RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two spheres of their radios in the ratio 4 : 3. Find its volumes ratio?
A.64:13
B.13:64
C.27:64
D.64:27
Answer: D.64:27
Explanation: Sphere volume (V) = 4/3 πR(power3) : 4/3 π r(power3) = 4(power3) : 3(power3)
= 64 : 27
Answer is D.
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
A.407
B.756
C.347
D.248
Answer: B.756
Explanation: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
= (525 + 210 + 21)
= 756.
ANSWER B 756
Question: The sum of the present ages of A, B, C is 27 years. Three years ago their ages were in the ratio 1:2:3. What is the present age of A?
A.10
B.6
C.8
D.9
Answer: B.6
Explanation: Three years ago:
a:b:c = 1:2:3
Let a = 1x, b = 2x, and c = 3x.
Today:
(x+3) + (2x+3) + (3x+3) = 27
x = 3
So the present age of A is x+3 = 6
The answer is B.
Question: If u = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =
A.-2
B.-1
C.0
D.2
Answer: D.2
Explanation: Let us transform the formula:
u = (x – 5)² + (x +1)² – 6 =
x² – 10x + 25 + x² + 2x + 1 – 6 =
2x² – 8x + 20 = 2 × (x² – 4x + 10) =
2 × ((x² – 4x + 4) + 6) =
2 × ((x – 2)² + 6)
Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.
x – 2 = 0
x = 2
The correct answer is choice (D).
Question: When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 6. If 1 < m < 300, what is the greatest possible value of m?
A.157
B.177
C.197
D.227
Answer: D.227
Explanation: 13*9 = 117
Let's start with 6, and keep adding 13 until we find a number with the form 9k+2.
6, 19, 32, 45, 58, 71, 84, 97, 110 = 9*12+2
The next possible number is 110 + 117 = 227
The next possible number would be greater than 300.
The answer is D.
Question: The two lines y=x and x=-5 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
A.7.5
B.10
C.12.5
D.15
Answer: C.12.5
Explanation: The point of intersection is (-5,-5).
The triangle has a base of length 5 and a height of 5.
area = (1/2)*base*height = (1/2)*5*5 = 12.5
The answer is C.
Question: A Techno company has 14 machines of equal efficiency in its factory. The annual manufacturing costs are Rs 42,000 and establishment charges are Rs 12,000. The annual output of the company is Rs 70,000. The annual output and manufacturing costs are directly proportional to the number of machines. The shareholders get 12.5 profit, which is directly proportional to the annual output of the company. If 7.14 machines remain closed throughout the year, then the percentage decrease in the amount of profit of the shareholders would be:
A.12%
B.12.5%
C.13.5%
D.13%
Answer: B.12.5%
Explanation: Explanation :
The original profit is:-
=>70,000−42,000−12,000=16,000.
If 7.14% of 14 i.e. one of the machines closed throughout the year, then the change in profit will be :-
=>(13/14)×[70,000−42,000].
=>14,000.
Thus, decrease in the profit % is:-
=>(2000/16000) × 100.
=>12.5%.
Answer : B
Question: From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 6 kilometers per hour, while Ferry Q takes a route that is two times longer. If Ferry P is slower than Ferry Q by 3 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P?
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: The distance traveled by Ferry P is 18 km.
Then the distance traveled by Ferry Q is 36 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 36/9 = 4 hours, which is 1 hour more than Ferry P. The answer is A.
Question: Two persons , Ram & Lakshman , who are at a distance of 100 km from each other, move towards each other from two places P and Q at speeds of 20 kmph and 25 kmph respectively. Lakshman reaches P, returns immediately and meets Ram at R, who started on the return journey to P immediately after reaching Q. What is the distance between Q and R?
A.33 1/3 km
B.25 km
C.30km
D.27 1/3 km
Answer: A.33 1/3 km
Explanation: Ram takes 100/20 = 5 hours to cover the distance from P to Q. By that time Lakshman covers
covers 5 *25 = 125 km
Lakshman covers 25 km more than the distance PQ . Now the distance between them = 75 km
Time taken by them to meet = Distance/ Relative speed = 75/(20+25) = 75/45 = 5/3 hrs.
Distance between Q and R is nothing but the distance covered by Ram in 5/3 hours = 20 *5/3 = 100/3 km or 33 1/3 km
Answer: A
Question: Mark is playing poker at a casino. Mark starts playing with 130 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark's remaining chips are $20 chips, how much money did Mark bet?
A.$1,960
B.$1,740
C.$1,820
D.$3,080
Answer: C.$1,820
Explanation: Total chips 130
20% of $100 chips = 26 chips * $100 = $2,600
80% of $20 chips = 104 chips * $20 = $2,080
If x is the number of chips bet and y is the amount of chips remaining:
x + y = 130
y = 130 - x ~ (1)
[First round bet] + [Second round bet] = $2,600 + $2,080
[0.1x * $100 + 0.9x * $20] + [0.3y * $100 + 0.7y * $20] = $4,680
10x + 18x + 30y + 14y = 4680
28x + 44y = 4680 ~ (2)
Substitute (1) into (2) to solve for x:
28x + 44(130 - x) = 4680
28x + 5720 - 44x = 4680
16x = 1040
x = 65
Substituting x:
[First round bet] = [0.1x * $100 + 0.9x * $20] = 0.1(65)($100)+0.9(65)($20) = $650 + $1,170 = $1,820
Answer is C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
A.29
B.27
C.36
D.88
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 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer:C
Question: Six water bottle gather at the place. Three teams of 3 bottle each will be packed. How many ways are there to create these 3 teams?
A.27
B.45
C.90
D.175
Answer: B.45
Explanation: Arrange the 6 water bottle in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (B)
You get 6!/(2! * 2! * 2!) * 2!
Answer : B
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability E that the number of men is equal to that of women?
A.E=18/35
B.16/35
C.14/35
D.13/35
Answer: A.E=18/35
Explanation: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Question: A certain fraction of a 15% salt solution by weight was replaced by a 25% salt solution by weight. The resulting solution has 21 % salt by weight. What fraction of the original solution was replaced?
A.1/2
B.3/5
C.2/3
D.7/10
Answer: B.3/5
Explanation: 15% salt solution was mixed with 25% salt solution to give 21% salt solution. So we can find the ratio of the weights in which the two were mixed.
w1/w2 = (25 - 21)/(21 - 15) = 4/6 = 2/3
So for every 2 parts of 15% solution, we have 3 parts of 25% solution. So 3/5th of the original solution was replaced.
Answer (B)
Question: In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:
A.3
B.7
C.8
D.6
Answer: D.6
Explanation: A : B = 100 : 90.
A : C = 100 : 87.
\inline \fn_jvn {\color{Black}\therefore \frac{B}{C}=\left ( \frac{B}{A} \times \frac{A}{C}\right )=\left ( \frac{90}{100}\times \frac{100}{87} \right )=\frac{30}{29}}
When B runs 30 m, C runs 29 m.
When B runs 180 m, C runs \inline \fn_jvn {\color{Black}\left ( \frac{29}{30} \times 180\right )m}=174m
\inline \fn_jvn {\color{Blue}\therefore } B beats C by (180 - 174) m = 6 m.
Answer: D) 6m
Question: A 50 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
A.24.28
B.14.28
C.16.28
D.18.28
Answer: B.14.28
Explanation: 1: 2/5 = 5: 2
2/7 * 50 = 14.28
ANSWER:B
Question: A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe. If the largest size of this shoe is 10% longer than the smallest size, how long, in inches, is the shoe in size 15?
A.18.25
B.20.75
C.22.25
D.24.25
Answer: D.24.25
Explanation: Let x be the length of the size 8 shoe.
Then 0.1x = 9/4
x = 90/4 inches
The size 15 shoe has a length of 90/4 + 7/4 = 97/4 = 24.25 inches
The answer is D.
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
A.120%
B.190%
C.100%
D.200%
Answer: C.100%
Explanation: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 15
III. P is a multiple of 23
A.I only
B.II only
C.III only
D.None of the above
Answer: B.II only
Explanation: Answer = B) II only
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 50.
A.3
B.4
C.12
D.32
Answer: C.12
Explanation: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by50, remainder will be -4 i.e. n will be 4 less than a multiple of 50. So you must add 12 to n to make it a multiple of 50
C
Question: The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 7 students?
A.14 years
B.17 years
C.19 years
D.38 years
Answer: D.38 years
Explanation: Solution
Sum of the ages of 14 students	= (16 x 35) - (14 x 21)
= 560 - 294.
= 266.
∴ Required average	= 266 / 7
= 38 years.
Answer D
Question: The ratio of investments of A, B and C is 10:12:14. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments.
A.2:3:6
B.4:6:8
C.3:2:4
D.2:4:3
Answer: B.4:6:8
Explanation: The ratio of investments of A, B and C is 10:12:14 or 5:6:7. [divided by 2]
The ratio of shares of A, B and C is 5:9:14.
Therefore, Ratio of their periods of investments is
(5/5) : (9/6) : (14/7) = 1:3/2:2 = 2:3:4 or 4:6:8
ANSWER:B
Question: The average of runs of a cricket player of 10 innings was 36. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
A.76
B.80
C.85
D.87
Answer: B.80
Explanation: Explanation:
Average = total runs / no.of innings = 36
So, total = Average x no.of innings = 36 x 10 = 360.
Now increase in avg = 4runs. So, new avg = 36+4 = 40runs
Total runs = new avg x new no. of innings = 40 x 11 = 440
Runs made in the 11th inning = 440 - 360 =80 Answer: B
Question: If |x - 25| = 50 what is the sum of all the values of x.
A.0
B.-100
C.-50
D.50
Answer: D.50
Explanation: There will be two cases
x-25 = 50 and x-25 = -50
Solve for x => x=50+25=> x=75 or x= -50+25=> x=-25
The sum of both values will be 75 + -25 =50
Answer is D
Question: Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?
A.7 : 8
B.7 : 2
C.7 : 1
D.7 : 6
Answer: D.7 : 6
Explanation: Explanation:
Let x be the investment of Ravi in 6% and y be in 7%
x(6)(n)/100 = y(7)(n)/100
=> x/y = 7/6
x : y = 7 : 6
Answer: D
Question: Mike needs 30% to pass. If he scored 212 marks and falls short by 28 marks, what was the maximum marks he could have got?
A.343
B.677
C.800
D.867
Answer: C.800
Explanation: If Mike had scored 28 marks more, he could have scored 30%
Therefore, Mike required 212 + 28 = 240 marks
Let the maximum marks be m.
Then 30 % of m = 240
(30/100) × m = 240
m = (240 × 100)/30
m = 24000/30
m = 800
Answer:C
Question: A Museum decorated with bunch of lights and those lights glow for every 13 seconds. How many times did it glow between 1:57:58 and 3:20:47??
A.380
B.381
C.382
D.383
Answer: C.382
Explanation: find out difference between both times that is 1:22:49 total no of seconds that is 4969 then divided by 13 so the ans is
382
ANSWER:C
Question: The total surface area of a cuboid length 12 m, breadth 10 m and height 8 m.
A.576
B.566
C.596
D.556
Answer: C.596
Explanation: Total surface area of cuboid
= 2 (lb+bh+lh)
= 2 (120 + 80+ 96)
= 2 (296) => 596 m(power2)
Answer is C.
Question: The weight of four dogs is determined to be 25 pounds, 31 pounds, 51 pounds and 41 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?
A.31
B.33
C.35
D.37
Answer: D.37
Explanation: Total weight of the 4 dogs = (25+31+51+41) = 148
Avg = 148/4 = 37
Total weight of 5 dogs = 148+y or 4(37)+y
Average of 5 dogs as per Question = 37
Equation:
4(37) + y = 5 (37), or y = 37.
Choose D
Question: If 20% of a class averages 80% on a test, 50% of the class averages 60% on the test, and the remainder of the class averages 40% on the test, what is the overall class average?
A.80%
B.74%
C.58%
D.56%
Answer: C.58%
Explanation: 2 students scored 80%
5 students scored 60%
3 students scored 40%
(2)(80) + 5(60) + 3(40) =
160 + 300 + 120 =
580
580/10 students = 58 --> 58% average
ANSWER:C
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
A.228
B.640
C.267
D.187
Answer: B.640
Explanation: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer: B
Question: ohn invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
A.3/5
B.2/3
C.7/10
D.3/4
Answer: A.3/5
Explanation: X(1+10/100) + Y(1-15/100) = X+Y
this gives 2X = 3Y
or X/Y = 3/2
So, fraction invested in X = 3/5
ANSWER:A
Question: It is currently 8:34 PM. At what time in the morning was it exactly 39,668 minutes ago?
A.7:22
B.7:24
C.7:26
D.7:28
Answer: C.7:26
Explanation: Divide 39,668 by 60 to convert to minutes: 39,668/60 = 661 R8. That is 661 hours, 8 minutes. All of the answer choices are during the same hour before :34, so we can assume the 661 hours takes the time back into the 7AM hour to 7:34AM. Going back 8 more minutes yields the time 7:26AM. C
Question: Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 36, find the ages of Toby and Debby?
A.10 and 14
B.5 and 9
C.4 and 8
D.6 and 10
Answer: C.4 and 8
Explanation: Let the age of Debby be x and Toby be x-4
3 ( x + x-4 ) = 36
x = 8
The ages of Toby and Debby are 4 and 8.
Answer : C
Question: There are 27 different three-digit integers that can be formed using only the digits 2, 3 and 4. If all 27 of the integers were listed, what would their sum be?
A.8991
B.9001
C.9011
D.9021
Answer: A.8991
Explanation: There must be nine 2's in the hundreds place, nine 2's in the tens place, and nine 2's in the units place. This is also true for the 3's and 4's. Then the sum is:
9(222+333+444)=9*(999)=8991.
The answer is A.
Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
A.2/27
B.1/42
C.1/18
D.1/38
Answer: B.1/42
Explanation: Answer: Option B
2/3 : 6/7 : 1/3 : 1/8 = 1/42
Question: What is the value of n if the sum of the consecutive odd intergers R from 1 to n equals 169?
A.47
B.25
C.37
D.33
Answer: B.25
Explanation: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.
Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.
a=1 (first term)
d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2
*On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.
But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.
Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.
It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Question: Of the a students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
A. a + w- x- y
B. a - w- x- y
C. a- w - x + y
D. w + x + y- z
Answer: A. a + w- x- y
Explanation: {Total} = {French} + {German} - {Both} + {Neither}
a = x + y - w + {Neither}
{Neither} = a + w - x - y.
Answer: A.
Question: The speed of a boat in still water is 14 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 8 minutes is
A.1.6 km
B.2.5 km
C.3.6 km
D.4 km
Answer: B.2.5 km
Explanation: Explanation:
Speed downstreams	=(14+ 5)kmph
= 19 kmph.
Distance travelled	= (19 x 8/60)km
= 2.5 km
Option B
Question: The sum w of prime numbers that are greater than 60 but less than 70 is
A. 67
B. 128
C. 191
D. 197
Answer: B. 128
Explanation: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum w of 61 and 67 is 128.
Answer B.
Question: A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 4 new workers. How many different ways can she assign the new workers?
A.1485
B.2700
C.3300
D.4860
Answer: A.1485
Explanation: whatever : my take selecting team of 4 out of 12 to assign to the shifts = 12C4 = 495 ways.
now 4 out of 12 means total of 3 group possible.
so putting them in shifts = counting methode: first, second, third,
= 3*2*1 = 6
here alt and alt are the same: so 6/2 = 3 ways.
total ways of selecting = (selecting 4 out of 12)*arranging those teams in shifts
= 495*3 = 1485
Ans: A
Question: If a - b =2 and
a2+b2=36
, find the value of ab.
A.16
B.32
C.48
D.12
Answer: A.16
Explanation: Explanation:
We know
2ab=(a2+b2)âˆ’(aâˆ’b)2
2ab=36âˆ’4=32
=>ab=16
Option A
Question: Tom bought 2 shares and sold them for $88 each. If he had a profit of 10% on the sale of one of the shares but a loss of 12% on the sale of the other share, then on the sale of both shares Tom had
A. a loss of $4
B. a profit of $4
C. a profit of $8
D. a loss of $8
Answer: A. a loss of $4
Explanation: total CP = 8800/110 + 8800/88 = 80 + 100=180
SP=88*2=176
loss= Rs 4/-
Answer: A
Question: Machine A produces 100 parts thrice as fast as Machine B does. Machine B produces 100 parts in 30 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 6 minutes?
A.20
B.80
C.40
D.60
Answer: D.60
Explanation: Machine B produces 100 part in 30 minutes. Machine A produces 100 parts thrice as fast as B, so Machine A produces 100 parts in 30/3=10 minutes.
Now, Machine A produces 100 parts in 10 minutes which is 100/10 = 10 parts/minute.
10 parts X a total of 6 minutes = 60
D