If A and B are positive integers, does B have more prime factors than

Question

If A and B are positive integers, does B have more prime factors than A?

(1) B is the square root of A
(2) A ÷ B is an integer

GMATinsight · Answer

Question: Does B have more prime factors than A?

Statement 1: B is the square root of A

By taking square root, the magnitude (may) gets influenced but the number of prime factors remain same hence

No. of prima factors of A = No. of prima factors of B

SUFFICIENT

Statement 2: A ÷ B is an integer

Case 1: a = 9 and b =3, No. of prima factors of A (i.e. 1) = No. of prima factors of B (i.e. 1)
Case 2: a = 12 and b =3, No. of prima factors of A (i.e. 2) > No. of prima factors of B (i.e. 1)

NOT SUFFICIENT

Answer: Option A

SanketB20 · Answer

IanStewart · Answer

From Statement 1, A and B have the same number of prime divisors; when we square root a perfect square, we don't change how many prime divisors we have. So Statement 1 is sufficient.

From Statement 2, if A/B is an integer, then A = mB. So A has all of the prime divisors B has, along with any additional prime divisors m has. Either way, A has at least as many prime divisors as B. So B cannot possibly have more prime divisors than A, and Statement 2 is also sufficient, and the answer is D.

carouselambra · Answer

If A and B are positive integers, does B have more prime factors than A?

(1) B is the square root of A
 Sufficient. 
Examples : B=2, A=4
 B=3, A=9
Here, even though the value of A increases, the basic number of prime factors remain the same.

(2) A ÷ B is an integer
 Not sufficient. 
Examples : B=3, A=9 (here, the number of prime factors are the same)
 B=20, A=4 (here, B has more prime factors than A does)

winterschool · Answer

If A and B are positive integers, does B have more prime factors than A?

(1) B is the square root of A
(2) A ÷ B is an integer

Statement 1 :

B is the square root of A, 
number of prime factor of B = number of prime factor of A

Sufficient

Statement 2:

A/B = integer, 1 or any positive integer

number of prime factor of B not greater than those of A

Sufficient

Answer D

SairamRamo · Answer

S1  B is the square root of A

A number and its power always has the same number of distinct prime numbers

S1 is sufficient

S2  A ÷ B is an integer

Either A and B can have the same distinct prime numbers or A can have more distinct prime numbers than B where B is a subset of A

S2 is not sufficient

IMO A

Villiavello · Answer

Please can someone assist as to why I did not get this correct:

1: B is the square root of A

I immediately wanted to say sufficient, but then I remembered that square root 1 = 1, and there is the option that this could be showing:
1 = 1

Similarly with B:

2: A ÷ B is an integer

This could also be 1/1 = 1

Thus, this shows that there are two possibilities for each, and using them together also presents itself with these two separate possibilities.

IanStewart · Answer

I don't follow what you mean when you say there are two possibilities. In DS, we care specifically whether there are two (or more) possible answers to the question asked. Here, the question is "does B have more prime factors than A?" Using Statement 1 alone, say, that question has only one possible answer. As you point out, we might have A = 1 and B = 1. In that case, A and B are the same number, so naturally they have the same number of prime factors (they both have zero prime factors). But for any other values of A and B you might choose, you will also find that A and B have the same number of prime factors. So there's only one possible answer to the question (the answer is "no, B does not have more prime factors than A"), and Statement 1 is sufficient. Similarly for Statement 2, even when you consider the possibility that A = B = 1, you do not get a new answer to the question, so you don't find there are two possibilities.

If A and B are positive integers, does B have more prime factors than

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GMAT Data Sufficiency (DS) Questions

If A and B are positive integers, does B have more prime factors than

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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