RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 190 m long?
A.44
B.99
C.88
D.77
Answer: A.44
Explanation: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 190 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer:A
Question: If it is assumed that 80 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?
A.375
B.420
C.480
D.500
Answer: A.375
Explanation: Minimum no of mail to be sent for getting 300 responses at 80%
= 300/0.8 = 375
Option A
Question: A box contain 7 one rupee coins and 5 ten rupee coins.A coin is drawn at random.What is the probability that the coin drawn is ten rupee coin?
A.5/12
B.7/12
C.12/5
D.12/7
Answer: A.5/12
Explanation: Total number of coins = 7+5 = 12
no. of ten rupee coins = 5
probability of drawn a ten rupee coin= 5/12
Answer is A
Question: By selling a book for 270, 20% profit was earned. What is the cost price of the book?
A.215
B.225
C.230
D.235
Answer: B.225
Explanation: SP = 120% of CP; :. CP = 270 × 100/120 = 225
Option 'B'
Question: The sum of ages of 5 children born 3 years different each is 50 years. What is the age of the Elder child?
A.8
B.9
C.10
D.16
Answer: D.16
Explanation: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
x+12= 4+12= 16
D
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
A.50
B.20
C.30
D.25
Answer: A.50
Explanation: Let the actual distance traveled is 'x' km
Then by given conditions, we have
x/10 = (x+20)/14
14x = 10x + 200
x = 50 km
Ans- A
Question: When I was married 10 years ago my wife is the 6th member of the family. Today my father died and a baby born to me.The average age of my family during my marriage is same as today. What is the age of Father when he died?
A.40 yrs
B.50 yrs
C.60 yrs
D.70 yrs
Answer: C.60 yrs
Explanation: let average age 10 yrs ago was x yrs,
total age 10 yrs before was 6x yr ,
at present,father died, now members remains= 5,
now total age after 10 yrs is (no. of member)*(x+10) yrs,i.e.total age is 5(x+10)
and after baby born total age = 5(x+10)+0, because baby age is 0 yrs
as per ques. both time, age is same i.e. 6x=5x+50+0
after solving.. x=50,i.e. father's age before 10 yrs was 50 yrs,
now father died after 10 yrs hence age at dead time= 50+10=60 yrs.
ANSWER:C
Question: At a company, the average wage of male employees is $4 per hour, and the average wage of female employees is $8 per hour. If the average wage of all employees is $7 per hour, what is the ratio of the number of male employees to the number of female employees?
A.1 to 3
B.2 to 3
C.3 to 2
D.5 to 3
Answer: A.1 to 3
Explanation: Average hourly wage of male employees = 4 $
Average hourly wage of female employees = 8 $
Average hourly wage of all employees = 7 $
Let number of male employees = m
number of female employees = f
7= (4m + 8f ) / m+f
=>7m + 7f = 4m + 8f
=> 3m = 1f
=> m/f = 1/3
Answer A
Question: AMS employs 6 professors on their staff. Their respective probability of remaining in employment for 10 years are , 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years 6 of them still work in AMS is ?
A.0.06048
B.1.22
C.0.1
D.0.16
Answer: A.0.06048
Explanation: Asking 6 of them continue ,
it has 1 case.
3 6 professors continue
=0.4*0.5*0.6*0.7*0.8*0.9 =0.06048
A
Question: Calculate how many ways a woman who has 4 bags and 6 books can put the books in her bag?
A.4296
B.4056
C.4016
D.4096
Answer: D.4096
Explanation: First books can be put in 4 ways, similarly second, third , forth, fifth and sixth book also can be put in 4 ways.
So total number of ways = 4 x 4 x 4 x 4 x 4 x 4 = 4096
D
Question: The product of two fractions is 3/4 and their quotient is 6/18. If the denominator of one is 1/3 of the other's numerator, then find the pair of fractions?
A.1/3, 9/5
B.1/2, 3/2
C.1/2, 6/5
D.Data inadequate
Answer: B.1/2, 3/2
Explanation: Explanation:
Let A = x/y, and B be two fractions
It is given that A*B = 3/4
Therefore x/y * B = 3/4
B = 3y/4x
Therefore, A = x/y and B = 3y/4x
It is given that A/B = (x/y) / (3y/4x) = 6/18
Therefore x/y * 4x/3y = 6 /18
Therefore 4x2/3y2 = 6/18
x2/y2 = 18/(4*18)
Therefore, x2/y2 = ¼
x/y = 1/2
B = 3y/4x = 3/4 (1/(x/y)) = 3/4 [1/(1/2)] = 6/4
Therefore A = 1/2 and B = 3/2
ANSWER B
Question: A train 220 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is:
A.41
B.40.6
C.40.8
D.42
Answer: B.40.6
Explanation: Speed of the train relative to man =220/20
=11 m/sec.
=11x18/5km/hr
= 198/5km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 198/540.6 km/hr.
Answer:B
Question: A contractor is engaged for 30days on the condition that he receives Rs.25 for each dayhe works &is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many dayswas he absent?
A.8
B.10
C.12
D.15
Answer: B.10
Explanation: 30 * 25 = 750
425
-----------
325
25 + 7.50 = 32.5
325/32.5 = 10
B
Question: The units digit of (35)^(87) + (93)^(51) is:
A.2
B.4
C.6
D.8
Answer: A.2
Explanation: The units digit of powers of 3, cycles in a group of 4: {3, 9, 7, 1}
51 has the form 4k+3, so the units digit of 93^51 is 7.
The units digit of powers of 5 is always 5.
7+5 = 12, so the units digit is 2.
The answer is A.
Question: An e-commerce website marks his wares 30% more than the real price and allows 10% discount. Their profit is:
A.17%
B.19%
C.21%
D.23%
Answer: A.17%
Explanation: Let the CP = 100 Rs.
Mark Price = 130
Discount = 10%
Selling price 90/100 Ã— 130
Hence profit = 17%
Answer: A.
Question: Albert borrowed a total of $ 5700 from Brian and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years?
A.157.5
B.160
C.161
D.165
Answer: A.157.5
Explanation: Let x be the amount borrowed form Brian. So amount borrowed form Charlie = 5700-x.
1494 = 21/100x + 27/100(5700-x)
=>x = 750.
Interest paid = 3*7/100*750 = 157.5
A
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more?
A.38
B.40
C.83
D.87
Answer: B.40
Explanation: 760 ---- 22
760 ---- 20
x ----- 19
x*19 = 760*20
x = 800
760
-------
40
Answer: B
Question: Workers at a campaign office have 1000 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?
A.300
B.800
C.1100
D.600
Answer: D.600
Explanation: (1/5)*1000 = 200
Remaining = 1000-200 = 800
(1/4) of remaining = (1/4)*800 = 200
Remaining now = 800-200 = 600
Answer: Option D
Question: Jamboree and GMAT Club Contest Starts
QUESTION #15:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
A. 660
B. 600
C. 500
D. 300
Answer: C. 500
Explanation: The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.
Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together
In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,
Total arrangements = 6!/2!
Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.
Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.
Hence, Arrangements when two E’s are together = 5! * (2!/2!)
Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2 = 240.
Option C is correct!
Question: 2, 6, 12, 20, 30, 42, 56, (...)
A.61
B.72
C.64
D.70
Answer: B.72
Explanation: Explanation :
The pattern is 1×2, 2×3, 3×4, 4×5, 5×6, 6×7, 7×8.
Hence, next number is 8×9 = 72
Answer : Option B
Question: If the average (arithmetic mean) of a and b is 20, and c – a = 30, what is the average of b and c?
A.25
B.30
C.40
D.35
Answer: D.35
Explanation: a+b/2 = 20
=> a+b = 40
a = c - 30...sub this value
c-30+b = 40
=>c+b = 70
=>c+b/2 = 35
Answer : D
Question: Solution A is 20% salt and Solution B is 70% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
A.6:4
B.6:14
C.2:3
D.4:6
Answer: C.2:3
Explanation: Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (70 - 50)/(50 - 20) = 2/3
So the volume of the two solutions will be equal. Answer has to be 2:3
C
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
A.50
B.60
C.70
D.80
Answer: C.70
Explanation: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
ANSWER:C
Question: The average age of an adult class is 50 years. 12 new students with an avg age of 32 years join the class. Therefore decreasing the average by 4 years. Find what was the original average age of the class?
A.10
B.12
C.42
D.20
Answer: C.42
Explanation: Let original strength = y
Then , 50y + 12 x 32 = ( y + 12) x 46
â‡’ 50y + 384 = 46y + 552
â‡’ 4y = 168
âˆ´ y = 42
C
Question: A man distributes 0.375 of his money to his wife and 0.4 to his son. He still has Rs.3,375
left with him. How much did his wife get?
A.Rs. 3625/-
B.Rs. 4625/-
C.Rs. 5625/-
D.Rs. 6625/-
Answer: C.Rs. 5625/-
Explanation: Let, total money = M.
So, M*(1-0.375-0.4)=3375; => M= 3375/(1-0.375-0.4); => M = 15000
So, his wife got = 15000*(0.375)= 5625.
So, his wife got Rs. 5625/-
ANSWER:C
Question: 24 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres?
A.30
B.36
C.60
D.Data inadequate
Answer: B.36
Explanation: Capacity of the tank = 24 Ã— 13.5= 324 litres
When the capacity of each bucket = 9 litres, then the required no. of buckets
= 324â„9 = 36
Answer B
Question: A box contains seven purple, five blue and eleven yellow balls.
What is the minimum number of tries required to get one blue and one yellow ball ?
A.16
B.17
C.18
D.19
Answer: D.19
Explanation: 11 yellow+7 purple+after that we have only one option that is to be blue so answer is 19
ANSWER:D
Question: If a man reduces the selling price of a fan from Rs. 420 to Rs. 402, his loss increases by 3%. The cost price of the fan is :
A.Rs.600
B.Rs.650
C.Rs.475
D.Rs.525
Answer: A.Rs.600
Explanation: Explanation :
Solution: let C.P. be Rs. X. then, 3% of x = (420-402) =18 => 3x/100 = 18 => x =Rs.600.
Answer : A
Question: Gokul buys 9 horses and 4 cows for Rs. 13,400. if he sells the horses at 20% profit and the cows at 10% profit, then he earns a total profit of Rs. 1880. The cost of a cow is:
A.Rs. 2200
B.Rs. 2190
C.Rs. 2000
D.Rs. 600
Answer: C.Rs. 2000
Explanation: Explanation :
Solution: Let C.P. of each horse and be Rs. X and C.P. of each cow be Rs. Y. then,
9x+4y =13,400 -------> (1)
And, 20% of 9x + 10% of 4y = 1880.
9x/5 + 2y/5 = 1880 => 9x+2y =9400 -------> (2)
solving (1) and (2), we get : x = 600 and y =2000.
.'. cost price of each cow = Rs. 2000.
Answer : C
Question: Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 6 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If four minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
A.12
B.24
C.36
D.48
Answer: D.48
Explanation: the difference of the speed is 1m per second so in four minute Sacha will be 240 m ahead of Bruno..
Bruno will cover this in 240/5=48 secs..
D
Question: The area of a parallelogram is 72 sq m and its base is 12m . Then the length of the height is?
A.6m
B.7m
C.60m
D.13m
Answer: A.6m
Explanation: b*h=72. h*12=72 =>h=6m. Answer: (A)
Question: A can run 2 km distance in 2 min 20 seconds, while B can run this distance in 3 min 5 sec. . By how much distance can A beat B?
A.900 m
B.500 m
C.120 m
D.180 m
Answer: B.500 m
Explanation: A takes time 2.20 minutes=140sec
B takes time 3 minutes=185 sec
difference= 185-140=45sec
now we are to find distance covered in 40 sec by B
180sec=2000m
1sec=100/9 m
45sec=45x100/9=500m
ANSWER:B
Question: To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 10%, and reduce the price it charges its consumers by 10% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?
A.1. 23.5
B.2. 50%
C.3. 100%
D.4. 300%
Answer: A.1. 23.5
Explanation: Take smart numbers
Let,
L = 20: B = 10: H= 10 of initial box and Price = 50$
Therefore Price / cubic inch = 50 / (20*10*10) =0.025
Now, when dimensions are reduced by 10% and price also reduced by 10%
L = 18; B=9; H=9 and Price = 45$
Therefore price / cubic inch = 45 / (18*9*9) =0.030
Percentage change = (0.030 - 0.025) *100/ 0.025 = 23.5%
Answer is A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
A.12
B.18
C.36
D.72
Answer: C.36
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x =	(120 + 120)/12
=> 2x = 20
=> x = 10.
Therefore Speed of each train = 10 m/sec =(10 x	(18/5))	km/hr = 36 km/hr.
Answer :C
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 20, how many more dollars, in terms of x, will it cost per person?
A. x/6
B. x/16
C. x/20
D. 3x/40
Answer: C. x/20
Explanation: Just plugging in values
X= 200
Cost per person if we consider 10 = 20
Cost per person if we consider 20 = 10
Difference between costs is 10 dollars.
Plugging in the value of x into the answer choices, let's see which one yields a result of 10. And that is C.
Question: A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the president or the member chosen to be the treasurer?
A. 1/720
B. 1/80
C. 2/10
D. 1/9
Answer: C. 2/10
Explanation: This question is much easier than it appears.
Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the president is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the president or the the treasurer is 1/10+1/10=2/10.
Answer: C
Question: A straight line in the xy- plane has a slope of 4 and a y-intercept of 4. On this line, what is the x-coordinate of the point whose y-coordinate is 800 ?
A.233
B.299
C.333
D.199
Answer: D.199
Explanation: Eq of line = Y = MX +C
M = 4,
C= 4
Y=4X + 4,
Substitute Y by 800 as given in question.
800=4X+4 , X = 199.
correct option is D
Question: Simplify: 5005-5000+10
A.4505
B.4509
C.4501
D.4500
Answer: A.4505
Explanation: 5005-5000+10=5005-(5000/10)=5005-500=4505
Answer is A
Question: Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?
A.4%
B.5%
C.6%
D.7%
Answer: B.5%
Explanation: Thus total value of Bond at the end of 2016 is 420 ( ie, 1080 - 660 )
So, Per unit value of Bond at the end of 2016 is 420/40=10.50
Hence, percentage increase is 0.50/10∗100=5%, answer will be (B)
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 13 different shirts, 10 different pairs of jeans, and 8 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
A.30
B.90
C.240
D.1040
Answer: D.1040
Explanation: Total # of outfits = 13 * 10 * 8 = 1040
Answer - D
Question: How many bricks, each measuring 25cm*11.25cm*6cm, will be needed to build a wall 8m*6m*22.5m
A.6100
B.6200
C.6300
D.6400
Answer: D.6400
Explanation: Explanation:
To solve this type of question, simply divide the volume of wall with the volume of brick to get the numbers of required bricks
So lets solve this
Number of bricks =
Volume of wall /Volume of 1 brick=800∗600∗22.5 /25∗11.25∗6=6400
Option D
Question: In what time will a railway train 80 m long moving at the rate of 36 kmph pass a telegraph post on its way?
A.8 sec
B.1 sec
C.9 sec
D.6 sec
Answer: A.8 sec
Explanation: T = 80/36 * 18/5
= 8 sec
Answer:A
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 4 Ohms and y is 5 Ohms?
A.7/9
B.20/9
C.7/20
D.9/20
Answer: B.20/9
Explanation: 1/R = 1/x + 1/y
1/R = 1/4+1/5 = 9/20
R = 20/9
The answer is B.
Question: Which of the following number is divisible by 24 ?
A.3125736
B.35718
C.63810
D.537804
Answer: A.3125736
Explanation: 24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
3125736 is divisible by (3 x 8), i.e., 24.
A)
Question: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = 8?
A.-1
B.6
C.10
D.14
Answer: B.6
Explanation: We know that t1 = 23
So, using the given formula we have:
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26
The same way we find that t2= 20
It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
So, ourANS is B.
Question: If equal numbers of people are born on each day, find the approximate percentage of the people whose birthday will fall on 29thFebruary.(if we are to consider people born in 20thcentury and assuming no deaths).
A.0.374
B.0.5732
C.0.0684
D.None of these
Answer: C.0.0684
Explanation: Explanation :
Let the number of people born on each day = n.
Total years in the 20th century = 100.
Total number of leap years (years in which 29th February appear) = 25.
Sample Space (days) = 365*75 + 366*25 = 36525 days.
So, Sample Space (population) = 36525*n
Favourable Set (population) = 25*n
Hence, the required probability = 25 * n /36525*n = 0.000684.
= 0.0684%.
Answer : C
Question: I know a number which when multiplied by multiple of 9 i.e 9 18 27 36 45 ... the output consist of number containing only one digit.
Can you identify the number ?
A.12345678
B.12345674
C.12745679
D.12345679
Answer: D.12345679
Explanation: D
12345679
12345679 × 9 = 111111111 (only 1s)
12345679 × 18 = 222222222 (only 2s)
12345679 × 27 = 333333333 (only 3s)
12345679 × 36 = 444444444 (only 4s)
12345679 × 45 = 555555555 (only 5s)
Question: What is the maximum value of vx - yz. If the value of v,x,y,z have to be chosen from the set A where A(-3,-2,-1,0,1,2,3)
A.15
B.66
C.25
D.88
Answer: A.15
Explanation: Explanation:
To maximize the value of vx - yz, we make yz negative and vx as maximum as possible using given value.
vx−yz=(−3)2−(−3×2)vx−yz=(−3)2−(−3×2) = 15
Answer:A
Question: In terms of percentage profit, which among following the best transaction
A.C.P. 36, Profit 17
B.C.P. 50, Profit 24
C.C.P. 40, Profit 19
D.C.P. 60, Profit 29
Answer: D.C.P. 60, Profit 29
Explanation: Explanation:
Hint: Calculate profit percent as
Profit% = (profit/cost) * 100
Option D
Question: Excluding stoppages, the speed of a train is 35 kmph and including stoppages it is 22 kmph. Of how many minutes does the train stop per hour?
A.82
B.17
C.22
D.82
Answer: C.22
Explanation: Explanation:
T = 13/35 * 60 = 22
Answer: Option C
Question: What will be the difference between simple interest and compound interest @10% per annum on a sum of Rs. 1000 after 4 years?
A.Rs. 31
B.Rs. 32.10
C.Rs. 40.40
D.Rs. 64.10
Answer: D.Rs. 64.10
Explanation: Solution
S.I.	=Rs(1000x10x4 / 100)
= Rs.400.
C.I.	=Rs.[1000x(1x10/100)4-1000]
= Rs. 464.10
∴ Difference = Rs.(464.10 - 400)
= Rs. 64.10
Answer D
Question: A man can row his boat with the stream at 19 km/h and against the stream in 11 km/h. The man's rate is?
A.4 kmph
B.2 kmph
C.7 kmph
D.8 kmph
Answer: A.4 kmph
Explanation: DS = 19
US = 11
S = ?
S = (19 - 11)/2 = 4 kmph
Answer:A
Question: Set A consists of 19 elements. The average of set A is L. If a new element is added to the set and the average grows by K, what is the value of the new element?
A.a) L(1 + K / 5)
B.b) L * (K/100) - 20L
C.c) 20L(1+K/100)
D.d) 20(1+K/100)-19L
Answer: A.a) L(1 + K / 5)
Explanation: Let's assume the value of new element to bea. So converting the word problem into equation,
(19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K
But according to the answer options, problem writer wanted to conveyk% percent rise in average value.
If we consider this case than resulting equation will be,
(19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]
==> a= 20L + KL/5 -19L
==> a= L + KL/5 , which is equivalent to option [A]
Question: Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1800 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
A.$16,200
B.$5,600
C.$8,100
D.$15,000
Answer: A.$16,200
Explanation: x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $1800 triples to $5400, in 28 years, it will again triple to $5400*3=$16,200
Answer A
Question: If 3 pounds of dried apricots that cost x dollars per pound are mixed with 3 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
A.(3x + 3y)/5
B.(3x + 3y)/(x + y)
C.(3x + 3y)/(xy)
D.5(3x + 3y)
Answer: A.(3x + 3y)/5
Explanation: Total Cost = Weight(in pounds) * Price/pound;
To find Total cost/pound, Divide by total pounds.
Cost of Dried apricots = 3x;
Cost of prunes = 3y;
Cost per pound = (3x + 3y)/5;
Ans is (A).
Question: The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 2 type B widgets, and the weight of 4 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?
A.3:5
B.5:7
C.7:9
D.9:11
Answer: D.9:11
Explanation: 4B = 7C and so B = 7C/4
7A = 2B and so A = 2B/7 = C/2
A+B = C/2 + 7C/4 = 9C/4
B+C = 7C/4 + C = 11C/4
The ratio of A+B:B+C = 9:11
The answer is D.
Question: The product of two positive integers is 675 and their difference is 2. What is the bigger number?
A.21
B.23
C.25
D.27
Answer: D.27
Explanation: Let's use trial and error to find the two numbers.
25*23 = 575 (too low)
27*25 = 675
The answer is D.