RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A 5-year investment note offers a 10% return on purchase, and a compounding 5% for each year after the first. If there is a $500 penalty for early redemption, and the note is redeemed for $6430 after the second year, what was the original purchase price?
A.$ 6,000
B.$ 6,048
C.$ 6,100
D.$ 6,150
Answer: A.$ 6,000
Explanation: Since the note was redeemed after 2 years, so a penalty of $500 has to be submitted. So the amount that is redeemed after 6430 is after the deduction of $500.
Hence the amount after being compounded is 6930.
Let the initial amount be P.
After the return, the amount becomes 1.1P.
Now use this 1.1P as the principle in the compound interest formula to get the amount 6930.
A=1.1P(1+5/100)A=1.1P(1+5/100)
where A=6930.
Therefore, use
6930=1.1P(1+5/100)6930=1.1P(1+5/100) to get P as $6000.
ANSWER:A
Question: The value of 51/4 * (125)0.25 is:
A.5
B.5(5)
C.5√5
D.√5
Answer: A.5
Explanation: Sol.
51/4 * (125)0.25 = 50.25 * (53)0.25 * 5(3*0.25) = 50.25 * 50.75
= 5(0.25 + 0.75) = 51=5.
Answer A
Question: For which of the following does f(x)−f(y)=f(x−y) for all values of x and y?
A.f(a)=a^2
B.f(a)=a/2
C.f(a)=a+5
D.f(a)=2a−1
Answer: B.f(a)=a/2
Explanation: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(x) = x^2 and f(y) = y^2
so L.H.S = x^2 - y^2
and R.H.S = (x-y)^2 ==> x^2 + y^2 -2xy.
so L.H.S not equal to R.H.S
with option 2. f(x) = x/2 and f(y) = y/2
L.H.S = x/2 - y/2 ==> 1/2(x-y)
R.H.S = (x-y)/2
so L.H.S = R.H.S which is the correct answer.
B
Question: In a group of 100 adults, 40 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
A.48
B.52
C.54
D.40
Answer: D.40
Explanation: 12 left-haded women compose 100-40=60% (or 3/5) of all women, so there are total of 5*12=60 women --> 100-60=40 men.
Answer: D.
Question: A man, a woman and a boy can together complete a piece of work in 4 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?
A.36days
B.32days
C.34days
D.42days
Answer: A.36days
Explanation: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/4
1 man’s 1 day work = 1/6
1boy’s 1 day’s work = 1/18
(1 Man + 1 boy) ‘s 1 day’s work = 1/6 + 1/18 = 2/9
Therefore, 1 woman’s 1 day’s work = 1/4 – 2/9 = 1/36
Therefore, the woman alone can finish the work in 36 days.
Answer: Option A
Question: A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
A.20 seconds
B.44 seconds
C.40 seconds
D.50 seconds
Answer: B.44 seconds
Explanation: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 410+140 = 550 meter
Time = Distance/speed
=550∗2/25=44seconds
Option B
Question: The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then what is the area of the park (in sq. m)?
A.153500
B.153650
C.153600
D.153700
Answer: C.153600
Explanation: Let length =3x km,
breadth =2x km
Distance travelled by the man at the speed of 12 km/hr in 8 minutes =2(3x+2x)=10x
Therefore,12×860=10xx=425 km=160 m
Area =3x×2x=6x2
=6×1602=153600 m2
Answer is C.
Question: A store reported total sales of $400 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
A.2%
B.17%
C.25%
D.65%
Answer: C.25%
Explanation: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 400 million
February sales last year = 320 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 400 million and the old value = 320 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(400 – 320)/320] x 100
= 25%.
The answer is C.
Question: A person deposits 1/16 of his income as Provident Fund and 1/15 of the remaining as insurance premium. If he spends 5/7 of the balance on domestic needs and deposits an amount of Rs. 50 in the bank, his total income would be
A.150
B.200
C.250
D.300
Answer: B.200
Explanation: (1-(1/16))(1-(1/15))(1-(5/7)) of Income = 50
Hence income = 200
ANSWER:B
Question: Factor: 5x4y3 â€“ 80y3
A.A) 5y3(x2 + 4)(x + 2)(x -2)
B.B) 2y3(x2 + 4)(x + 2)(x -2)
C.C) 3y3(x2 + 4)(x + 2)(x -3)
D.D) 3y3(x2 + 4)(x + 3)(x -2)
Answer: A.A) 5y3(x2 + 4)(x + 2)(x -2)
Explanation: 5x4y3â€“ 80y3.
= 5y3(x4 â€“ 16).
= 5y3[(x2)2 - 42].
= 5y3(x2 + 4)(x2 - 4).
= 5y3(x2 + 4)(x2 - 22).
= 5y3(x2 + 4)(x + 2)(x -2).
Answer: (A) 5y3(x2 + 4)(x + 2)(x -2)
Question: Two dice are tossed. The probability that the total score is a prime number is
A.1/6
B.5/12
C.1/2
D.7/9
Answer: B.5/12
Explanation: n(S)=36
E= {(1,1),(1,2), (1,4),….(6,5)}
n(E)=15
P(E)=15/36
=5/12
Option B
Question: How many seconds will a 800 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
A.48
B.36
C.26
D.11
Answer: A.48
Explanation: Explanation:
Here distance d = 800 mts
speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s
time t = = 48 sec.
Answer: A
Question: Yid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Yid have meant to type?
A.10
B.16
C.21
D.24
Answer: C.21
Explanation: Yid intended to type a seven-digit number Should be 21.
there are two possibilities for placing 2 3s .
case 1: two 3s were missed consecutively. i.e. he typed 33 and it came blank on screen.
-5-2-1-1-5- in this arrangement we can fit 33 in 6 ways . (Six dashes, each dash represent one possible place for placing 33)
case 2: two 3s are not together, i.e. they have one or more digits between them .
-5-2-1-1-5- , in this arrangement
if we place first 3 at first dash i.e. 35-2-1-1-5- then the other 3 can fit into 5 places.
if we place first 3 at second dash i.e. -532-1-1-5- then the other 3 can fit into 4 places.
if we place first 3 at third dash i.e. -5-231-1-5- then the other 3 can fit into 3 places.
if we place first 3 at fourth dash i.e. -5-2-131-5- then the other 3 can fit into 2 places.
if we place first 3 at Fifth dash i.e. -5-2-1-135- then the other 3 can fit into 1 place.
so total 15 ways.
case 2 + case 1 = 6+ 15 = 21 ways
Answer C
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the 1st and last places?
A.A)340
B.B)360
C.C)256
D.D)196
Answer: B.B)360
Explanation: Explanation:
The word MEADOWS has 7 letters of which 3 are vowels.
V - - - - - V
As the vowels have to occupy 1st and last places, they can be arranged in the 3C2 i.e., 3 ways. While the consonants and vowel can be arranged among themselves in the remaining 5 places in 5! i.e., 120 ways.
Hence the total ways are 120 * 3 = 360.
B
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
A.56 kg
B.56 kg
C.56 kg
D.176 kg
Answer: D.176 kg
Explanation: 25x + 46 = 26(x – 5)
x = 176
Answer:D
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was
A.548
B.9674
C.2397
D.2700
Answer: D.2700
Explanation: Explanation:
Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000
=(45/100*6000)=2700
Answer: D
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
A.16
B.17
C.10
D.19
Answer: B.17
Explanation: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
Answer: B
Question: The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?
A.7
B.2
C.4
D.5
Answer: B.2
Explanation: Explanation:
Let the two-digit number be 10a + b
a = b + 2 --- (1)
10a + b = 7(a + b) => a = 2b
Substituting a = 2b in equation (1), we get
2b = b + 2 => b = 2
Hence the units digit is: 2.
Answer:B
Question: If u > 0, which of the following could be true?
I. u^3 > u^2
II. u^2 = u
III. u^2 > u^3
A.I only
B.III
C.IIIII
D.All of the above
Answer: D.All of the above
Explanation: 1. u^3 > u^2 Well this is true for all u > +1 (but not for values 0 < u < 1)
2. u^2 = u This is true for only one positive number, 1
3. u^2 > u^3 Again this is true only for values of u such that 0 < u < 1
So the answer is D, since there exists at least one value of u which satisfies the equation/ in equation(s)
Question: A can give B 300 meters start and C 600 meters start in a kilometer race. How much start can B give C in a kilometer race?
A.111.12
B.111.67
C.428.57
D.111.11
Answer: C.428.57
Explanation: A runs 1000 m while B runs 700 m and C runs 400 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 400)/700 = 571.43 m.
B can give C = 1000 - 571.43 = 428.57 m.
Answer:C
Question: Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true
A. y = 1.2 × 10^a, where a is a positive integer.
B. y = 1.5 × 10^b, where b is a positive integer.
C. y = 1.8 × 10^c, where c is a positive integer.
D. y = 2.5 × 10^d, where d is a positive integer.
Answer: B. y = 1.5 × 10^b, where b is a positive integer.
Explanation: Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option B is correct answer?
Question: If n = 2.0254 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n?
A. -0.0053
B. -0.0003
C. 0.0007
D. 0.0046
Answer: D. 0.0046
Explanation: n*=2.03
n*-n=2.03-2.0254
0.0046
Answer: D
Question: A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 35 cents?
A.2
B.4
C.6
D.8
Answer: A.2
Explanation: 0.10(x)+0.35(20-x)=2.5
0.10x+7-0.35x=2.5
so x=18
20-x=2
ans is A
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 310,000 cells two hours ago, approximately how many cells will be populating the colony two hours from now?
A.77,500
B.1,240,000
C.2,480,000
D.3,720,000
Answer: B.1,240,000
Explanation: 310,000 × 2 × 2 = 310,000 × 4 = B
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 350. The profit percent of the retailer is
A.10%
B.45.8%
C.25%
D.52%
Answer: B.45.8%
Explanation: Explanation:
cost price = (225 + 15) = 240 sell price = 350
gain = (110/240)*100 = 45.8%. Answer: B
Question: How many two-digit numbers are there whose remainder when divided by 11 is 1, and whose remainder when divided by 6 is 5?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: 2 digit numbers whose remainder when divided by 10 is 1 are
11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91
Out of above , numbers whose remainder when divided by 6 is 5 are
11 , 41 and 71
Answer B
Question: How much water must be added to a 30 quarts of a 75% acid solution to reduce it to a 15%
solution of acid?
A.120 qts
B.220 qts
C.320 qts
D.420 qts
Answer: A.120 qts
Explanation: I’m adding water, so we have
WATER + WATER = WATER
Starting off with 30 quarts and adding x quarts, we should end up with (30 + x) quarts
30 + x = (30 + x)
The problem describes the solution in terms of acid, we have set it up in terms of water. So, we
have to change the percentages and put them in the problem.
.25(30) + x = .85(30 + x)
Again, we multiply both sides of the equation by 100 to get rid of the decimal point.
25(30) + 100x = 85(30 + x)
750 + 100x = 2550 + 85x
15x = 1800
x = 120 qts
correct answer A
Question: To be considered grade AF, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AF eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AF eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
A.800
B.840
C.864
D.900
Answer: B.840
Explanation: We're asked for the smallest possible mass, so what could the lowest mass be per egg AF? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B.
Question: 3639 + 11.95 - x = 3054. Find the value of x.
A.407.09
B.479.75
C.523.93
D.596.95
Answer: D.596.95
Explanation: Explanation:
Let 3639 + 11.95 – x = 3054
Then, x = (3639 + 11.95) – 3054
= 3650.95 – 3054
= 596.95
ANSWER: D
Question: The sume of the present ages of a father and his son is 60 years.Six years ago ,father’s ago was five times the age of the son.After 6 years,son’s age will be :
A.12 years
B.14 years
C.18 years
D.20 years
Answer: D.20 years
Explanation: Solution
Let the present ages of son and father be x and (60 - x)years recepectively.
Then,(60 -x)-6 =5(x-6) ⇔ 54 -x = 5x - 30 ⇔ 6x = 84 ⇔ x =14.
∴ son's age after 6 years = (x + 6) = 20 years. Answer D
Question: Meena wrote all the numbers from 1 to 49,999 inclusive. How many digits did she write in total?
A.154,889
B.196,889
C.238,889
D.250,889
Answer: C.238,889
Explanation: 1-9=>1*9 digits
10-99=>2*90=180 (numbers between 10-99 is 90 where each has 2 digits)
100-999=>3*900=2700
1000-9999=>4*9000 = 36,000
10000-49999=>5*40,000 = 200,000
The answer is 238,889
The answer is C.
Question: On the first day of her vacation, Louisa traveled 160 miles. On the second day, traveling at the same average speed, she traveled 280 miles. If the 160-mile trip took 3 hours less than the 280-mile trip, what was the average speed, in miles per hour?
A.40
B.45
C.46
D.48
Answer: A.40
Explanation: (time)*(rate) = (distance)-->(rate) = (distance)/(time)--> given:(rate) = 160/t =280/(t+3)-->4/t = 7/(t+3)-->4t+12=7t ---->3t= 12 . t= 4 ---->(rate ) = 160/4 = 40
Answer: A
Question: If d is the standard deviation x, y, and z, what is the standard deviation of x - 5, y - 5, z - 5 ?
A.d
B.3d
C.15d
D.d + 5
Answer: A.d
Explanation: If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case SD won't change as we are subtracting 5 from each term in a set --> SD=d.
Answer: A.
Question: Which of the following CAN be the least common multiple of two positive integers 15 and 30?
A.15
B.30
C.10
D.5
Answer: B.30
Explanation: LCM of 15,30 is 30
Answer : B
Question: A traveler changes 150 pounds into rupees at the rate of Rs. 7000 for 100 pounds. He spends Rs. 9060 and changes the remaining amount back to pounds at the rate of 100 pounds to Rs. 7200. How many pounds will he get?
A.20 pounds
B.77 pounds
C.66 pounds
D.55 pounds
Answer: A.20 pounds
Explanation: Explanation:
Amount of rupees for exchange of 150 pounds = (150/100)*(7000/1) = Rs. 10,500
Out of these Rs.10,500, traveler spent Rs. 9060
Remaining balance in rupees = 10,500 – 9060 = Rs. 1440
Now these Rs. 1440 are exchanged back to pounds with the rate of 100 pounds for Rs. 7200
Amount in pounds = (1440 * 100) / 7200 = 20 pounds
ANSWER:A
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 180 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
A.2989
B.2765
C.6000
D.2989
Answer: C.6000
Explanation: Total production of salt by the company in that year
= 5000 + 5180 + 5360 + .... + 6980 = 72060.
Average monthly production of salt for that year
= 72060/12
= 6005.
Answer:C
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.90?
A.426
B.430
C.443
D.480
Answer: D.480
Explanation: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 7.9$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.9 $ left. so we buy 1 pack of 50 for 1$. We now have 0.9$ left, so we buy 30 individual envelopes. If we add up the numbers, we get 400+50+30=480 envelopes. Answer D
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 140 m length?
A.82.1 sec.
B.12.5 sec
C.19.1 sec.
D.17.1 sec.
Answer: B.12.5 sec
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 140 = 250 m.
Required time = 250/20 = 12.5 sec.
Answer: B
Question: If in a given number 5 8 9 4 3 2 7 6 1 4, we interchange the first and the second digits, the third and the fourth, the fifth and the sixth and so on, then counting from the right end, which digit will be sixth?
A.3
B.2
C.4
D.5
Answer: B.2
Explanation: after interchange
8 5 4 9 2 3 6 7 1 4
now count from right
sixth digit be 2
ANSWER:B
Question: Mixture of milk & water has been kept in two separate bowl. Ratio of milk to water in one of the bowls is 5 : 1 and that in the other bowl 7 : 2. In what ratio the mixtures of these 2 bowl should be added together so that the quantity of milk in the new mixture may become 80%?
A.2:3
B.3:4
C.4:7
D.5:7
Answer: A.2:3
Explanation: Lett. mixtures of the two containers be added together in the ratio of x
= = [ixoox l00%
Since the percentage quantity ofmilk in the new mixture is SO% — so% (45x + 42y) x 5 4 x 54(x y) 225x 210y 216.3E+216y
9x=6y
x:y=2:3
A
Question: Find out the square of a number which when doubled exceeds its one eighth by 15 ?
A.16
B.25
C.19
D.64
Answer: D.64
Explanation: Let the number be p, then the square will be p^2
According to question:
2p = (p/8) +15
=> 16p = p + 120
=> p = 8
p^2 = 8^2 = 64.
Answer : D
Question: Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
A.45 × 120 + 5(2) × 10
B.113 × 25 × 2
C.27 × 25 × 8 + 15 × 6 + 4 × 40
D.226 × 5 + 113 × 45 =
Answer: D.226 × 5 + 113 × 45 =
Explanation: Others equal 5650.
Answer D
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
A.1000
B.2777
C.9999
D.2777
Answer: A.1000
Explanation: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer: a
Question: A baseball card decreased in value 20% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
A.28%
B.30%
C.32%
D.36%
Answer: A.28%
Explanation: Let the initial value of baseball card = 100
After first year , value of baseball card = (1- 20/100)* 100 = 80
After second year , value of baseball card =(1 - 10/100)* 80 = 72
total percent decrease of the card's value over the two years = (100-72)/100 *100%
=28%
Answer A
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 11 consecutive spaces in a random direction, what is the probability the piece ends no more than 11 spaces from the square numbered 49?
A.23%
B.24%
C.25%
D.26%
Answer: A.23%
Explanation: No more than 11 spaces from 49 means in the rangefrom 49-11=38 to 49+11=60, inclusive. Total numbers in this range 60-38+1=23, the probability favorable/total=23/100
Answer: A
Question: A block of wood has dimensions 10cm x 10cm x 90cm. The block is painted red and then cut evenly at the 45 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?
A.5%
B.10%
C.15%
D.20%
Answer: A.5%
Explanation: The area of each half is 100+4(450)+100 = 2000
The area that is not painted is 100.
The fraction that is not painted is 100/2000 = 1/20 = 5%
The answer is A.
Question: Ashok secured average of 78 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
A.38
B.98
C.99
D.17
Answer: B.98
Explanation: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 78
Therefore total marks in 6 subjects = 78 * 6 = 468
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 468 – 370 = 98
ANSWER: B
Question: The cost of 20 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
A.Rs 42
B.Rs 56
C.Rs 58.50
D.Rs 64.75
Answer: A.Rs 42
Explanation: Explanation :
Let the required cost be Rs. x. Then,
More packets, More cost (Direct Proportion)
More weight, More cost (Direct Proportion)
Packets 20 : 27
Weight 900 : 1000 :: 28 : x
(20 x 900 x x) = (27 x 1000 x 28)
x = (27 x 1000 x 28) /20 x 900
=42
Answer A
Question: 4, 5, 7, 11, 19, (...)
A.22
B.35
C.27
D.32
Answer: B.35
Explanation: Explanation :
4
4 × 2 - 3 = 5
5 × 2 - 3 = 7
7 × 2 - 3 = 11
11 × 2 - 3 = 19
19 × 2 - 3 = 35
Answer : Option B
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
A.1800
B.900
C.2500
D.2700
Answer: A.1800
Explanation: Explanation:
Let required number of bottles be xx
More machines, more bottles (direct proportion)
More minutes, more bottles(direct proportion)
Hence we can write as
(machines) 6:10
(minutes) 1:4}::270:x
⇒6×1×x=10×4×270
⇒x=10×4×270/6
=10×4×90/2
=10×4×45=1800
Answer: Option A
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 12 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
A.A)11
B.B)23
C.C)24
D.D)29
Answer: B.B)23
Explanation: lets solve by creating equation..
W = 31..
Total = 50..
Not W = 50 -31= 19..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..
so who won Nobel but not Wolf = x+3 = 11..
But people who won BOTH W and N = 12..
so total who won N = 11+12 = 23..
B
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
A.150
B.240
C.108
D.369
Answer: C.108
Explanation: Explanation:
The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer: C
Question: 396, 462, 572, 427, 671, 264
A.396
B.427
C.671
D.264
Answer: B.427
Explanation: In each number except 427, the middle digit is the sum of other two.
Answer :B
Question: 8900 ÷ 6 ÷ 4 = ?
A.370.837
B.370.835
C.370.832
D.370.833
Answer: D.370.833
Explanation: Explanation:
Given Exp. 8900 * 1/6 * 1/4
= 370.833
ANSWER: D
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.70/10 sq.metre, whose base & perpendicular distance from the other side being 84m & 24m respectively?
A.s.2400
B.s.2016
C.s. 1400
D.s. 3480
Answer: B.s.2016
Explanation: Area of the parallelogram = Length of the base * Perpendicular height
= 84 * 24 = 2016 m.
Total cost of levelling = Rs. 2016
B