is different from same factors. Hence A is insufficient.

the two numbers are between 1 and 10. No clarity. Rem (7/2) is different from Rem (4/2). Hence, B is insufficient.

Combining the two statements

Let's take some cases. For example primes

Rem(3/2) is different from Rem (7,5)
They have the same number of unique factors and lie between 1 and 10. Yet, insufficient

Hence, E

Ctlam1993 · Answer

What do they mean by same number of unique factors?

IanStewart · Answer

I honestly have no idea what they could mean by "unique" factors. It's a bit like saying two families have "the same number of unique children", when all you're trying to say is that the families have the same number of children. Inserting the word "unique" makes a simple statement bizarre and confusing.

So the word "unique" just doesn't belong in a sentence like this. If instead you were asking instead about the word "factors", then if Statement 1 read, as it would on the real GMAT:

1. j and k each have the same number of factors.

then the Statement is just saying that the number of divisors of j is the same as the number of divisors of k. So if j has four divisors, say, then k also has four divisors. One possibility, then, is that j and k are both prime numbers, because every prime number has precisely two divisors (every prime is divisible only by 1 and itself). You can use prime numbers alone to answer this question.

Basshead · Answer

What is the remainder when integer k is divided by integer j?

(1) j and k each have the same number of unique factors.
3/2 = remainder 1

5/3 = remainder 2

INSUFFICIENT.

(2) 1 < j < k < 10
3/2 = remainder 1

5/3 = remainder 2

INSUFFICIENT.

(1&2) Same cases work here. INSUFFICIENT.

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What is the remainder when integer k is divided by integer j?

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