RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Pipe A can fill a tank in 30 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?
A.4 minutes
B.15/4 minutes
C.192/7 minutes
D.224/7 minutes
Answer: B.15/4 minutes
Explanation: Pipe A can fill a tank in 30 minutes --> the rate of A = 1/30tank/minute;
Pipe B can fill the same tank6 times fasterthan pipe A --> the rate of B = 1/30 + 6/30 = 7/30 tank/minute.
Their combined rate = 1/30 + 7/30 = 4/15 tank/minute;
Therefore, A and B can fill the tank in 15/4 minutes.
Answer: B
Question: What is the area inscribed by the lines y =3, x = 2, y = x+3 on an xy-coordinate plane?
A.a) 1
B.b) 2
C.c) 4
D.d) 6
Answer: B.b) 2
Explanation: First, let's graph the lines y = 3 and x = 2
At this point, we need to find the points where the line y = x+3 INTERSECTS the other two lines.
For the vertical line, we know that x = 2, so we'll PLUG x = 2 into the equation y = x+3 to get y = 2+3 = 5
Perfect, when x = 2, y = 5, so one point of intersection is (2,5)
For the horizontal line, we know that y = 3, so we'll PLUG y = 3 into the equation y = x+3 to get 3 = x+3. Solve to get: x = 0
So, when y = 3, x = 0, so one point of intersection is (0,3)
Now add these points to our graph and sketch the line y = x+3
At this point, we can see that we have the following triangle.
The base has length 2 and the height is 2
Area = (1/2)(base)(height)
= (1/2)(2)(2)
= 2
Answer:
B
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
A.16%
B.16.66%
C.18%
D.21%
Answer: B.16.66%
Explanation: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
A.65 days
B.85 days
C.15 days
D.45 days
Answer: C.15 days
Explanation: B's 1 day work = (1/12 - 1/20) = 1/30
Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15
So, A and B together will complete the work in 15 days.
Answer:C
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 5 years the amount to be paid is?
A.3377
B.2688
C.2688
D.9125
Answer: D.9125
Explanation: A = 7500(26/25)^5 = 9125
Answer: D
Question: Paulson spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%.Find the percentage increase in his savings .
A.25
B.35
C.50
D.20
Answer: C.50
Explanation: Let the original income=$100. Then, expenditure=$75 and
savings =$25
New income =$120, New expenditure =
$((110/100)*75)=Rs.165/2
New savings = $(120-(165/2)) = $75/2
Increase in savings = $((75/2)-25)=$25/2
Increase %= ((25/2)*(1/25)*100)% = 50%.
Answer C) 50.
Question: A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?
A.1/5
B.2/3
C.3/7
D.4/7
Answer: C.3/7
Explanation: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
C
Question: In an election, candidate A got 65% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.
A.330000
B.309400
C.347000
D.356000
Answer: B.309400
Explanation: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 65 %
Therefore, the number of valid votes polled in favour of candidate A = 65 % of 476000
= 65/100 × 476000
= 30940000/100
= 309400
B)
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
A.11
B.12
C.77
D.17
Answer: B.12
Explanation: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer:B
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
A.5/6
B.5/1
C.5/8
D.5/6
Answer: D.5/6
Explanation: P(at least one graduate) = 1 - P(no graduates)
= 1 - 6C3/10C3
= 1 - (6 * 5 * 4)/(10 * 9 * 8)
5/6
Answer:D
Question: log3 N+log7 N what is 3 digit number N that will be whole number
A.343
B.729
C.829
D.929
Answer: A.343
Explanation: No of values N can take is 1
7^3=343
ANSWER:A
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
A.7 PM
B.9 PM
C.4 PM
D.5 PM
Answer: D.5 PM
Explanation: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer:D
Question: If a coin is tossed twice, what is the probability that on the first toss the coin lands heads and on the second toss the coin lands tails?
A.1/6
B.1/3
C.1/4
D.1/2
Answer: C.1/4
Explanation: first toss the coin lands heads = 1/2
the second toss the coin lands tails = 1/2
For independent even A and B, (A∩B) = A*B
probability that on the first toss the coin lands heads and on the second toss the coin lands tails = 1/2*1/2 = 1/4
Hence, answer will be C.
Question: Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
A.17.5%
B.62.5%
C.87.5%
D.140%
Answer: D.140%
Explanation: You are mixing a collection consisting of 20% biographies with a collection consisting of 100% biographies to give a collection consisting of 37.5% biographies. The weights of the two collections will be:
w1/w2 = (A2 - Avg)/(Avg - A1) = (1 - 3/8)/(3/8 - 1/5) = (5/8)/(7/40) = 25/7
So if initial collection had a total of 25 books (including 1/5th biographies i.e. 5 biographies), 7 new biographies were added.
Biographies have increased by (7/5)*100 = 140%
Answer (D)
Question: If 6x^2 + x - 12 = (hx + b)(cx + d), then |h| + |b| + |c| + |d| =
For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/
A. 10
B. 12
C. 15
D. 18
Answer: B. 12
Explanation: 6x^2+x-12 = 6x^2 + 9x -8x -12
=> 3x(2x+3) -4(2x+3)
=> (2x+3)(3x-4) = (hx+b)(cx+d)
Hence h=2, b=c=3, d=-4
So, 2+3+3+ |-4| = 2+3+3+4 = 12
Answer B.
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 4 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
A.30
B.45
C.60
D.90
Answer: A.30
Explanation: Whole trip = distance by foot + distance by bus + distance by car
x = 1/5x + 2/3x + 4
x - 13/15x = 4
2/15x = 4 => so x = (15/2)*4 = 30Km
Answer A
Question: Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed?
A.10 pm
B.1 pm
C.2 pm
D.3 pm
Answer: B.1 pm
Explanation: Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the Printer were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm
B
Question: Each shelf of a bookcase contains 20 books. If the librarian took out 38 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?
A.A)11
B.B)15
C.C)16
D.D)12
Answer: A.A)11
Explanation: Denoting x the number of the shelves,
we can build an equation: 20x=16(x−1)+22+38
Solving the equation, we get x=11
Answer: A
Question: The average (arithmetic mean) of the even integers from 16 to 44 inclusive is how much greater than the average (arithmetic mean) of the even integers from 14 to 56 inclusive?
A.10
B.5
C.15
D.20
Answer: B.5
Explanation: So, according to A mean of a set of even numbers from 16 to 44 =(16+44)/2=30 and mean of a set of even numbers from 14 to 56 =(14+56)/2=35
Difference=35-30=5
Answer: B.
Question: I sold two watches for Rs. 300 each, one at loss of 20% and other at the profit of 20%. What is the percentage of loss (-) or profit (+) that resulted from the transaction?
A.(+)4
B.(-)1
C.(+)1
D.(-)4
Answer: D.(-)4
Explanation: Solution: In such cases, always loss occurs. It can be calculated by this formula,
= (loss or gain percentage)2/100 = 4.
That is 4% of loss.
Graphic Change method
100==20%(loss) ==>120==20%(gain) ==>96.
% Loss = 4%.
Answer: Option D
Question: What value should come in place of question mark (?) in the following equations ?
4.78% of 1255 + 3.24% of 440=0.5% of ?
A.14260
B.14492
C.14636
D.14849
Answer: D.14849
Explanation: Explanation :
0.5 x ?/100 = 4.78 x 1255/100 + 3.24 x 440/100
= 59.989 + 14.256
∴ ? = 74.245 x 100/0.5 = 14849
Answer : Option D
Question: A Man can row upstream at 27kmph and downward stream at 10 kmph. Find Man's rate still in water.
A.8.5km/hr
B.32km/hr
C.4.9km/hr
D.28km/hr
Answer: A.8.5km/hr
Explanation: Rate in still water =1/2(10+7)km/hr
=8.5km/hr .
correct option is :A
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 785 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
A.191
B.197
C.193
D.212
Answer: B.197
Explanation: Total movies submitted are 785.
As per question we need to take 1/4 of 785 to be considered for top 10 movies = 196.25
approximate the value we 197.
IMO option B is the correct answer...
Question: What is the measure of the angle X made by the diagonals of the any adjacent sides of a cube.
A.30
B.45
C.60
D.75
Answer: C.60
Explanation: C.. 60 degrees
All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be X=60.C
Question: Ten friends went to an ice cream parlour, and everyone decided to contribute equally to the total bill of $50. If one of the friends had a coupon for 10% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
A.4.2
B.4.5
C.4
D.4.8
Answer: B.4.5
Explanation: At the non-discounted price, each friend would pay $5, as $50 divided by 10 friends is $5 per friend. But if the bill is 10% off, then each friend would pay 10% less. 10% of $5 is $0.5, so each friend saves $0.5 and pays the remaining $4.5
CORRECT OPTION:OPTION B
Question: How many times the keys of a writer have to be pressed in order to write first 150 counting no's?
A.342
B.352
C.362
D.372
Answer: A.342
Explanation: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 150 = 51 * 3 = 153
-----------
342
A
Question: A train sets off at 2 p.m. at the speed of 68 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
A.10:37 p.m
B.10:20 p.m
C.9:30 p.m
D.9:38 p.m
Answer: C.9:30 p.m
Explanation: D = 68 * 1 Â½ = 102 km
RS = 85 â€“ 68 = 17
T = 102/17 = 6 h
3.30 + 6 h = 9.30 p.m.
Answer: C
Question: A bag contains 23 purple jellybeans, 12 green jellybeans, and 15 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be yellow?
A.15%
B.20%
C.25%
D.30%
Answer: D.30%
Explanation: p = 23 , g=12 , y=15
total = 50
p(yellow)=(15/50)*100 = 30% . Ans = D
Question: If two typists can type two pages in two minutes, how many typists will it take to type 18 pages in three minutes?
A.3
B.4
C.6
D.12
Answer: D.12
Explanation: In 2 minutes 2 typists type 2 pages which means that in 3 minutes they will type 3 pages but to type 18 pages (6 times) we need 6 times more typists i.e. 2 x 6 = 12 typists.
D
Question: If a man can cover 18 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
A.243 km
B.162 km
C.1767 km
D.1887 km
Answer: A.243 km
Explanation: 18 m/s = 18 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 18 * 18/5 * 15/4 km = 243 km.
Answer: A
Question: A large field of 500 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?
A.205
B.215
C.225
D.260
Answer: C.225
Explanation: Average of the two areas =500/2=250
one-fifth of the average of the two areas=250/5=50
⇒ Difference of the two areas =50
Let area of the smaller part =x hectares.
Then, area of the larger part =x+50 hectares.
=>x+x+50=500
=>2x=450
=>x=225
ANSWER:C
Question: The length of a rectangular plot is 10 meters more than its width. If the cost of fencing the plot at $15.50 per meter is $806, what is the length of the plot in meters?
A.16
B.18
C.20
D.22
Answer: B.18
Explanation: perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20
cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 806
62L = 1116
L = 18 meters
The answer is B.
Question: If the price of gasoline increases by 20% and a driver intends to spend only 14% more on gasoline, by how much percent should the driver reduce the quantity of gasoline that he buys?
A.1%
B.2%
C.4%
D.5%
Answer: D.5%
Explanation: Let x be the amount of gasoline the driver buys originally.
Let y be the new amount of gasoline the driver should buy.
Let P be the original price per liter.
(1.2*P)y = 1.14(P*x)
y = (1.14/1.2)x = 0.95x which is a reduction of 5%.
The answer is D.
Question: Calculate the average of all the numbers between 15 and 55 which are divisible by 4.
A.39
B.33
C.34
D.30
Answer: C.34
Explanation: Explanation:
numbers divisible by 4 are 16,20,24,28,32,36,40,44,48,52,,,
Average = (16+20+24+28+32+36+40+44+48+52) / 10 = 340/10 = 34
ANSWER: C
Question: Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 30 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?
A.40
B.50
C.60
D.80
Answer: B.50
Explanation: L+M=M+N-50 / N=2L+10
30=M+N-L-M
30=N-L
30=2L+10-L
20=L
2(20)+10=50
B
Question: Out of 10 consonants and 3 vowels, how many words of 3 consonants and 2 vowels can be formed?
A.79200
B.1050
C.25200
D.21400
Answer: A.79200
Explanation: Solution
Number of ways of selecting (3 consonants out of 10) and (2 vowels out of 3)
10c3 x 3c2= (10x9x8/3x2x1)x(3/1) =660
Number of group,each having 3 consonants and 2 vowels = 660 .
Each group contains 5 letter.
Number of ways of arranging 5 letters among themselves
= 5 ! = (5 × 4 × 3 × 2 × 1) = 120 .
So, Required number of words = (660 × 120) = 79200 .Answer A
Question: The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.7,430 for a cell phone, then what was the cost price of the cell phone?
A.Rs.5,845
B.Rs.6,040
C.Rs.5,700
D.Rs.6,925
Answer: B.Rs.6,040
Explanation: Explanation:
123% of CP =SP
Therefore, CP = Rs.7,430x100/123 = Rs.6040
Answer: Option B
Question: Solve the following quadratic equation by factoring.
A.-2,7
B.2,-7
C.1,8
D.1,-8
Answer: A.-2,7
Explanation: We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
Therefore the two solutions are : (u+2)(u-7)=0 -> (u+2)(u-7)=0 therefore u=-2, u=7
ANSWER A -2,7
Question: In a camp, there is a meal for 120 men or 200 children. If 180 children have taken the meal, how many men will be catered to with remaining meal?
A.12
B.20
C.40
D.57
Answer: A.12
Explanation: There is a meal for 200 children.
180 children have taken the meal.
Remaining meal is to be catered to 20 children.
Now, 200 children 120 men.
20 children = (120/200)x 20 = 12 men.
A
Question: The girl child birth in a town is 40% of boy child birth. What is the number of boy child as a percentage of girl child birth?
A.150%
B.250%
C.125%
D.35%
Answer: B.250%
Explanation: The number of girl child birth in a town is 40% of boy child birth
If the boy child birth=10
Girl child birth=4
We are asked to find the number of boy child birth as a percentage of girl child birth
B/G=10/4=2.50=250%
Answer is B
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 10 m of the same rod?
A.38 kg
B.25.6 kg
C.28 kg
D.26.5 kg
Answer: A.38 kg
Explanation: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 10 :: 42.75 : x
=> 11.25 x x = 10 x 42.75
=> x = (10 x 42.75) / 11.25
=> x = 38
Answer : A
Question: While playing a certain dice game, Chris wins if the sum of the two dice is 6, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
A.1/2
B.17/36
C.137/379
D.11/36
Answer: C.137/379
Explanation: Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 6 = (1,5)(2,4)(3,3)(4,2)(5,1)= 5 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 6 in any attempt =5/36=
Probability of NOT getting sum as 6 in any attempt = 1-(5/36)= 31/36
Probability of losing game =(31/36)*(31/36)*(31/36)=242/379
I.e. Probability of wining game = 1-(242/379) = 137/379
Answer : Option C
Question: Nine persons went to a hotel for taking their meals. Eight of them spent 13 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?
A.115
B.117
C.119
D.126
Answer: D.126
Explanation: Let the average expenditure of all the nine be x.
Then, 13 × 8 + (x + 8) = 9x or 8x = 112 or x = 14.
∴ Total money spent = 9x = (9 × 14) = 126.
Answer D
Question: Mary bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?
A.$10
B.$11
C.$12
D.$13
Answer: B.$11
Explanation: From the given information,we can conclude that Mary bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for 1000*.90 = $900 . With the remaining money ($1000 - $900 = $100), he can buy 10 more shares. So, the reduced price per share = $100/10 = $10.
Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=B
Question: If x is three times larger than y , and if 2y+3 is 20% of 25, what is the value of ?
A.1
B.3
C.4
D.6
Answer: B.3
Explanation: Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey x=4y, if it really wanted to convey so.
From other questions that I have seen, proper wordings could be:
If m is three times as large as y
OR simply,
If x is three times y
B)
Question: Given the following equation 15% of 5215 + 16% of 4135 = q, Find the approximate value should come in place of the q.
A.1640
B.1448
C.1430
D.1440
Answer: D.1440
Explanation: q = 15% of 5215 + 16% of 4135
q = 15/100*5215 + 16/100*4135
q = 1443.85
≈ 1440
Answer D
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?
A.65 sec
B.36 sec
C.48 sec
D.33 sec
Answer: B.36 sec
Explanation: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.4 = 1.5 km = 1500 m.
Required time = 1500 * 3/125
= 36 sec.
Answer:B
Question: Johnny borrows $30,000 from Tony at 3% daily interest compounded daily. How much does Johnny owe Tony after 3 weeks?
A.30000*0.02^56
B.30000*1.12
C.30000*2.12
D.30000*1.03^21
Answer: D.30000*1.03^21
Explanation: A=A= P(1+r100)^n
So, A=30000(1+3/100)^7âˆ—3
So, A= 30000(1.03)^21
Hence answer will be (D)
Question: In a zoo there are 30 penguins, 22 zebras, and 8 tigers with some zookeepers. If the total number of heads are 132 less than the number of feet, the number of zookeepers is
A.12
B.14
C.16
D.18
Answer: A.12
Explanation: Explanation: Let number of zookeepers be x. Then, Total number of feet = 2 x 30 + 4 x 22 + 4 x 8 + 2x = 2x + 180. Total number of heads = 30 + 22 + 8 + x= 60 + x. Therefore (2x + 180) - 132 = (60 + x) + or x = 12. Answer: A
Question: When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 21. Which of the following is true?
A. 23x + 17y =19
B. 17x –23y = 16
C. 17x +23y =19
D. 14x + 5y = 6
Answer: B. 17x –23y = 16
Explanation: From the problem it follows:
n=17x+5
n=23y+21
So, 17x+5=23y+21
17x-23y=16
The answer is B
Question: If n is a positive integer, which of the following is a possible value of |51 - 5n|?
A.7
B.1
C.14
D.15
Answer: C.14
Explanation: When 51>5n, then |51 - 5n| = 51 - 5n = (50-5n) + 1 = {multiple of 5} + 1
When 51<=5n, then |51 - 5n| = -(51 - 5n) = (5n-50) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only C fits.
Answer: C
Question: Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 55% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
A.270%
B.310%
C.350%
D.390%
Answer: D.390%
Explanation: Let x be the number of new biographies added to the library.
Let b be the original number of biographies, so the original number of books was 5b.
0.55(5b+x) = b+x
1.75b = 0.45x
x = 3.9b
The answer is D.
Question: A carpenter makes 3 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: If two soldiers sleep on one bunk bed, school needs 143/2= 72 bunk beds.
1 carpenter can make 3 beds and 5 carpenters can make 15 beds/day.
15 beds will be ready in 1 day, so to have 72 beds ready, carpenters require 72/15 = 5 (closest integer) days
C is the answer
Question: Barbata invests $2000 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
A.1200
B.3000
C.1000
D.3600
Answer: C.1000
Explanation: Let the additional invested amount for 8% interest be x;
Equation will be;
2000+0.05*2000+x+0.08x = 2000+x+0.06(2000+x)
0.05*2000+0.08x = 0.06x+0.06*2000
0.02x = 2000(0.06-0.05)
x = 2000*0.01/0.02 = 1000
Ans: "C"
Question: A chair is bought for Rs.200/- and sold at Rs.340/- find gain or loss percentage
A.70% loss
B.20% gain
C.25% gain
D.30% gain
Answer: A.70% loss
Explanation: Formula = (Selling price ~ Cost price)/Cost price * 100
= (340 - 200)/200 = 70% gain
A