Problem Solving

How do we solve the attached Q?
thanks
M

smehmood wrote:How do we solve the attached Q?
thanks
M

Sum of four numbers is: 30 * 4 = 120

Start from (II): 120 - (9+10) = 101 { You cant get anything more out of this statement, so itself it is INSUF }

(I): the max number is 60 (INSUFF)

Combine two: 101 - 60 = 41, therefore 2 numbers are more than 30.

C is the answer

But I doesn't say that max number is 60?

Yes it does.

Look at it this way. After statement 2, you have 101 remaining. using the two remaining number combinations, how can you get 101:

100 + 1
60 + 41
30 + 71

But.. Statement 1 states the max number is 60, we use 60 as the max number to see how small the fouth number could possibly be. Since the fourth number is 101-60=41, we know that the 3rd and 4th number must be above 30.

yes C is the answer

using A there can be two options 0,1,59,60 so 2 numbers are more than 30
or 0,31,44,45 now 3 are more than 30... So A is insufficient

Using B 9,10, 1, 100 - 1 is more than 30
or 9,10,31,70 - 2 are more than 30 -- Insufficient

Now using both together...

9,10,41,60 -- 2 more than 30


So keeping 9 and 10 as fixed and no number greater than 60 .. there will be always
2 numbers greater than 30.... C is sufficient

Answer is C.

Statement 1 is insufficient to answer

statement 2 shows two numbers whose sum is 19. It is also insuff.

Combining 1 & 2 : One can answer .

The sum of other two numbers is 111. One number is varies from 60, 59,58....to 55. Other number is varies from 55 to 60.