If p is a prime number, how many positive factors of Y are not factors

Question

If p is a prime number, how many positive factors of Y are not factors of X?

(1) X = 4p
(2) Y = 8p

DavidTutorexamPAL · Answer

Instead of solving explicitly, we'll use a few numbers to try generating contradictory solutions.
This is an Alternative approach.

(1), (2) give information about only one of X, Y so can't be sufficient.

Combined:
If we notice that both 4 and 8 are powers of 2, than a good guess would be that the question has something to do with powers of 2.
We'll try p = 2 and p = not 2, such as p = 3.
p = 2 gives X = 8, which has factors 1,2,4,8 and Y = 16 which has factors 1,2,4,8,16. In this case the difference in positive factors is 1.
p = 3 gives X = 12, which has factors 1,2,3,4,6,12 and Y = 24 which has factors 1,2,3,4,6,8,12,24. In this case the difference in positive factors is 2.
Insufficient!

(E) is our answer.

push12345 · Answer

Neither of statement alone is sufficient as individually they don't give info About X or Y

Combining both

Prime nos are all odd except 2

If we take 2
X=8=2^3 i.e. 4 factors
Y=16=2^4 i.e. 5 factors
Difference=5-4 =1

If any other prime p ..p is odd here
X=2^2*p
P has only 2 factors as it is prime
So x has 3*2=6 factors

Y has =2^3*p =4*2 = 8 factors
Difference=2

Since here we get 1 and 2 as difference between factors on taking different prices so combining is not yielding us result

So E is answer

Give kudos if it helps

Posted from my mobile device

CrackverbalGMAT · Answer

This is a tricky question on Numbers, testing you on the concepts of Prime numbers and factors. This is also a DS question where you can decide that the individual statements are insufficient, just by looking at them.

From the question statement, we know that p = 2,3,5, 7,………. We can also infer that Y should be a bigger number than X, since there are some factors of Y which may not be factors of X.

Statements I and II alone are insufficient, since they either talk about X or Y, but not both. Answer options A, B and D can be eliminated. Possible answer options are C or E.
Combining data from both the statements, we have X = 4p and Y = 8p. Therefore, we can conclude that Y = 2X or X =  \frac{Y}{2} .

For p = 2, X = 8 and Y = 16. Y has one more positive factor than X i.e. Y itself. But, for p = 3 or 5 or 7, Y will have 2 factors more than X, namely 8 and Y itself.

Therefore, even after combining, we are not sure whether Y will have one factor more than X or two factors more. This is because we not know the value of p, which is the definitive value we need to answer this question uniquely.
It’s a good idea, in such questions, to try a few values to see how the answers turn out. Based on this, you will be able to decide on whether the data is sufficient.

Hope this helps!

If p is a prime number, how many positive factors of Y are not factors

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If p is a prime number, how many positive factors of Y are not factors

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards