To solve for the greatest common factor, it is necessary to get your numbers into prime factor form. For each of your numbers, this is:

Next, for each of your sets of prime factors, you need to choose the exponent for which you have the smallest value; therefore, for your values, you choose:

: 

: 

: 

Taking these together, you get:

Solving for the overlap of two sets is easy when you have all of your data. You know that the two circles added up will have to equal   or . This is the total amount in the "universe" () minus the amount that is found outside of the two circles ().

Because the overlap happens once in each circle, you know that:

Given your data, you know:

Solving, this means:

Solving for the overlap of two sets is easy when you have all of your data. You know that the two circles added up will have to equal  or . This is the total amount in the "universe" () minus the amount that is found outside of the two circles ().

Because the overlap happens once in each circle, you know that:

Given your data, you know:

Solving, this means: . The overlap is the whole of circle !

Solving for the overlap of two sets is easy when you have all of your data. You know that the two circles added up will have to equal   or .  This is the total amount in the "universe" () minus the amount that is found outside of the two circles ().

Because the overlap happens once in each circle, you know that:

Given your data, you know:

Solving, this means:

Do not be tricked by this question! In order to solve for the overlap, you need to know the amount that is in the area outside of the circles but still inside the universal box area! You cannot figure out the answer without knowing this fact; therefore, you must select "No answer is possible."  We know that the two circles do not exhaust the universe because . This is not large enough to fill the complete . If it were, you would know that the overlap is .

The costs of the beverages will be as follows:

Add these amounts:

20% of this is 

, which rounds to $5.30.

The gray portion of the circle graph represents Wells; the yellow portion represents Hawley. The gray portion is larger, so Wells won more votes, making (b) greater.

The size of the orange portion of the circle, which represents Creighton, is larger than the combined sizes of the dark blue and green portions, which represent Barnes and Yale, respectively. This makes (a) the greater quantity.

(a) The four Turkish coffees cost  before the discount. The discount is , so the price after discount is .

(b) The two Cafe Americanos cost ; the two lattes cost . The total cost is .

This makes (b) the greater quantity.

The above graph only reflects the relative numbers of students who voted for each of the six candidates; it does not give any information about the numbers of students who voted for each candidate, or the number of students who did not vote.