GMATPrep - Practice Test #1 - Problem Solving - Need Help

[dominate11]

Can someone please help explain these questions.

1. 2^(4-1)^2 / 2^(3-2) = ?

3. For all positive integers m, <m> = 3m when m is odd and <m> = .5m when m is even. Which of the following is equivalent to <9> X <6> ?

11. In n is a postive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n? 1) 10 2) 11 3) 12 4) 13 5) 14

I appreciate any guidance...

[Neo2000]

For 1
2 ^(3)^2 = 2^9/2 = 2^8 = 256

3. For all positive integers m, <m> = 3m when m is odd and <m> = .5m when m is even. Which of the following is equivalent to <9> X <6> ?

<9> implies that m is odd => <9> = 3(9) = 27
Similarly for <6> = (.5)6 = 3

So finally you get 27 X 3 = 81

[gabriel]

Can someone please help explain these questions.

1. 2^(4-1)^2 / 2^(3-2) = ?

3. For all positive integers m, <m> = 3m when m is odd and <m> = .5m when m is even. Which of the following is equivalent to <9> X <6> ?

11. In n is a postive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n? 1) 10 2) 11 3) 12 4) 13 5) 14

I appreciate any guidance...

ok so the first has been answered by neo.. so let me get to the other two

3.) since <m>= 3m when m is odd ... therefore < 9> = 3*9 since 9 is odd... also <m> = 0.5*m when m is even ... therefore <6>=.5*6 since 6 is even... therefore the answer to <9> X <6> = 27*3=81.... btw i am assuming that X means the multiplication..

11.) okay 990= 9*11*10... therefore from 1 to n we need to have 9,10 and 11 and the least value for such a n is 11.... because the sequence of numbers from 1 to 11 includes all the three no ...

2 more questions in the same league that should help u understand the concept better... find the least n such that the product of numbers from 1 to n is a multiple of 350..... also find the least n such that the product from 1 to n is a multiple of 455... try solving them and let me know if u dont get it ...

[anuroopa]

Hi
I am not sure if Neo's answer is right - according to the exponent rule- (x^y)^z = x^zy

So,
so it should be 2^6 - 2^1= 2^5

Neo, could you elaborate on ho u got ur answer

[Neo2000]

Hi
I am not sure if Neo's answer is right - according to the exponent rule- (x^y)^z = x^zy

While this is correct, what the question is asking for is x^(y)^z which is how i got the answer.

Hope this helps. If not, do let me know

[gabriel]

Hi
I am not sure if Neo's answer is right - according to the exponent rule- (x^y)^z = x^zy

So,
so it should be 2^6 - 2^1= 2^5

Neo, could you elaborate on ho u got ur answer

Nope..... neo has got it right... the only thing wrong with his answer is that 2^8 = 256... not 64

[Neo2000]

[
Nope..... neo has got it right... the only thing wrong with his answer is that 2^8 = 256... not 64

whatcha talking about?? i did write 2^8 = 256



<wicked grin>

[anuroopa]

thnks neo - I understood the q wrong