RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In the xy-coordinate system, if (m, n) and (m 1 2, n 1 k) are two points on the line
with the equation x 5 2y 1 5, then k 5
A.1/2
B.1
C.2
D.5/2
Answer: B.1
Explanation: Step 1: Analyze the Question
For any question involving the equation of a line, a good
place to start is the slope-intercept form of the line,
y = mx 1 b. Remember that if you have two points on a
line, you can derive the entire equation, and if you have an
equation of the line, you can calculate any points on that
line.
Step 2: State the Task
We are solving for k, which is the amount by which the
y-coordinate increases when the x-coordinate increases
by 2.
Step 3: Approach Strategically
The slope of a line is the ratio between the change in y and
the change in x. In other words, every time the x-coordinate
increases by 1, the y-coordinate increases by the amount
of the slope.
The equation of the line in the question stem is defined as
x = 2y + 5. We must isolate y to have slope-intercept form:
So the slope of this line is 1/2 . This means that for every
change of +1 in the x direction, there is a change of + 1/2
in the y direction. Then we know that, because there is an
increase in 2 units in the x direction when moving from
m to m + 2, there must be a change of 1 unit in the y
direction when moving from n to n + k. So k = 1.
Since there are variables that eventually cancel (m and n
are not part of the answers), we can Pick Numbers. Let’s
say that you choose the y-coordinate of the point (m, n) to
be 0 to allow for easier calculations. Using the equation
we’re given to relate x- and y-coordinates, we can calculate
the x-coordinate:
So (m, n) is the point (5, 0).
Now we’ll plug our values of m and n into the next point:
(m + 2, n + k). That yields (7, k). All we have to do is plug
an x-coordinate of 7 into the equation to solve for k, the
y-coordinate:
Answer is B
Question: Sarah is driving to the airport. After driving at 20 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 50 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
A.140
B.175
C.210
D.70
Answer: D.70
Explanation: After driving at 20 miles per hourfor one hour, this distance left to cover is d-20. Say this distance is x miles.
Now, we know that the difference in time between covering this distance at 20 miles per hour and 50 miles per hour is 1+ 1/2 = 3/2 hours.
So, we have that x/20 - x/50 = 3/2 --> 5x/100 - 2x/100 = 3/2 --> 3x/100 = 3/2 --> x = 50.
Total distance = x + 20 = 70 miles.
Answer: D
Question: If the price of an item is decreased by 50% and then increased by 20%, the net effect on the price of the item is
A.A decrease of 99%
B.A decrease of 40%
C.A decrease of 1%
D.A increase of 1%
Answer: B.A decrease of 40%
Explanation: initially assume 100 rupees
50% discount in 100 gives price of 50 rupees
then 20% raise in 50 is only 10 rupees.
therefore total price =60 rupees.
hence 40% is the loss
ANSWER:B
Question: What distance will be covered by a bus moving at 72 kmph in 30 seconds?
A.700 m
B.500 m
C.800 m
D.600 m
Answer: D.600 m
Explanation: D
600 m
72 kmph = 72 * 5/18 = 20 mps
D = Speed * time = 20 * 30 = 600 m.
Question: Some men can do a work in 10 days. with 10 less than original no of men it takes 10 more days to complete the work. what is the original no of men?
A.20 men
B.25 men
C.30 men
D.35 men
Answer: A.20 men
Explanation: let the no. of men be x
x men can do in 10 days,so one man can do in 10*x days
now (x-10) men can do in (10+10=20 days),so one man can do in 20*(x-10)days
10x=20(x-10)
or x=2x-20
or x=20 men
ANSWER:A
Question: The tax on a commodity is diminished by 19% and its consumption increased by 15%. The effect on revenue is?
A.2%
B.8.85%
C.5.85%
D.6.85%
Answer: D.6.85%
Explanation: 100 * 100 = 10000
81 * 115 = 9315
-----------
10000-----------685
100-----------? => 6.85% decrease
Answer: D
Question: 70 percent of the members of a study group are women, and 40 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?
A.0.28
B.0.27
C.0.25
D.0.32
Answer: A.0.28
Explanation: Say there are 100 people in that group, then there would be 0.7*0.40*100=28 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=28/100.
Answer: A
Question: When 20 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
A.3 : 4
B.2 : 1
C.3 : 2
D.Data inadequate
Answer: B.2 : 1
Explanation: Let the first and the second numbers be x and y respect then
y + 20% of x = 140% of y
or, y + 0.2x = 1.4y
or, 0.2x = 0.4y
∴ x : y = 0.4 : 0.2 = 2 : 1
Answer B
Question: If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7?
A.1
B.2
C.4
D.6
Answer: D.6
Explanation: x=7q+5
4x=7*4q+20
4x=7*4q+7*2+6
4x=7(4q+2)+6
4x=7k+6 (k=4q+2)
Answer D
Question: Complete the series
13, 9, 5, 1, -3...
A.-4
B.0
C.3
D.-7
Answer: D.-7
Explanation: In the above series clearly we know we can get the next term by subtract 4 from the previous term so the answer is Option D) -7
Question: The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 49 kg more than the weight of the third boy, what is the weight of the lightest boy?
A.87 kg
B.39.2 kg
C.98.2 kg
D.65.2 kg
Answer: B.39.2 kg
Explanation: Let the weights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 49
=> 5k = 49=> k = 9.8
Therefore the weight of the lightest boy
= 4k = 4(9.8) = 39.2 kg.
Answer:B
Question: Bob can eat 27 chocolates in an hour. Alice can eat 2 chocolates in 10 minutes, and Kelly can eat 7 chocolates in 20 minutes. How long will it take them to share and eat a large box of 120 chocolates whilst watching a movie?
A.2 hrs
B.1 hrs
C.3 hrs
D.4 hrs
Answer: A.2 hrs
Explanation: Bob can eat 27 chocolates in a hour,
Alice can eat 2 chocolates in 10 minutes or 12 choc in 1 hr
, and Kelly can eat 7 chocolates in 20 minutes or 21 chocs in 1 hr.
Three together can eat 27+12+21 = 60 choclates in 1 hr .
it take them 2 hrs to share and eat a large box of 120 chocolates whilst watching a movie
ANSWER:A
Question: The cost price of a TV is Rs.1500 and it was sold for Rs.1230, find the loss %?
A.20%
B.18%
C.16%
D.21%
Answer: B.18%
Explanation: B
18%
1500 ---- 270
100 ---- ? => 18%
Question: The ages of two person differ by 20 years. If 4 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
A.30, 10
B.25, 5
C.29, 9
D.50, 30
Answer: C.29, 9
Explanation: Let their ages be x and (x + 20) years.
Then, 5(x - 4) = (x + 20 - 4)
=> 4x = 36
=>x =9
Their present ages are 29 years and 9 year.
ANSWER:C
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 10% ?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: Let n be the number of man. Probability = n/10 * (n-1)/9= n(n-1)/90.
For the probability to be less than 10%, n(n-1) < 9.
Maximum number that satisfies this condition is 3. For 4, it is > 9. Hence the answer is D.
Question: A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds. The length of the train (in metres) is:
A.184
B.176
C.175
D.96
Answer: A.184
Explanation: Explanation:
Let the length of train be L m.
Acc. to question
(276+L)/20 = L/8
2208+8L=20L
L= 2208/12 = 184 m
Answer A
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 2?
A.y = -1/2*x + 3
B.y = 1/2*x - 2
C.y = 1/2*x + 3
D.y = 2x + 3
Answer: B.y = 1/2*x - 2
Explanation: Since our line has to perpendicular to y = − 2x + 3
Slope of this line , m = -2
Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)
y-intercept of line L is same as y intercept of line y = 2x − 2
y - intercept of line L = -2
Required line = 1/2* x - 2
Answer B
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 66 km downstream?
A.30/83 hours
B.33/13 hours
C.31/13 hours
D.30/13 hours
Answer: B.33/13 hours
Explanation: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 66 km downstream = d/s = 66/26
= 33/13 hours.
Answer:B
Question: A rectangular grass field is 60 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
A.1350
B.1200
C.9676
D.1679
Answer: B.1200
Explanation: Area = (l + b +2d) 2d
= (60 + 55 +2.5 * 2) 2*2.5 => 600
600 * 2 = Rs.1200
Answer:B
Question: The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 10 devices are bought, then the probability, to the nearest thousandth, that 7 devices function properly is
A.0.057
B.0.478
C.0.001
D.0
Answer: A.0.057
Explanation: Solution
Let q being the probability a device does not function properly and p = 1 - q = 0.9 the probability that a device functions properly. Since there are only two possible results, it is a binomial distribution. The P probability that 7 out of 10 devices function properly is given by
C(10,7)*0.9 7*0.1 3 , where C(10,7) is the number of ways that 7 items are selected from 10 and is given by
P = C(10,7) = 10! / (7!3!)
A calculation of P gives
P = 0.057
Answer A
Question: What is the smallest positive perfect square that is divisible by 12, 14, and 42?
A.900
B.1089
C.1600
D.1764
Answer: D.1764
Explanation: The number needs to be divisible by 2^2*3, 2*7, and 2*3*7.
The smallest such perfect square is 2^2*3^2*7^2 = 1764
The answer is D.
Question: If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?
A.16 2/3%
B.16 4/3%
C.16 7/3%
D.16 6/3%
Answer: A.16 2/3%
Explanation: Let the price of the article be Rs. 100.
20% of 100 = 20.
New price
= 100 + 20 = Rs. 120
Required percentage
= (120 - 100)/120 * 100
= 20/120 * 100
= 50/3
= 16 2/3%.
Answer:A
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
A.1/211
B.2/211
C.1/216
D.3/211
Answer: C.1/216
Explanation: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Question: The average age of 30 students of a class is 20 years. Out of these, the average age of 10 students is 16 years and that of the other 19 students is 22 years. The age of the 30th student is:
A.22 years
B.24 years
C.15 years
D.16 years
Answer: A.22 years
Explanation: Explanation :
Age of the 30th student = [30 x 20 - (10 x 16 + 19 x 22)] = (600 - 278) = 22 years.
Answer : A
Question: The volumes of two cones are in the ratio 1 : 20 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A.4:5
B.4:9
C.4:2
D.5:2
Answer: A.4:5
Explanation: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r1^2 . h1/r2^2. h2 => 1/20
= (1)^2h1/(2)^2h2
=> h1/h2 = 4/5
i.e. h1 : h2 = 4:5
Answer: A
Question: 25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
A.None of these
B.600
C.12
D.24
Answer: B.600
Explanation: Explanation :
He can go in any bus out of the 25 buses.
Hence He can go in 25 ways.
Since he can not come back in the same bus that he used for travelling,
He can return in 24 ways.
Total number of ways = 25 x 24 = 600. Answer : Option B
Question: A shipment of 8 TV sets contains 1 black and white sets and 7 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?
A.1/7
B.1/4
C.5/14
D.11/28
Answer: B.1/4
Explanation: 7/8 * 6/7 = 3/4
1-(3/4) = 1/4
Answer B
Question: How long is an IPv6 address?
A.32 bits
B.128 bits
C.64 bits
D.128 bytes
Answer: B.128 bits
Explanation: An IPv6 address is 128 bits long.
Answer:B
Question: A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident
A.30%
B.35%
C.40%
D.45%
Answer: B.35%
Explanation: Explanation:
Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5
P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5
Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%
Option B
Question: The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 507 sq meters, then what is the width (in meters) of the rectangular plot?
A.11
B.12
C.13
D.14
Answer: C.13
Explanation: Area = L*W = 3W^2 = 507
W^2 = 169
W = 13
The answer is C.
Question: If 3 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?
A.33
B.27
C.72
D.69
Answer: C.72
Explanation: (3 * 4)/48 = (9 * 2)/ x
x = 72 kg
Answer:C
Question: Find the invalid no.from the following series 9, 16, 21, 28, 33, 37
A.13
B.18
C.40
D.37
Answer: D.37
Explanation: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 37 is wrong.
Answer : D
Question: How long does a train 105 m long running at the speed of 68 km/hr takes to cross a bridge 90 m length?
A.13.9 sec
B.10.7 sec
C.17.9 sec
D.61.9 sec
Answer: B.10.7 sec
Explanation: Speed = 68 * 5/18 = 19m/sec
Total distance covered = 105 + 90 = 205 m.
Required time = 205/19 = 10.7 sec.
Answer:B
Question: In Parkin's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?
A.43.0
B.45.5
C.46.0
D.49.0
Answer: A.43.0
Explanation: In Parkin's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=A
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
A.720
B.620
C.520
D.820
Answer: A.720
Explanation: The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Answer is A.
Question: A driver just filled the car's gas tank with 36 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance?
A.1
B.1.5
C.2
D.2.5
Answer: C.2
Explanation: Let x be the number of liters of ethanol added to the gas tank.
0.05(36) + x = 0.1(36+x)
0.9x = 3.6 - 1.8 = 1.8
x = 2 liters
The answer is C.
Question: In a class, the average age of 42 boys is 12 years and the average of 28 girls is 10 years. what is the average age of the whole class?
A.11.2 Years
B.12.6 Years
C.13 Years
D.13.5 Years
Answer: A.11.2 Years
Explanation: Total age of 70 students
(42X 12+28 X 10) = 784
Average = 784/70 = 11.2 Years
A)
Question: A child crawls 20 ft towards north , turns right and crawls 30 ft, turns right again and crawls 35 ft. He turns left now and crawls 15 ft. He turns left again and crawls 15 ft . Finally he turns to his left to crawl another 15 ft. how far is he from his starting point and in which direction?
A.45 ft north-east
B.30 ft east
C.30 ft west
D.15 ft west
Answer: B.30 ft east
Explanation: Considering every move of a child straight one, if in (x,y) coordinates, starting point is (0,0), then given 6 moves can be represented as:
1) 20 ft. towards north ---> (0,20)
2) 30 ft. towards right ---> (30,20)
3) 35 ft. towards right ---> (30,-15)
4) 15 ft. towards left ---> (45,-15)
5) 15 ft. towards left ----> (45, 0)
6) 15 ft. towards left ----> (30, 0)
So child is at 30 ft. from his starting point towards east.
ANSWER:B
Question: In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
A.168.
B.80.
C.56.
D.48.
Answer: B.80.
Explanation: ways to select one shelf = 2
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 7+3 = 10
ways to select all of them together = 2*4*10 = 80
Hence, B is the answer.
Question: In how many ways can the letters of the word SPHERICAL be arranged such that all the vowels always appear together?
A.9!*6!
B.9!
C.7!*3!
D.9!*3!
Answer: C.7!*3!
Explanation: The 9 letters can be grouped into 6 consonants and one set of 3 vowels.
The number of ways to arrange 7 units is 7!
Then, for each arrangement, the 3 vowels can be arranged in 3! ways.
The total number of arrangements is 7!*3!
The answer is C.
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
A.5729
B.5760
C.2889
D.3600
Answer: D.3600
Explanation: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 2.5 = 3600.Answer: D
Question: In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is :
A.5
B.6
C.7
D.10
Answer: C.7
Explanation: Let no of cows be x, no of hens be y.
So heads=x+y
Legs=4x+2y
Now, 4x+2y = 2(x+y)+ 14
2x = 14
x = 7.
ANSWER:C
Question: Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
A.12
B.16
C.14
D.13
Answer: B.16
Explanation: 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs.Answer: B
Question: A man swims downstream 40 km and upstream 16 km taking 4 hours each time, what is the speed of the man in still water?
A.7
B.7.5
C.6.8
D.7.8
Answer: B.7.5
Explanation: 40 --- 4 DS = 10
? ---- 1
20 ---- 4 US = 5
? ---- 1 M = ?
M = (10 + 5)/2 = 7.5
Answer: B
Question: A river boat leaves Silver Town and travels upstream to Gold Town at an average speed of 6 kilometers per hour. It returns by the same route at an average speed of 3 kilometers per hour. What is the average speed for the round-trip in kilometers per hour?
A.4.0
B.3.8
C.7.2
D.7.5
Answer: A.4.0
Explanation: Pick a number which is LCM of 3 and 6 = 12.
Upstream time = 12/6 = 2 hrs
Downstream time = 12/3 = 4 hrs
Total time = 6 hrs
Total distance = 24
Average Speed = 24/6 = 4.0 km/hr
Question: How much 60% of 50 is greater than 40% of 30?
A.18
B.45
C.74
D.96
Answer: A.18
Explanation: Explanation:
(60/100) * 50 – (40/100) * 30
30 - 12 = 18
A
Question: A train 440 meters long is running with a speed of 60 kmph. The time taken by it to cross a tunnel 180 meters long is?
A.40.33 sec
B.41.33 sec
C.37.2 sec
D.40 sec
Answer: C.37.2 sec
Explanation: D = 440 + 180 =620
S = 60 * 5/18 = 16.66667 mps
T = 620/16.66667 = 37.2 sec
ANSWER:C
Question: If 35 percent of 400 is 20 percent of x, then what is 70 percent of x?
A.200
B.490
C.700
D.900
Answer: B.490
Explanation: 35/100(400) = 2/10(x)
X = 700..
70 percent of x =70/100(700) =490
Option B.
Question: A worker can load one truck in 6 hours. A second worker can load the same truck in 4 hours. If both workers load one truck simultaneously while maintaining their constant rates, how long, in hours, will it take them to fill one truck?
A.2.1
B.2.4
C.2.7
D.3.0
Answer: B.2.4
Explanation: The workers fill the truck at a rate of 1/6 + 1/4 = 10/24 = 5/12 of the truck per hour.
Then the time to fill one truck is 12/5 which is 2.4 hours.
The answer is B.
Question: On a certain number line, conditions are a<b<c<d<0 and abcd>0. Which of the following must be true?
I ab>0 II cd>0 III de>0
A.I &II only
B.II only
C.III only
D.I only
Answer: A.I &II only
Explanation: Givena<b<c<d and abcd>0.
Suppose, for the product to be greater than 0, we can two variables as -ve or four variables can be -ve.
We are given : I ab>0 II cd>0 III de>0
case 1: a and b can be negative/positive and if they are... we get greater than 0.
case 2: we have cd , then c and d both can be negative/positive and if they are... we get greater than 0.
ab > 0 , cd > 0
So cases 1 and 2 are fine.
A
Question: If a and b are different values and a – b = 4(√a - √b), then in terms of b, a equals:
A.√b
B.b
C.b - 8√b + 16
D.b + 2√b + 1
Answer: C.b - 8√b + 16
Explanation: (√a)^2 - (√b)^2 = 4(√a - √b) -----> ( √a + √b) ( √a - √b) = 4(√a - √b) -------> √a + √b = 4, so
√a = 4 - √b, square both sides and solve. Answer is C.
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 1?
A.-1
B.0
C.1
D.2
Answer: D.2
Explanation: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 1
= x2(x - 2)2 + 1
= (1 + √2)2(1 + √2 - 2)2 + 1
=(√2 + 1)2 (√2 - 1)2 + 1
=[(√2)2 - (1)2]2 + 1
=(2 - 1)2 =1 + 1=2
Correct Option: D
Question: Peter got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Peter’s sister was 10 years younger to him at the time of his marriage. The age of Peer’s sister is:
A.32
B.36
C.38
D.39
Answer: C.38
Explanation: Sol.
Let Peter’s present age be x years. Then, his age at the time of marriage = (x - 8) years.
∴ x = 6/5 (x - 8) ⇔ 5x = 6x - 48 ⇔ x = 48.
Peter’s sister’s age at the time of his marriage = (x - 8) - 10
= (x - 18) = 30 years.
∴ Peter’s sister’s present age = (30 + 8) years = 38 years.
Answer C
Question: If x is an integer and 2.134 × 10^x is less than 240,000, what is the greatest possible value for x?
A.7
B.6
C.5
D.4
Answer: C.5
Explanation: x is an integer and 2.134 × 10x is less than 240,000, what is the greatest possible value for x?
for 2.134 × 10x is less than 240,000 to remain true, the greatest number is 213,400, which makes x=5
C. 5
Question: The population of a bacteria culture doubles every 4 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
A.10
B.12
C.14
D.36
Answer: D.36
Explanation: This one's easy.
1000 * 2^t = 500,000
2^t = 500
Now gauging, since 2^8 = 256, then 2^9 = 512
So t = 9
But be careful, 't' is in time intervals of 4 minutes
So answer is 9*4 = 36 minutes
Answer (D)
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
A.33
B.50
C.99
D.88
Answer: B.50
Explanation: L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100 = 50%
Answer: B
Question: Find the no.of ways of arranging the boy and 10 guests at a circular table so that the boy always sits in a particular seat?
A.10!
B.9!
C.8!
D.6!
Answer: A.10!
Explanation: Ans.(A)
Sol. Total number of persons = 10 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 10P10 = 10! Ways ... The number of required arrangements = 10! x 1=10! = 10! ways