How many factors does y have?

Question

(1) y is the cube of an integer.
(2) y is the product of 2 distinct positive digits.

rohit8865 · Answer

(1)
if y=n^3 then no of factors =3+1=4
but if y=0 then it has as many factors
not suff

(2) y=n*p where n,p are 2 distinct positive digits
if y= 6*8 then factors =2^4*3= 5*2=10 factors
but if y=2*3 then no. of factors=4
insuff

combining we know p is not multiple of 0 
and it is cube of a digit with 2 distinct positive digits
thus possible values are 3*9=27 or 4*2=8
both the cases no. of factors =4
suff

Ans C

JeevesAsk · Answer

Wouldnt distinct imply two different numbers?

Therefore 
(2) y=xy 
Where x and y could be two different positive numbers?

RR88 · Answer

Option C

How many factors does Y have ?

I: Y = N^3
: Prime factorization of N will decide the no. of factors Y have. For instance, Y = p^3 * q^3 : No. of factors = 4^2. If Y = p^3 * q^3 * r^3 : No. of factors = 4^3.
Insufficient.

II: Y = A*B; such that A # B from {1,9}
: Y = 1*8 = 8 = 2^3; no. of factors = 4
: Y = 1*3 = 3 = 3^1; no. of factors = 2
Insufficient

I + II:
: Y = A*B = N^3 
: Y = 4*2 = 2^3 (8); no. of factors = 4
: Y = 2*7 = 2^1 * 7^1 # N^3 ( False case )
: Y = 9*3 = 3^3 (27); no. of factors = 4
There are only two possible scenarios from I + II: either Y = 8 or 27. And, for both the values of Y, no. of factors = 4. Hence, sufficient.

stonecold · Answer

Nice Question.
Here is what i did in this one =>
We need to get the number of factors of y.

Statement 1 ->
y is a perfect cube.
y can be negative or zero or positive.
It would have been nice if the Question Stem had read-> y is a polite integer.
Anyways its clearly not possible to get the factors.
Not sufficient.

Statement 1 ->
From this statement we can infer that y must be positive.
y=2*3=> 6(4 factors)
y=1*5=>5(two factors)
y=3*9=>27=> 4 factors.
Hence not sufficient.

Combing the two statements => The only values that y can take are 8 and 27 and they both have 4 factors.

Hence C.

DexterZabula · Answer

Bunuel

Taking both statements together:

If y = 2^3 = 1x8, number of factors = 3+1 = 4
If y = 4^3 = 2x32, number of factors = 6+1 = 7

Where am I thinking incorrectly?

Bunuel · Answer

32 is not a digit (0, 1, ..., 9).

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

How many factors does y have?

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

How many factors does y have?

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