Word problem-IV

[\'manpreet singh]

I am solving lot of word problems, so in continuation to the series on word problems(hell i hate them!!!!), here are some more problems which got me stuck.i find i am consuming around 2mins and 20 sec on average if I solve 20 questions in a row. I want to know is it ok ...as I am doing only word problems or do I need to be more fast.


Q.1) In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are
expected to vote for Candidate A ?
(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

Q.2) Of the 200 students at College T majoring in one ormore of the sciences, 130 are majoring in chemistryand 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from
(A) 20 to 50
(B) 40 to 70
(C) 50 to 130
(D) 110 to 130
(E) 110 to 150

[niketdoshi123]

Q.1) In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are
expected to vote for Candidate A ?
(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

Let us assume that there are total of 100 registered voters in that city. (Always assume a smart number , so that you don't waste time in multiplying and dividing.)
So,
Democrats = 60 (60% of registered voters)
Republicans = 40 (remaining registered voters)
Votes for candidate A = 75% of Democrats + 20% of Republicans
= (.75)*60 + (.20)*40
= 45 + 8 = 53
(Votes for candidate A/Total number of registered voters)*100 = 53*100/100 = 53%
Hence correct answer is B

[Anurag@Gurome]

Q.1) In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

Democrats = 60%
Republicans = 40%

Voters for A = (75% of 60% + 20% of 40%) = (3/4 of 60% + 1/5 of 40%) = (45% + 8%) = 53%

The correct answer is B.

[Anurag@Gurome]

Q.2) Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

As total number of students is 200 and 150 are majoring in Biology, the maximum number of students who are not majoring in either chemistry or biology is (200 - 150) = 50

Total = Biology + Chemistry - Both + None
Hence, None = (Total - Biology - Chemistry + Both) = (200 - 130 - 150 + Both) = (Both - 80)

Now, 30 ≤ None ≤ 50
---> 30 ≤ (Both - 80) ≤ 50
---> (30 + 80) ≤ Both ≤ (50 + 80)
---> 110 ≤ Both ≤ 130

The correct answer is D.

[niketdoshi123]

Q.2) Of the 200 students at College T majoring in one ormore of the sciences, 130 are majoring in chemistryand 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from
(A) 20 to 50
(B) 40 to 70
(C) 50 to 130
(D) 110 to 130
(E) 110 to 150

Total students = 200
Neither = 30 (at least)
Total Students who are majoring in either one or both the sciences = 170
Chemistry majors + Biology majors = 280

So students majoring both the sciences = 110 (at least). By this we can eliminate options a), b) & c).

Now , at most the number of students not majoring in either chemistry or biology can be
200-150(students majoring biology) =50

Range = 50-30 = 20
Hence this range satisfies option D

[\'manpreet singh]

Thanks Anurag and Niket, i found Anurag's method more simple and fast for second question in particular


I guess i need to work more on such problems as i take time before starting with these word problems.

[Jeff@TargetTestPrep]

I am solving lot of word problems, so in continuation to the series on word problems(hell i hate them!!!!), here are some more problems which got me stuck.i find i am consuming around 2mins and 20 sec on average if I solve 20 questions in a row. I want to know is it ok ...as I am doing only word problems or do I need to be more fast.


Q.1) In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are
expected to vote for Candidate A ?
(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

Solution:

We are given that 60 percent of the voters are Democrats and the rest are Republicans. Thus, 40 percent are Republicans. We also know that 75% of the voters who are Democrats and 20% of the voters who are Republicans are expected to vote for candidate A.

The easiest way to solve this problem is to assume that the total number of registered voters is 100 (We could use other numbers, but 100 is an easy number to work with in percentage problems).

We know that 60% of the registered voters are Democrat and 40% are Republicans, so there are 60 Democrat registered voters and 40 Republican registered voters.

Now, since 75% of the 60 Democrat registered voters are expected to vote for Candidate A, we know that 0.75 x 60 = 45 Democrats are expected to vote for Candidate A. Similarly, because 20% of the 40 Republican registered voters are expected to vote for Candidate A, we know that 0.2 x 40 = 8 Republicans are expected to vote for Candidate A.

Thus, there are 45 + 8 = 53 voters expected to vote for Candidate A. Because we initially used 100 as the total number of voters, it follows that 53 out of 100, or 53% of the voters, are expected to vote for Candidate A.

Answer:B