DS from prepGmAT

Question 1

Lets assume the six countries are A,B,C,D,E and F

According to the question, the total representative sent is A+B+C+D+E+F=75 and also A has sent the second greatest number of reps.


Stat 1 - One country say B, has sent 41 reps which means B+C+D+E+F=75-41=23. This is INSUFFICIENT as A can be more than 10 or evn less than 10.


Stat 2- A has sent fewer than 12 reps.Here A can either be 9 or 11.So INSUFFICIENT.

Combining the two statements will still be insufficient because,

if B is 41 and A has sent the second greatest and A is 11 then C+D+E+F=23 can be obtained with different values for C,D,E and F all less than A.

However if B is 41 and if A is 9 then C+D+E+F=25 . C,D,E and F can have different values less than A and satisfy the question.

Therefore the answer is E

Hey Jimat! Initially I thought the answer would be C. But then did some manual manipulation and found that we can achieve the answer with B only! Because, in B it is saying that n = 6.
Again a should be < 6 at least as 8! is a factor of a^6. [Found out by manual calculation - but would like to get some mathematical explanation]. And with a = 2,3,4,5 and 6, I have found out that 8! is only divisible by 2^6. So IMO B.
Though found out an explanation but it required a lot of manual intervention and it is something like back-tracking. Can anyone pls give some concrete mathematical explanation of this Qs?

Wohhhh! Really a good explanation to go with.

Hi Guest,

Can you explain this part pls (so becomes 3x5x7 x 2x2^2x2^3x6 = a^n.p where p= 3.5.7.6 )

Thanks

Hey Moneyman,

Hi Guest,

Can you explain this part pls (so becomes 3x5x7 x 2x2^2x2^3x6 = a^n.p where p= 3.5.7.6 )

refer the below explanation -
In the Qs, it is saying 8! wll be multiple of a^n! Right? Now
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= (2^3) * 7 * (2 * 3) * 5 * (2 ^2) * 3 * 2
= 2^6 * (3 * 5 * 7)
= a^n * p ---------- Say as 8! is multiple of a^n so p is that multiple.
According to B, if n = 6, then we can easily find out that a = 2.

Hope this can resolve ur query!

Fantastic explanation Amitava!! Thank you

camitava wrote:Hey Moneyman,

Hi Guest,

Can you explain this part pls (so becomes 3x5x7 x 2x2^2x2^3x6 = a^n.p where p= 3.5.7.6 )

refer the below explanation -
In the Qs, it is saying 8! wll be multiple of a^n! Right? Now
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= (2^3) * 7 * (2 * 3) * 5 * (2 ^2) * 3 * 2
= 2^6 * (3 * 5 * 7)
= a^n * p ---------- Say as 8! is multiple of a^n so p is that multiple.
According to B, if n = 6, then we can easily find out that a = 2.

Hope this can resolve ur query!

I bold (2*3) because I don't know where it disappeared. could you explain more.
and can you explain why the first statement wrong?

A)a^n=64

so here 4^3=64 and also can be multpile of 8!

and also 8^2 =64 so different values of a Insuff

B)

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= (2^3) * 7 * (2 * 3) * 5 * (2 ^2) * 3 * 2
= 2^6 * (3 * 5 * 7)
= a^n * p ---------- Say as 8! is multiple of a^n so p is that multiple.
According to B, if n = 6, then we can easily find out that a = 2.

here wats happening .. seperation of alll the two's.....
so
2^3*[2*(2^2)*2]*3*5*7
2^3[2^3]*3*5*7
2^6*3*5*7

so hope this clears

Vishu

Stmt I)

can be 2^6 or 4^3 (CANT BE 64^1 SINCE N>1)

INSUFF

Stmt II

The only number for which n=6 can be a multiple of 64 is 2 (similar to Vishu's explanation above)

B)

refer the below explanation -
In the Qs, it is saying 8! wll be multiple of a^n! Right? Now
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= (2^3) * 7 * (2 * 3) * 5 * (2 ^2) * 3 * 2
= 2^6 * (3 * 5 * 7)
= a^n * p ---------- Say as 8! is multiple of a^n so p is that multiple.
According to B, if n = 6, then we can easily find out that a = 2.

Hope this can resolve ur query!

Actaully this must be

8! = a^n * k (by definition of mutiple where k is any integer)

= 2^7 * (3 * 5 * 7)
or 2^ 6 * (2 * 3* 5 *7) where k = 2 3 5 7 (can be any integer k)

But since n=6 per stmt II the only number that fits the bill is 2

Actaully this must be

= 2^7 * (3 * 5 * 7)

true !! i overlooked

thanks ramya

vishu

Thanks guys

Cramya,

shouldn't it be 2 ^7 * 9 * 5 * 7 ?

You r correct AJ.