Pls correct my reasoning.

for Q1) my reasoning was since 3^a*4^b = c and base 3 is "even" and base 4 is "odd" then there wont be any other answer except a=2 and b=1. But I was wondering what are the other values of a and b can be for this equation to be true. Sorry, I am asking too much

for Q2) I thought that x=2^a*3^b*5^c. isnt's now x is a product of three distinct prime factors. But I relaize that I misunderstood the stem - "x is a product of distinct prime numbers". So I agree with your explanation.

Can you clarify Q1) please.

Thanks for the awesome explanation. You rock Bunuel!

nusmavrik wrote:

Q1 If 3^a*4^b = c, what is the value of b?

(1) 5^a = 25

(2) c = 36

Q2 How many distinct positive factors does the positive integer x have?

(1) x is the product of 3 distinct prime numbers.

(2) x and 3^7 have the same number of positive factors.

OA :

Q1 C

Q2 D

But I disagree with them- it should be B and B. Please can you take a look thanks.

- Nishant

Both OA's are correct.

If 3^a*4^b = c, what is the value of b?Note that we are not told that the variables are integers only.

(1) 5^a = 25 -->

a=2, but we can not get the values of

b. Not sufficient.

(2) c = 36 -->

3^a*4^b = c: it's tempting to write

3^2*4^1=36 and say that

b=1 but again we are not told that the variables are integers only. So, for example it can be that

3^a=36 for some non-integer

a and

b=0, making

4^b equal to 1 -->

3^a*4^b =36*1=36. Not sufficient.

(1)+(2) As

a=2 and

c = 36 then

9*4^b=36 -->

b=1. Sufficient.

Answer: C.

2. How many distinct positive factors does the positive integer x have?MUST KNOW FOR GMAT:

Finding the Number of Factors of an IntegerFirst make prime factorization of an integer

n=a^p*b^q*c^r, where

a,

b, and

c are prime factors of

n and

p,

q, and

r are their powers.

The number of factors of

n will be expressed by the formula

(p+1)(q+1)(r+1).

NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450:

450=2^1*3^2*5^2Total number of factors of 450 including 1 and 450 itself is

(1+1)*(2+1)*(2+1)=2*3*3=18 factors.

For more on number properties check:

math-number-theory-88376.html(1) x is the product of 3 distinct prime numbers -->

x=abc, where

a,

b and

c are the different prime factors, so # of positive factors of

x is

(1+1)(1+1)(1+1)=8. Sufficient.

(2) x and 3^7 have the same number of positive factors --> we can get the # of factors of 3^7 (which is simply 7+1=8) and thus we know the # of factors of

x. Sufficient.

Answer: D.

Hope it's clear.