Questions from Test magic

f2001290 wrote: 1)The subset of [x, y, z] is x, y, z, xy, xz, yz, xyz. How many subsets of [x, y, z, w] contain w?

According to the example shown we have to make all possible combination of the given elements in the set .. so accordingly tye subsets that conatin w wuld be .... then w and another number =3c1 .. then w and 2 other numbers =3c2 .. then w and 3 other numbers =3c3 … and w itself so number of sunbsets is 3c1+3c2+1+1 = 8

f2001290 wrote: 2)K=wxyz, where w, x, y, z are prime numbers. Not including 1 and K, how many factors does K have?

For any number “n” = a^x*b^y*c^z … so on ( where a,b,c are primes )… the number of factors is given by (x+1)* (y+1)*(z+1)… so applyin this formula to K we have the number of factors = (1+1)*(1+1)*(1+1)*(1+1) = 16 .. this also includes 1 and K so subtract 2 from 16 and we have our answer = 14

f2001290 wrote:3)Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

We have 10x+20y/(x+y) =18 .. solving we get x/y = ¼ .. so we have 6 , 10 pound box and 24, 20 pound box .. now suppose we remove a 20 pound boxes … so we have 10*6+20(24-a) = (30-a)*14 .. solving for a we get a = 20 …

f2001290 wrote: 5)In a class of 120 students, 80 can speak English, 70 can speak Spain, and 60 can speak French. If every student in the class can speak at least one of the languages, at least how many of students in class can speak all the three languages?

Yup this q cannot be answered with the given information .. we can tell the max number of people who can speak all 3 languages … but not the minimum number of people ..



PS the 4th question has been moved to the DS section ...