FCI ARITHMETIC REASONING questions for practice,FCI these questions are just for exercise,This FCI model aptitude questions will help your preparation for FCI Written test examination
1. If Jean's weekly income doubled she would be making $120 a week more than Barbara. Jean's weekly income is $80 more than half of Betty's . Betty makes $200 a week. How much does Barbara make?
The answer is C. This kind of question is difficult unless you break it down into parts, and solve it step by step. It's only in the next to last sentence that we're actually given someone's salary . We're told that Betty makes $200 a week. The question asks for Barbara's salary, but it becomes clear after careful reading
that we can't find Barbara's salary unless we find Jean's . Jean's weekly income is $80 more than half of Betty's. Jean's salary is $80 more than half of $200, so Jean's salary is $80 more than $100, or$180 . The first sentence tells us that if Jean's weekly income doubled she would bemaking $120 a week more than Barbara. Two times Jean's salary of $180 would be $120 a week more than Barbara's salary . So, two times $180, which equals $360, would be $120 a week more than arbara's salary . $360 is $120 more than what number? $360 - $120 - $240, Choice C.
2 A conference with 3600 participants gathers in Albany. One of every twelve people attending the conference who have ordered meals has special dietary needs. Half of those attending the conference signed
up for meals. How many have special dietary needs?
a.266 c .150
Choice (C) is the answer: It's important in a question like this to identify and break down the information you are given. From the question, we know: 3 . 3600 people are attending the conference 1/2 of the 3600 people have ordered meals One out of 12 (or 1112) of those who ordered meals has special dietary needs
It's important to remember that in order to solve this we must keep in mind that only half of the attendees have ordered meals. So half of the 3600 people, or 1800, ave ordered meals. Of these, one out of every twelve has special dietary needs, so 1/12 of the 1800 people who signed up for meals have special dietary needs. There are many ways to solve this problem from this point on. "One way is to simply multiply 1800 by 1/12 to find the answer. (To multiply fractions, multiplythe numerators by each other, and the denominators by each other.) 1/12x1800= 1/12x1800/1=1800/12=150 So, 150 of those who have ordered meals have special ietary needs, Choice (C). Or you could have used decimals. 1/12 is expressed in decimal form as .0833 (to find the decimal form of a fraction, divide the numerator, the top number, by the denominator, the bottom number). 1800 x 1 / 12 = 1800 x .0833 = 149.94 or 150 people . (It comes out a little unevenly because the decimal has been rounded off) You also could have set up a ratio, comparing those with special needs who ordered
meals to all who ordered meals. A Review of Ratios Ratios are intimidating for many people in an exam setting . Yet, we use ratios in "real life" - inches to miles on a map, or the ratio of ingredients in recipes in cooking. A ratio shows the relationship between two numbers. In this case, it shows the relationship between hose who have dietary restrictions and ordered meals to all those who ordered meals. One out of every twelve people who have ordered meals has special dietary needs, so we need to examine the relationship between the numbers one and twelve, and apply it to the 1800 people who have ordered meals. Special
die needs as 1 as what number All who ordered meals 12 1800 One way to do this is to cross multiply. To cross multiply, we multiply the top of one number y
the bottom of the other . 1 = ? 1 12 1800 12 1800 1- 1 2 Ix 1800 12 x ? =1800 12 x what number ? = ? = 1800 /150 = 150 (You have to divide the 1800 by he 12, because you want to "isolate" the ? on one side, since that will give you the answer. Since the 12 and the ? were being multiplied by each other, the only
way you could "free" the ? was to move the12 over to the other side of the equal sign by dividing the 1800 by the 12. If you get as far as 12 x ? = 1800 but still can't member whether ould'multiply or divide, you can still get the correct answer, because the difference between multiplying add dividing is so large that commonsense will tell you which is right . In this case, dividing gives you 150 people, and multiplying gives you 270,000 (obviously too big a number).So, in a ratio problem, as long as you set up the relationship between the numbers involved correctly (part is to whole as part is to whole),you should be able to solve it .) Another way some people do ratios is by remembering that "the product of the means equals the product of the extremes" . This means that when you multiply the Inside' numbers in a ratio problem together, and then multiply the "outside" numbers together, they will always equal each other. In this case, we would set it up his- 1 is to 12 as ? is to 1800 The "inside" numbers, 12 and ?, would be multiplied together, 12 x ?, and would equal then "outside" numbers that have been ultiplied together, 1800 and l . So 12x?=1800x1 12 x ?'=1800 -1800/ 12=150 All of this may have seemed totally unnecessary, but it's important to keep these ethods in ind for other questions, when using them may be very helpful . Again, there are many ways to solve math problems. If you use different methodsthan those in this booklet, and your results are consistently correct, there's no need to change what you're doing.
3 It costs $360 for Office X's service contract with a typewriter company to service 18 typewriters for six months. At this same rate, how much would it cost Office X to service six typewriters for three
3. The answer is D. This problem is actually easier than it may look at first, and there are a number of ways to do it. One way would be to first determine how much he office is per typewriter. We're told that it costs $360 to service 18 typewriters for six months. So, for a six month period, it would cost,per typewriter, the total ount, $360, divided by the total number of typewriters, 18. $360 _ 18 = $ 20 per typewriter. So it costs $20 to service each typewriter for a six month period. We need to find out how much it would cost to service six typewriters for a three month period. We know the service cost of each typewriter is $20 for six months. For three months, it would be half that amount, or $10 per typewriter. Since we are consideringsix typewriters, the cost I-13
4 In December, an office spent $480, or 15% of its non-personnel expenses that month, for postage. What were its total non-personnel expenses for December?
4. would be six typewriters at $10 each. for a total of 6 x $10 = $60. Or we could have said that we're being asked to find the cost of one third of the ewriters (6is
1/3 of 18),for half the time (3 months is half of six months). One third iters would cost 1/3 as much: 1/3 x $360 = $120, and since the time olved is 1/2 of the total time, 1/2 of $120 equals $60_ or we could have set it up using fractions : 360 x 1/2 x 1/3 = 360/6 = 60. The answer is A. Many people miss this question, because hey aren't quite sure what to do with the 15% figure they're given. We are told that $480 is 15% of the office's nonpersonnel expenses for December. So in order to find the answer we need to know what number 480 is 15% of . So, we are asking "480 is 15% of what number?" . To find this, we divide 480 by 15%. 480 - 15% 480 - .15 = 3200 It's always a good idea to go back to the problem and check our answer to see if it makes sense. Is 480 15% of 3200? If we divide 480 by 3200, we get .15 = 15%. So 480 is 15% of 3200, and if we multiply 3200 by .15, we get 480. Some people aren't sure whether to multiply or divide. Again, common ense should tell you which, in this case, if you had multiplied, you would have gotten $72 as an answer,which doesn't make much sense. It's important in these exams to step back and evaluate the reasonableness of your solutions , yet people often fail to do this . It was also possible in this question to work backwards rom the answers given to get the right answer. If you weren't sure how to do it, you could have multiplied each choice by 15%, to see which one was equal to $480. Choice A, 3200 x .15 = 480, would have become the obvious choice. This is a legitimate way to solve these types of problemsSome people select Choice D, because they incorrectly ultiply, and then aren't sure where to put the decimal points . If you get confused, we suggest you use the sales tax to help you remember. For example, a 7% sales tax reflects a tax of $ .07 on every dollar . in the corner of your scrap paper you could write, 7% = .07; .07 = 7%
or 8.25% = .0825 ; .0825 = 8 .25%. (If you do this, when a percent like .0035% comes along on a word problem, you'll be able to convert it to decimal from more asily, especially if you're nervous. Consulting the sales tax example, we'd notice that 7% = .07 meant the decimal was moved two places to the left when going from percents to decimals, so .0035% would equal .000035 . Or, if we had to convert a decimal like .00046 to a percent, onsulting the sale tax, we'd see that in the ase of .07 = 7%, the decimal was moved two places to the right, so we'd do the same here. .00046 would then equal .046%. Sorry if this was unnecessary, but many people get confused when dealing with decimals and percents on an exam). I- 1 4
5 Catherine bought an equal number of $11 .00, $9.00, and $8.00 tickets for a concert . She spent $196 for all of the tickets . How many of each did she buy?
b. 7 d. Cannot be determined from information given
6. Agency Y employs 13,800 people . Of these, 42% are male, and 50% of the males are age 30 or younger. How many males are there in Agency Y who are older than 30?
7. A machine can collate 126 books, each with 400 page, in 14 days. If it continues to collate at this same rate, how many 400 page books could it collate in 30 days?
8. A typewriter and a dictation machine cost a total of $840. If the typewriter cost $360 more than the dictation machine, how much did the dictation machine cost?
9.A cabinet maker has a round piece of wood 1/2" in diameter and 3/4 yards long. She needs half the length for the back of a chair and the remaining piece for 3/4" pegs. How many pegs will she have?
10 Robin can wallpaper a room in four hours. Susan can wallpaper the same room in seven hours. How long will it take them to wallpaper the room if they work together?
c. 5.5 hours
b. 3.5 hours
a. 4.5 hours
d. 2.5 hours
11 Mary and Alice jog 3 miles each evening . If they run at a constant rate and it takes Mary 40 minutes while Alice finishes in half an hour, how much distance does Mary have left when Alice finishes?
c . 2/3 mile
b. 3/4 mile
a. 1 mile
d.1 .33 miles
12 As a fund raiser , a community organization buys tickets to the theater to resell 25% above cost. They buy 50 eight dollar tickets, 25 tendollar tickets and 25 fifteen dollar tickets . If they sell all but three of the ten dollar tickets, how much money have they made?
c . $248 .75
13 If a couch cost $640 after a 20% discount, what was its original price? a.$769 c,$800 b.$512 d.$780
14 A salesperson traveled 145 miles Monday, 72 miles Tuesday, and 98 miles Wednesday for $2300 worth of sales . If the business pays 210 a mile for gas and vehicle maintenance, approximately what percent of sales for the three days went to gas and vehicle maintenance?
15 If one of every eight junior year students at a high school takes Latin, approximately what percent of a junior year class of 650 took Latin?
c . 81
16 The proposed budget for a new social service program is $102,000. The budget states that the project has secured $14,500 worth of transportation services and $1,200 worth of office equipment as in kind contributions . What percent of the budget has been secured in kind?
a. 21 .4
c . 20.9
b. 15 .4
d. 13 .1
17 The purpose of the program in Question 16 is to distribute 250,000 pounds of food to disadvantaged persons . Approximately how many pounds of food will be distributed for each dollar budgeted for the program?
d. 2 .95
18 A community cannery charges 15¢ per quart and 25¢ for 2 pints for processing. People using the cannery can purchase jars there at 15% discount off the regular price of $4 .25 per case of a dozen quart or pint jars. How much will it cost to can 76 quarts of tomatoes and 20 pints of jelly if the jars are bought at the cannery? (Jars are not sold individually) .
19 A pharmacist combines ingredients x, y and z in a ratio of 1 :2 :7 to produce cough medicine. How many ounces of the second ingredient, ingredient y, is needed to make a 12 ounce bottle of the medicine?
c . 1 .2
d. 3 .6
20 Agency Y served 187,565 people in 1981 . If the agency served 210,515 people in 1982, this reflected an increase of
c. 12.2% b. 15 .6%
a. 19 .10% d. 10
21 The number of people attending a weekly training program in the month of January averaged 116 people . If there were 105 people attending the first week, 106 the second, and 125 the third, how many people attended the fourth week?
22 It takes 16 typists 11 days to complete a project . How long would it take 10 typists, if they worked at the same rate to complete the same project?
a.17 6 days
c . 6.9 days
23 If the sum of two numbers is 280, and their ratio is 7:3 . then the smaller number is
24 The population of Metropolis county in 1982 is 130% of its population in 1972- The population in 1972 was 145,000. What was the population in 1982?
25 A car travels 50 miles an hour, and a plane travels 10 miles a minute. How far will the car travel when the plane travels 500 miles?
c. 41 .6 miles
b. 37.5 miles
d. 39.7 miles
26 In a university with 2000 students the student-faculty ratio is 16 :1 . If 18% of the faculty have completed some of their own study at the university, approximately how many have not?
c . 23
27 A discount house advertises that they sell all merchandise at cost plus 10%. If Jane buys a TV set for $300, approximately what is the stores profit?
28 From 6 p.m. until midnight, the temperature dropped at a constant rate . From midnight until 1 a.m., it dropped 8° . If at 6 p.m., the temperature was 54° and by 1 a.m., it was37°, what was the temperature at 10 p.m.?
29 One eighth of a half gallon carton of ice cream has been eaten. The remainder is divided among three people . Approximately what percentage of a gallon does each person get?
b. 11 .3% d. 18.1%
30 On a promotional exam a woman scored 143 on a scale of 0-160. Her score converted to a scale of 0-100 is approximately :
31A woman paid a tax of $88.00 on property assessed at $28,000. Her neighbor, assessed at the same rate . paid a tax of $110 . What was the assessed value of the neighbor's house?
32 If Janet can build 22 tables in 14 days, and Anne can build 22 tables in 16 days, approximately how long will it take them to build 22 tables together?
a.9.5days c. 15 days
b. 7 .5 days d. 8 days
33 Cynthia loaned $35 to Mary. But Cynthia borrowed $14 from Jean, and $16 from Emily Emily owes $17 to Jean and $9 to Mary. One day they got together to settle their accounts. Who left with $10 less than she came with?
34 How many square tiles, each 12 inches on a side, will Ozzie need to cover a floor that is I1 feet wide and 18 feet long?
c . 163
35 A car has depreciated to 72% of its original cost. If the car is presently valued at $3245, approximately what was its original cost?
36 The sales tax on a typewriter is $13.41 and the sales tax rate is 4%. The purchase price, before the tax was added, was:
37 The sales tax on a typewriter is $13.41 and the sales tax rate is 4%. The purchase price, before the tax was added, was:
38 What is the interest on $600 at 8% for 30 days?
b. $11 .52
d . $4 80
39 A tax analyst eams four times as much in April as in each of the other months. What part of her entire year's earnings does she earn in April?
a.4/11 c .4/15
40 A train travels 70 miles when a bus travels 50 miles. How many miles will the train travel when the bus travels 60 miles?
c . 90
Answers will update later