If there are 6 Qs in a Gmat question paper

[hassan]

Hi Everybody ,

Setting the stage with a special thanks to the ManhattanModerators (Stacey ,Patrick & all ) who are striving an extra mile in ordert to help the Gmat test takers . Well as this would be my first post therefore just to state my aptitiude ability (which might help the moderator in guesing my mental ability ) ,i wrote my first Gmat in July 2008 and scored 500.All set to give it a next shot .
Previuosly i used the to follow the Permutation and combinations Formulae application to solve Counting and combinatorics Qs but right now i am following the Line method. Quite easy ,it Sounds . But I wonder if the Line method Sits well with the under mentioned problem , If yes i would like you to intute me on this and give me a solution otherwise tell me any alternate method .

Q :If there are 6 Qs in a Gmat question paper ,In how many wasys a student can solve one or more Questions ?

Ans : 63

Source (Winmax practise problem

[milqman]

I didn't get 63, I got 53

I counted up the ways that you could answer 1 question, then 2 questions, then 3 questions . . . until I got to all 6

1Q 2Q's 3Q's 4Q's 5Q's 6Q's
6!/(5!*1!)+6!/(4!*2!)+6!/(3!*3!)+6!/(2!*4!)+6!/(5!*1!)+1

Reducing:
6+15+10+15+6+1 = 53

Is there a case I am missing?

[hssan]

Well Milqman,

Quite close , but i think still we are missing something here .
Still the coirrect answer is 63.
I would request the moderators to share their intellect on this with us .

Regards

[RonPurewal]

6+15+10+15+6+1 = 53

Is there a case I am missing?

the middle term, 6!/(3!3!), is 20, not 10. that means that you're short by 10, and your total should be 63, not 53.

i'm surprised you even knew what this question meant.

[RonPurewal]

i hope that all the problems in this "winmax" thing aren't as poorly written as this one, because you are in for one heck of a wild ride if they are.

if this question means "in how many different combinations can the student get the questions right or wrong provided s/he gets at least one question right", then the answer is 63, as mentioned.

however, there are other interpretations. for instance, "in how many ways can the student solve..." could just as easily refer to different numbers of ways of selecting answer choices, in which case the numbers will be much, much higher, because there will then be 5 ways of answering each problem instead of just "right"/"wrong".

are these questions from this place?