- 187 Solution: First reduce, then multiply:
3
714
×× 5
15
7 =21 13
18
7The correct answer is^187.- B Since this is a fraction question with no amounts given, you should plug in
values. Choose a value for the number of students that will divide evenly by
8, 4, and 5. The best number here is 8 × 4 × 5 = 160. The denominator of the
fraction will be 160, and the numerator will be the number of students who
do not take calculus. First, determine how many males do not take calculus.
The number of male students is^38 (160) = 60. If^35 of these students take calculus,
then^25 of them do not.^25 (60) = 24. 24 male students do not take calculus. Now
solve for the number of females who do not take calculus. If there are 160
students and^38 are male, then^58 are female.^58 (160) = 100.^14 of these 100 females
take calculus, so^34 do not.^34 (100) = 75. So 75 female students do not take
calculus. Add this to 24, which is the number of male students who do not
take calculus. 24 + 75 = 99. Thus 16099 of the students do not take calculus. - A Represent John’s winnings as w:
the amount spent on his home =^13 w
The amount spent on his car is^14 of what he did not spend on his home.
Since he spent (^13 )w on his home, he has (^23 )w remaining.
1
4 (
2
3 )w =1
6 w
These two amounts + $200,000 will equal the total winnings. Expressed
algebraically, the equation is^13 w +^16 w + 200,000 = w. Now solve for w:
Multiply across the entire equation by 6:
2 w + w + 1,200,000 = 6w
Combine like terms:
1,200,000 = 3w
Divide both sides by 3:
400,000 = w- B With so many relationships, this question can be confusing. Start by
identifying the whole. The capacity of Jar Y is expressed in terms of the
capacity of Jar X, so the capacity of Jar X is the whole. Next, plug in a value for
the capacity of Jar X. Remember to choose a value that will be divisible by the
denominators of the fractions in the question. In this case, 12 would be a good
value for the capacity of Jar X since 12 is divisible by 3 and by 4. If the capacity
of Jar X is 12, then the capacity of Jar Y is 24. Jar X is filled to^13 of its capacity,
so it has^13 (12) = 4 units of water. Jar Y is filled to^34 of its capacity, so it has
3
4 (24) = 18 units of water. If the water in Jar X is poured into Jar Y, then Jar Y
will have 4 + 18 = 22 units of water. So the capacity of Jar Y is 24, and it will
have 22 units of water. Thus the fraction of water in Jar Y =^2224 =^1112.
224 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 224 12/05/17 11:52 am