GMAT prep Algebra problem

sachinkr wrote:GMAT prep Algebra problem on multiple of number.

I got C as answer., but the answer is B? I did not get why B is sufficient.

We know that 1*2*3*4*5*6*7*8 is a multiple of a^n. We also know that both a and n are greater than 1.

(2) n=6

So, a^6 is a factor of 1*2*3*4*5*6*7*8. In other words:

1*2*3*4*5*6*7*8/a*a*a*a*a*a is an integer.

Well, 8! has 7 2s as factors (2, 4=2*2, 6=2*3, 8=2*2*2), so a could be 2.
8! has only 2 3s as factors (3, 6=2*3), so a can't be 3.
Any other number is just too big.

So, if n=6, a must be 2.

here's how I see it:
Start by considering 1*2*3*4*5*6*7*8 = (2^7)*(3^2)*5*7. It always helps when you see all the numbers lined up in an orderly fashion! :D
Then you take (1). Says here that a^n = 64. Well, you have more than just one option: 2^6 = 4^3 = 8^2. So (1) by itself is not sufficient.
Now you look at (2): n = 6 and it's kind of obvious that you don't have anything other than 2 in (2^7)*(3^2)*5*7 that would meet that criterion. Just trying 3 (which is the smallest integer greater than 2) to the 6th power is waaay too much...
So B is the corrrect answer.

Could you help me about, how do you take the screen shot of GMAT prep.

japan1453 wrote:Could you help me about, how do you take the screen shot of GMAT prep.

On your keyboard you can press PRT SCR ( print screen ) and copy paste it with CTRL+V in paint program.

ere's How:

1. Press the Print Screen key on your keyboard. It may be labeled [PrtScn].

2. Open an image editing program, such as Microsoft Paint.

3. Go to the Edit menu and choose Paste.

4. If prompted to enlarge the image, choose Yes.

5. Optional: Use your image editor's crop tool to crop out unnecessary portions of the screen shot.

6. Go to the File Menu and choose Save As.

7. Navigate to the folder where you want to save the image.

8. Type a file name for the image.

9. Select a file type.

Thanks logitech. You are a real charitable.