RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If a committee of 2 people is to be selected from among 4 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A.24
B.40
C.50
D.80
Answer: A.24
Explanation: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 4C2=6.
But these 2 chosen couples can send two persons (either husband or wife): 2*2=2^2=4.
Total # of ways: 4C2*2^2=24.
Answer: A
Question: This year, MBB Consulting fired 10% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction?
A.99%
B.100.0%
C.102.8%
D.104.5%
Answer: A.99%
Explanation: 100 employees getting 1000$ avg, so total salary for 100 ppl = 100000
10% reduction in employees lead to 90 employees and a salary increase of 10% of previous avg salary
Thus the new avg salary is = 10%(1000)+1000 = 1100
so total salary of 90 employees is 90*1100 = 99000
Now the new salary is more than previous salary by x%. x = (99000/100000)*100 = 99%
So the Answer is A
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
A.16 a.m
B.10 a.m
C.17 a.m
D.15 a.m
Answer: B.10 a.m
Explanation: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: B
Question: The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface?
A.18 πr2
B.12πr2
C.3 πr2
D.6 πr2
Answer: B.12πr2
Explanation: Explanation:
2 * π * 2r * 3r = 12πr2
Answer: B
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?
A.7/22
B.7/25
C.8/21
D.8/23
Answer: C.8/21
Explanation: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
C)
Question: If xy represents a positive two digit number, where x and y are single digit integers, which of the following cannot be true?
A.x+y =9
B.(x)(y)=9
C.x-y = 9
D.y-x= 9
Answer: D.y-x= 9
Explanation: (A) xy = 45 or 63 or 27
(B) xy = 33 or 19
(C) 90
(D) impossible
(E) xy = 91
(D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).
ans D
Question: A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 200 oranges are used, how many limes are needed?
A.200
B.700
C.1400
D.2800
Answer: C.1400
Explanation: 10%= 200 fruit
100%=2000 fruit
70% of 2000 fruit=1400 fruit
1400 limes
ANSWER:C
Question: A company has 600 employees, 40% of whom are employed part time. If it hires 60 new employees, 15% of whom are employed part time, what will be the percent increase in part time employees?
A.1 2/3 %
B.2 2/3 %
C.4 %
D.3.61 %
Answer: D.3.61 %
Explanation: Total employee = 600
Part time Empl = 600 * 40/100 =240
New part time empl = 60 * (15/100)
=9
Total new part time Emp = 9+240= 249
Old part time Emp = 240
% increase = (new - old)*100/old
=9*100/249
= 3.61 %
Ans-D
Question: A password for a computer uses six digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?
A.1/32
B.1/64
C.1/8
D.2/5
Answer: B.1/64
Explanation: To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for six digits is 10 x 10 × 10 × 10 × 10 × 10 = 1,000,000 possible combinations.
Prime numbers constitute 2, 3, 5, 7 and 11. In addition to zero, this is 5 total possibility for each digit. So the number of satisfactory variants is 6 x 6 × 6 × 6 × 6 × 6. So the probability is 1/2 x 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/64.
The right answer is choice (B).
Question: The fourth proportional to 12, 16 and 18 is?
A.24
B.66
C.55
D.88
Answer: A.24
Explanation: (15*18)/12
= 24
Answer:A
Question: A side of beef lost 30 percent of its weight in processing. If the side of beef weighed 500 pounds after processing, how many pounds did it weigh before processing?
A.714.28
B.712
C.714.88
D.714.25
Answer: A.714.28
Explanation: Let weight of side of beef before processing = x
(70/100)*x = 500
=> x = (500 * 100)/70 = 714.28
Answer A
Question: Find a sum for first 5 prime number'ss?
A.22
B.28
C.29
D.32
Answer: B.28
Explanation: Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Option B
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
A.111
B.771
C.200
D.873
Answer: C.200
Explanation: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.
Answer: C
Question: A school has 4 section of Chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
A.50.25
B.52.25
C.51.25
D.53.25
Answer: B.52.25
Explanation: Required average marks
= 40×50+35×60+45×55+42×45/40+35+45+42
= 2000+2100+2475+1890/162
= 8465⁄162 = 52.25
Answer B
Question: How many integers are divisible by 3 between 10! and 10! + 40 inclusive?
A.6
B.7
C.8
D.13
Answer: D.13
Explanation: D - 7
10! is divisible by 3
There are 12 numbers between 10! and 10!+40 that are divisible by 3.
Hence 13
Question: A scuba diver descends at a rate of 35 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3500feet below the sea level..how long will he take to reach the ship?
A.160 minutes
B.120 minutes
C.100 minutes
D.76 minutes
Answer: C.100 minutes
Explanation: Time taken to reach = 3500/35= 100 minutes
ANSWER:C
Question: In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (−4, −4)?
A.4
B.2
C.0
D.−2
Answer: A.4
Explanation: slope = rise/run = 7/14 = 1/2
The equation of the line is y = (1/2)x + b
3 = (1/2)(10) + b
b = -2
The equation of the line is y = (1/2)x - 2
To find the x-intercept, let y = 0:
0 = (1/2)x - 2
x = 4
The answer is A.
Question: A sum of 11,500 amounts to 13,500 in 5 years at the rate of simple interest. What is the rate of interest?
A.2%
B.3%
C.6%
D.5%
Answer: B.3%
Explanation: B
3%
S.I. = (13500 - 11500) = 2000.
Rate = (100 x 2000)/(11500x5)% = 3%
Question: If two balls are randomly selected from a green urn containing 8 black and 8 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?
A.A.2/9
B.B.4/9
C.C.5/9
D.D.7/30
Answer: D.D.7/30
Explanation: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.
Probability (first ball is white) = 8/16
Probability(second ball is white) = 7/15
Probability (both balls are white) = (8/16)*(7/15) = 7/30
Answer D
Question: A man purchased 4 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
A.A)300
B.B)350
C.C)450
D.D)470
Answer: B.B)350
Explanation: Explanation:
10 * 150 = 1500
4 * 100 + 5 * 150 = 1150
1500 – 1150 =350
B
Question: If 1/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c 1 0; abc 1 0, then what is the value of ( a
+ b ) ( b + c ) ( c + a )?
A.Equal to 0
B.Greater than 0
C.Less than 0
D.Less than 1
Answer: A.Equal to 0
Explanation: 1/a+1/b+1/c=1/(a+b+c)
or (bc+ac+ab)/(abc)=1/(a+b+c)
or (ab+bc+ac)(a+b+c)=abc
or abc+(a^2)c+(a^2)b+(b^2)c+abc+(b^2)a+(c^2)b+(c^2)a+abc=abc
or 2abc+(a^2)c+(a^2)b+(b^2)c+(b^2)a+(c^2)b+(c^2)a=0
also,
( a+ b ) ( b + c ) ( c + a )=2abc+(a^2)c+(a^2)b+(b^2)c+(b^2)a+(c^2)b+(c^2)a
or ( a+ b ) ( b + c ) ( c + a )=0
ANSWER:A
Question: A truck traveled 120 km with a speed of 60 kmh. How much time did it take to reach the destination?
A.3 hours
B.4 hours
C.5 hours
D.2 hours
Answer: D.2 hours
Explanation: Time = Distance/Speed
120/60 = 2
Answer: D
Question: A worker makes a toy in every 2h. If he works for 120h, then how many toys will he make ?
A.40
B.60
C.45
D.39
Answer: B.60
Explanation: No. of toys = 120/2 = 60
Answer : B
Question: From the integer n, if n*n is odd, then what is true from below options?
A.n is odd
B.n*n*n is even
C.n is even and n*n*n is even
D.n is even
Answer: A.n is odd
Explanation: n is odd
Option A
Question: If a wholesaler distributes items to several outlets (A, B, C and D) in the ratio of 1/2 : 1/11 : 1/12 : 1/13 then find the total number of items the wholesaler distributes?
A.289
B.1289
C.1389
D.1281
Answer: B.1289
Explanation: Here, A : B : C : D = 1/2 : 1/11 : 1/12 : 1/13
1) L.C.M of 2 : 11 : 12 : 13 is 1716
2) Find the number of books each friend received --------- (To find no. of books each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/2) x 1716 = 858
B = (1/11) x 1716 = 156
C = (1/12) x 1716 = 143
D = (1/13) x 1716 = 132
3) Total number of toys = (858 x + 156 x + 143 x + 132 x) = 1289 x
Minimum number of pens (x) = 1
Therefore, total number of items= 1289 items.
Correct option :B
Question: Which is better investment 11% stock at 143 or 9 ¾% stock at 117
A.11% stock at 143
B.9 3/4 % stock at 117
C.Both
D.Cannot be compared
Answer: B.9 3/4 % stock at 117
Explanation: Let the investment in each (143*117)
Income in first case = (11/143*143*117)=1287
Income in second case=((39/117*4)*143*117)=1394.25
Clearly, 9 ¾% stock at 117
Option B
Question: If x is less than y by 35% then y exceed x by:
A.33.33%
B.25%
C.75%
D.53.85%
Answer: D.53.85%
Explanation: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 35%)
=> 35/(100-35)*100
=53.85%
ANSWER:D
Question: A is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?
A.10 days
B.77 days
C.66 days
D.55 days
Answer: A.10 days
Explanation: A can do the work in 30/2 i.e., 15 days.
A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10
So A and B together can do the work in 10 days.
Answer: A
Question: A man deposits $2000 in a bank at 4% per annum and $ 3000 in UTI at 14% per annum. Find the rate of interest for the whole sum.
A.15%
B.18%
C.11%
D.17%
Answer: D.17%
Explanation: Following the above formula,we have the rate of interest for the whole sum
=(2000*4)+(3000*14)/2000+3000=50000/5000=10%.
Answer is D
Question: The average age of three boys is 25 years and their ages are in proportion 3:5:7. What is the age in years of the eldest boy?
A.6
B.19
C.35
D.45
Answer: C.35
Explanation: 3x + 5x + 7x = 75
x =5
7x =35
Answer:C
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 117 grams of water?
A.100
B.102
C.104
D.106
Answer: C.104
Explanation: (16/18)*117 = 104 grams
The answer is C.
Question: The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 42 per kg. The inflation rate for the years 1994 and 1995 are expected to be 16% each. The expected price of sugar on January 1, 1996 would be
A.58.48
B.56.4
C.50.6
D.24.6
Answer: A.58.48
Explanation: Explanation :
Increase in the price of sugar = (16+2)= 18%
Hence, price of the sugar on Jan 1, 1996
=> (42 * 118 * 118)/( 100 * 100 ) = Rs 58.48.
Answer : A
Question: During a certain week, a seal ate 50% of the first 80 smelt it came across, and 20% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
A.48
B.40
C.55
D.64
Answer: A.48
Explanation: Total smelt = x.
Then, 0.5*80+0.2(x-80)=0.4*x --> x=120 --> 0.4*x=48.
Answer: A.
Question: An urn contains 5 red, 6 blue and 8 green balls. 4 balls are randomly selected from the urn, find the probability that the drawn ball are 1 blue and 1 red and 2 green balls ?
A.70/323
B.50/323
C.52/969
D.60/323
Answer: A.70/323
Explanation: Sample space = no. of ways 4 balls were drawn from urn = 19C4 = 3876
No. ways 1 blue and 1 red and 2 green balls were drawn from bag = 6C1 * 5C1 * 8C2 = 840
Probability = 840 / 3876 = 70/323
Ans - A
Question: 100 white and black tiles will be used to form a 20x20 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
A.75
B.80
C.85
D.70
Answer: D.70
Explanation: Answer = D
Please refer diagram below
80 - 10 = 70
Question: If y is 25 percent greater than x, then x is what percent less than y?
A.12.5%
B.15%
C.20%
D.25%
Answer: C.20%
Explanation: y = 1.25x
x = y/1.25 = 4y/5 = y - (1/5)*y
1/5 is 20%.
The answer is C.
Question: A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in one hour?
A.6 metre
B.12 metre
C.120 metre
D.1200 metre
Answer: C.120 metre
Explanation: Number of times wheel moves in 1 hour = 10 * 60 = 600
:. Distance moves = (600 *20) cms = 12000 cms
In metres = 120 metre
ANSWER:C
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 22 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.877 m
B.210 m
C.167 m
D.887 m
Answer: B.210 m
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 22)m = 330 m. Let the length of the platform be x meters. Then, (x + 330)/36 = 15
==> x + 330 = 540 ==> x
= 210 m.
Answer: B
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.177m
B.180m
C.167m
D.197m
Answer: B.180m
Explanation: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Question: Sandy bought 65 books for $1080 from one shop and 55 books for $840 from another shop. What is the average price that Sandy paid per book?
A.$14
B.$16
C.$18
D.$20
Answer: B.$16
Explanation: average price per book = (1080 + 840) / (65 + 55) = 1920 / 120 = $16
The answer is B.
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds b in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
A.25%
B.35%
C.45%
D.70%
Answer: B.35%
Explanation: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5 = 280. Kingfishers, therefore, are 280/4 = 70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers = 650. So all others are 1000 - 650= 350 or 35% of total birds.
The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.
2. Another method: If X is total --> Non Hawks = 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).
Our job is to find out b: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find 1-0.65 = 0.35 or 35%.B
Question: The sum of the even numbers between 1 and n is 81*82, where n is an odd number, then n=?
A.163
B.171
C.177
D.185
Answer: A.163
Explanation: Let n-1 = 2a.
2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 81*82
Then a = 81 and n = 163.
The answer is A.
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3659
A.3659
B.9654
C.5945
D.7963
Answer: A.3659
Explanation: The product of first two digits in a number equals the last two digits, except in 3659. Hence, it is the odd one.
The answer is 3659.
ANSWER:A
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.45
B.60
C.75
D.90
Answer: D.90
Explanation: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Answer: Option D
Hence, total number of notes = 3x = 90.
Question: John covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
A.10 Kmph
B.15 Kmph
C.17 Kmph
D.18 Kmph
Answer: B.15 Kmph
Explanation: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
B)
Question: What is the ratio Q of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
A.1/4
B.3/8
C.1/2
D.3/5
Answer: D.3/5
Explanation: Let X be the side of the cube. Therefore X^2*6= surface area.
the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.
6X^2/10X^2 = 3/5.= Q
Answer = D
Question: The number of cars present at a particular time was measured at 2,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 15% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
A.1,159
B.1,394
C.1,860
D.2,460
Answer: B.1,394
Explanation: The question states that all these 2,999 locations were measured twice, once on each day.
It also breaks the 2,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 2999
But, for the second day count, W = 1.15 T
i.e. for Second day count, T + 1.15T = 2999
i.e. 2.15 T = 2999
i.e. T = 1394
B
Question: The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?
A.17.5 km/hr
B.27.5 km/hr
C.67.5 km/hr
D.87.5 km/hr
Answer: D.87.5 km/hr
Explanation: Explanation:
Let the speeds of two trains be 7X and 8X km/hr.
8x = {\color{Blue} \frac{400}{4}}
=> x= 12.5 km/hrX=4004=>X=12.5Km/hr
So speed of first train is 12.5*7 = 87.5 km/hr
Answer: D
Question: The difference between the squares of two consecutive numbers is 37. Find the numbers.
A.38 and 19.
B.28 and 19.
C.18 and 19.
D.18 and 29.
Answer: C.18 and 19.
Explanation: Solution:
If the difference between the squares of two consecutive numbers is x, then the numbers are (x-1)/2 and (x+1)/2
(37-1)/2 and (37+1)/2
36/2 and 38/2
Therefore the required answer = 18 and 19.
Answer C
Question: If 4 people are selected from a group of 6 married couples, what is the probability that none of them would be married to each other?
A.1/33
B.2/33
C.1/3
D.16/33 probability
Answer: D.16/33 probability
Explanation: Each couple can send only one "representative" to the committee. We can choose 4 couples (as there should be 4 members) to send only one "representatives" to the committee in C46C64 # of ways.
But these 4 chosen couples can send two persons (either husband or wife): 2∗2∗2∗2=242∗2∗2∗2=24.
So # of ways to choose 4 people out 6 married couples so that none of them would be married to each other is: C46∗24C64∗24.
Total # of ways to choose 4 people out of 12 is C412C124.
P=C46∗24C412=1633P=C64∗24C124=1633
Answer: D.
Question: If in a race of 70m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
A.20m
B.16m
C.14m
D.10m
Answer: C.14m
Explanation: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (70 * 5) / 25 = 14m
Hence, A beats B by 14m.
ANSWER C
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
A.10
B.9
C.11
D.12
Answer: A.10
Explanation: 4/12 + x/15 = 1
x = 10
ANSWER A
Question: A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 80 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of family?
A.3/7years
B.B)31
C.C)30
D.D)33
Answer: A.3/7years
Explanation: Required average
= (80 x 2 + 35 x 2 + 6 x 3 )/(2 + 2 + 3)
= (160 + 70 + 18)/7
= 248/7
= 35 3/7years.
Answer is A
Question: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 4, when a # b = 100?
A.5
B.9
C.10
D.13
Answer: B.9
Explanation: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 4 = 10/2 + 4 = 9.
The correct answer is B.
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $131 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
A.3
B.5
C.7
D.9
Answer: D.9
Explanation: $131 = 25*$5 + 2*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 25, 22, 19, 16,...,1 for a total of 9 combinations.
The answer is D.
Question: The length of the bridge, which a train 135 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.76 m
B.178 m
C.240 m
D.187 m
Answer: C.240 m
Explanation: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (135 + x)/30 = 25/2
=> 2(135 + x)= 750 => x = 240 m.
Answer: C
Question: What is the smallest integer that, when increased by seven, is divisible by 14, 25, 36, and 81?
A.1020600
B.1020593
C.56693
D.28343
Answer: C.56693
Explanation: 14 = 2 * 7
25 = 5 * 5
36 = 2 * 2 * 3 * 3
81 = 3 * 3 * 3 * 3
So our answer is (2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 * 7) - 7 = 56693, which is option C.