Flasks M and N contain m and n liters of water respectively. Half of t

Question

Flasks M and N contain m and n liters of water respectively. Half of the water in flask M is poured into flask N (without spillage). Then half of the water in flask N is poured into flask M (without spillage). If flask M now contains 2 liters of water, what is the value of m?

(1) m and n are integers

(2) \(n = 4 - \frac{3m}{2}\)

(1) m and n are integers

(2)  n = 4 - \frac{3m}{2}

nick1816 · Answer

After the both transfers, volume of water in A= 3m/4+n/2 and volume of water in B= m/4+n/2
3m/4+n/2=2
3m+2n=8

1. m and n are both integers
3m+2n=8
3m=8-2n
There are 2 solutions possible
(m,n)= (0,4) or (2,1)
insufficient!!

2.  n = 4 - \frac{3m}{2} 
3m+2n=8
Statement adds nothing other then which is already given.
Insufficient

Combining both statements is also insufficient !!!
 IMO E

If we have to consider m and n as positive integers, then answer is A

prabsahi · Answer

After adding half of the water in flask M is poured into flask N

Flask M has m/2 lts
Flask N has n+ m/2

After adding half of the water in flask N is poured into flask M

Flask M has m/2 + (n +m/2)/2 =m/2 + n/2+m/4 = 3m/4 + n/2

flask M now contains 2 liters of water

Therefore

3m/4 + n/2= 2

Multiple by 4 both sides

3m + 2n =8

STATEMENT 1:

m and n are integers

m=2,n=1 
m=0,n=4

So STAT1 is insufficient.

STATEMENT 2:

Replacing in 3m + 2n=8

3m +2*(4-3m/2) = 3m +8 -3m =8

This gives nothing .You can try rearranging stat2 and its same as main equation.

So clearly both statements are insufficient.

option E looks like a possible choice .

Press Kudos if it helps!!

BrentGMATPrepNow · Answer

Hmm, I debated whether I needed to state that m and n are POSITIVE

This has raised some interesting questions. 
1) If I have a flask with zero liters of water, and then take that flask and pour zero liters into another flask, can we say that I poured HALF of the water out of the flask?
2) Alternatively, can one actually POUR zero liters of water? Doesn't POUR imply that there is  some  water? 
 
Anyone want to weigh in?

Cheers,
Brent

prabsahi · Answer

I guess point one was skeptical at first .And ideally emptiness cannot be poured from one vessel to another .(that's the minimum assumption we need to make from real life I guess,which is absolutely genuine)

In that case we will have option A as the preferred choice.

Archit3110 · Answer

given
 
M has m ltrs and N has n ltrs
so first case half of water poured from M to N 
so M now has m/2 and N now has ; m/2+n = m+2n/2
later half of N is poured to M ; now N has m+2n/4 and M has ; m/2 + m+2n/4 
total M vol = 3m+2n/4
given M=2 so we have eqn ;  3m+2n=8 
#1
m & n are integers ; 3m+2n=8
m=2 and n =1 sufficient

#2
 n = 4 - \frac{3m}{2}

substitute in eqn we get = 0 ; and different values of m =0,1,2 since we get 3m-3m=0 not sufficient
IMO A

nick1816 · Answer

If i go logically, then you don't have to mention. But Mathematically, there is need to mention that m and n are positive integers.

KanikaJain · Answer

I would actually differ at this point. It is true - that you cannot pour half of 0. I however feel that this point can be taken as a point of trick - check that i have written that x and y are integers. Why can I not have my flask empty?

As in GMAT everything is clearly mentioned, it is also mentioned m and n are integers - I feel that 'positive integers' should be mentioned. Negative cannot be taken into account as quantity cannot be negative, but it can be 0.

Flasks M and N contain m and n liters of water respectively. Half of t

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GMAT Data Sufficiency (DS) Questions

Flasks M and N contain m and n liters of water respectively. Half of t

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