First off, you should post your questions in the quant section of the forum.
Q1. You can clearly see that the angle over there is 90 degrees in measurement. A circle has 360 degrees in measurement, so that white portion is 90/360 = 1/4 or a quarter of the whole circle. This makes the shaded region 3/4 of the whole area of the circle. The formula for the area of a circle is Pi*(radius)^2 = Pi*16. 3/4 of Pi*16 will be indeed 12Pi.
Q2. With remainder questions it's always safe to pick numbers to eliminate choices quickly.
1. tells you that n is a multiple of 5. Pick two multiples of 5 and then check their remainders when divided by 6.
15 = 12 + 3 = 2*6 + 3 - in this case, remainder = 3
20 = 18 + 2 = 3*6 + 2 - in this case, remainder = 2
Since you got two possible values, then 1 is insufficient.
2. n is multiple of 12 means that n = 12k, with k an integer. But n = 12k = 2*6*k = (2k)*6. This means that n will be divisible by 6, so the remainder when dividing n by 6 will be zero. 2 is sufficient, so pick B.
Q3. Notice that the newer machine works 1.5 times faster (since it makes 150 bolts while the other makes only 100 bolts). In one hour, the two machines will produce 100 + 150 = 250 bolts. The question is how much does it take the two working together to make the remaining 50 bolts.
60 minutes......................250 bolts
x minutes........................50 bolts.
x will be 50*60/250 = 12 minutes.
Total time: 1 hour and 12 minutes, or 72 minutes.
