Lots to type

Let me try to handle one question at a time. Here goes the first one.

Ques 1 : Jar containing red, blue and white marbels

Solution 1 -

The ques :[highlight]Is the prob of getting red > prob of getting white OR is the no of red> no of white[/highlight]

For sufficiency : the ans should be ALWAYS YES or ALWAYS NO
For Insufficiency – SOMETIMES YES SOMETIMES NO

Lets assume 2 numbers -

Case 1:w>r (which wud mean the chances of picking white will be more)
red=5; blue=5; white=10

Case 2: r>w (which wud mean chances of picking red will be more)
red=10 ;blue =5, white =5


Statement 1: (Refer to the highlight while ans the ques)
substitute the values
from case 1 – inequality doesn't hold true => thus red has to be more than white and ans to the ques is YES
from case 2 – inequality holds true => thus red has to be more than white and ans to the ques is YES

Since ALWAYS YES → statement 1 is sufficient; choice B, C, E gone

Statement 2:(Refer to the highlight while ans the ques)
substitute the values
from case 1 – inequality doesn't hold true => thus red has to be more than white and ans to the ques is YES
from case 2 – inequality holds true => thus red has to be less than white and ans to the ques is NO

SOMETIMES YES SOMETIMES NO => Insufficient

Ans :A

Confirm : If you try to plug with equal numbers of white and red in Statement 1, it will not hold true proving that it cant be equal either and thus prob cant be same for both.
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Question 1:

The probability that red marble is chosen will be greater than the probability that white marble is chosen if there are more red marbles than white marbles.
So the question is just: Is r > w

Statement 1: r/(b + w) > w/(b + r)

Cross multiply to get r(b + r) > w(b + w) ... [(b + w) and (b + r) are definitely positive so cross multiplying is not a problem.]

Now, if r > w, (b + r) has to be greater than (b + w) and the inequality will hold.

If r were less than w, then (b + r) < (b + w) and the left side would have been smaller than the right side. Hence r cannot be less than w because it is given to us that the left side is greater than the right side.

So this implies that r must be greater than w. Sufficient.

Statement 2: b > r + w
But we cant compare r and w so not sufficient.

Answer (A).
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Question 4: Alice's take home pay.

I am putting down the Algebra solution (since you have the test tomorrow) though usually I would not do that. I would just skip to the options and plug them in to see what works.

Algebra: Say, her take home pay is $100 a month. She saves s every month and spends 100-s
At the end of the year, she saves 12s.
Given: 12s = 3(100-s)
s = 20
She saved 20/100 = 1/5 every month.

I would usually just try to plug in numbers. Say, if she saves 1/4 every month, she will have 12/4 = 3 at the end of the year. But this should be 3 times 3/4 which it isn't so 1/4 is too much. Go down a little.
Try 1/5. At the end of the year, she would have 12/5. She spends 4/5 every month. 12/5 is 3 times of 4/5 so got it!
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Karishma
Veritas Prep | GMAT Instructor
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