RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.
A.100
B.140
C.150
D.160
Answer: B.140
Explanation: 0.1x + 0.15y = 38
x+y = 300
x = 300-y
so 0.1(300-y) + 0.15y = 38
30-0.1y + 0.15y = 38
0.05y = 8
y = 160 grams
then x = 140 grams.
Answer: B
Question: A cistern which could be filled in 7 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
A.76 hrs
B.70/3 hrs
C.55 hrs
D.90 hrs
Answer: B.70/3 hrs
Explanation: 1/7 - 1/x = 1/10
=> 70/3 hrs
Answer: B
Question: The speed of the man in still water is 40 kmph. If he can row upstream at 20 kmph, find the downstream.
A.40
B.50
C.55
D.60
Answer: D.60
Explanation: M = (DS + US)/2
DS=2M-US
= 2*40-20
= 60
Answer:D
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
A.6400
B.6410
C.6440
D.6500
Answer: A.6400
Explanation: Number of bricks = Volume of Wall/Volume of Bricks
=800x600x22.5/21x11.25x6= = 6400
answer :A
Question: If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?
A.550
B.551
C.560
D.561
Answer: D.561
Explanation: This is a perfect example of why you should not use formulas without understanding them properly. If you understand them, you will not make a mistake and will save time.
The formula quoted by the original poster: n(n+1) is absolutely fine. But one needs to understand that n is the number of even terms starting from the first even term. (I discuss why this is so here:
Sum of even numbers from 40 to 60 using this formula will be:
30*31 - 19*20 = 10(3*31 - 19*2) = 550
Since number of terms is 11, required sum is 561
But, I would not use this formula for this question and would do it the way many of you have done:
Average = 50 (it is the middle number), Number of terms = 11 (No formula again. Any 10 consecutive integers have 5 even and 5 odd numbers. 41 to 60 will have 10 even integers and 40 is the 11th one)
Sum = 50*11 + 11 = 561
answer is D
Question: What number should replace the question mark?
16, 23, 19, 19, 22, 15, 25, ?
A.11
B.12
C.13
D.14
Answer: A.11
Explanation: A
11
There are two alternate sequences + 3 and - 4
Question: A man walks at a speed of 8 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
A.1 4/2 hours
B.1 2/5 hours
C.2 1/6 hours
D.2 1/1 hours
Answer: B.1 2/5 hours
Explanation: Required time
= (5 1/4)/8 + (5 1/4)/7
= 1 2/5 hours.
Answer:B
Question: Ravi and Ramu are partners in a business.Ravi contributes 1/6 of the capital for 16 months and Ramu received 2/3 of the profit. For how long Ramu's money was used ?
A.7 months
B.6 months
C.3 months
D.8 months
Answer: D.8 months
Explanation: Let the total Profit be Z.
Ramu's profit share is 2/3 of profit (i.e 2Z/3)
Ravi's profit is (Z-2Z/3) =Z/3
Hence the profit ratio is , Ravi : Ramu = Z/3 : 2Z/3 = 1:2
Let total Capital be Rs.X and Ramu has contributed for Y months.Since Ramu's profit share is 2/3, his invest share will be 2/3 in capital.
Ravi's invest for 16 months / Ramu's invest for Y months = Ravi's profit share / Ramu's profit share
i.e. (X/6 x 16) / (2X/3 x Y) = 1/2
Solving the above equation, we get Y = 8.
So Ramu's money has been used for 8 months.
Answer: D
Question: A letter lock consists of 4 rings, each ring contains 9 non-zero digits. This lock can be opened by setting four digit code with the proper combination of each of the 4 rings. Maximum how many codes can be formed to open the lock ?
A.4(9)
B.9(4)
C.9P4
D.None of these
Answer: B.9(4)
Explanation: Solution: There are 9 non-zero digits to arrange themselves at 4 different position. Each letter can be arrange at different position in 9 different ways.
So, required number of ways,
= 9 *9 *9 *9
= 94.
Answer: Option B
Question: Consider a sequence of numbers given by the expression 7 + (h - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?
A.409
B.1636
C.16360
D.16000
Answer: C.16360
Explanation: terms in this sequence are 7,12,17----402
now since this is an a.p. with a common difference of 5. therefore its sum can be given as
h(a+l)/2----------------1)
h= total no. of terms =80
a= first term=7
l= last term=402
subsituting values in the expression 1 we have
80(7+402)/2
= 40(409)
=16360=C
Question: A sum of Rs. 2704 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
A.1672
B.1664
C.1677
D.1698
Answer: B.1664
Explanation: (x*8*3)/100 = ((2704 - x)*3*5)/100
24x/100 = 40560/100 - 15x/100
39x = 40560 => x = 1040
Second sum = 2704 â€“ 1040 = 1664
Answer:B
Question: A sum of money is distributed among A,B,C,D in the proportion of 1:3:4:2. If C gets $500 more than D, what is the B's share?
A.$450
B.$500
C.$750
D.$800
Answer: C.$750
Explanation: Let the shares of A,B,C,D are x,3x,4x,2x
4x-2x = 500
x = 250
B's share = 3x = $750
Answer is C
Question: A number consists of two digits. If 3/5 of 1/5 of the number is 9. Find the sum of its two digits?
A.33
B.28
C.13
D.12
Answer: D.12
Explanation: Explanation:
x * 3/5 * 1/5 = 9
x = 75 => 7 + 5 = 12
Answer: D
Question: At what rate percent per annum will sum of money double in 20 years?
A.1.2 %
B.2 %
C.4 %
D.5 %
Answer: D.5 %
Explanation: Explanation:
Hint: If sum of money becomes (z times) in (T) years at simple interest, then rate of interest (R) can be calculated using the formula:
Rate of Interest (R) % =	100 (z – 1)/T
Here, principal amount is not given.
Hence, we can directly use the trick to calculate the rate of interest.
Rate of Interest (R) % =	100 (2 – 1)/20
Rate of Interest (R) %=5 % p.a.
ANSWER IS D
Question: If a = -0.4, which of the following is true?
A.a < a^2 < a^3
B.a^2 < a^3 < a
C.a^2 < a < a^3
D.a < a^3 < a^2
Answer: D.a < a^3 < a^2
Explanation: a=-0.4;
a^2=0.16;
a^3=-0.064;
Answer : D
Question: In the xy plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r=
A.6
B.5
C.4
D.3
Answer: B.5
Explanation: This question might look intimidating because of its language, but once you start solving it, you will realise that the options are given to you in such a way that you reach the correct answer easily.
The radius will lie somewhere between the distance of centre from the inner point and the distance from the outer point.
Distance between centre and inner point = Distance between (-2,-3) and (-2, 1)
We can solve for the distance by using the formula for distance between two points. But that is not required here.
If one of the co-ordinates is same, then the distance between two points is simply the difference between the other coordinate.
In this case, Distance = 1 - (-3) = 4
Distance between centre and utter point = Distance between (-2, -3) and (4, -3) = 4 - (-2) = 6
The radius has to be between 4 and 6
On looking at the options, only 5 satisfies
Correct Option: B
Question: One copy machine can make 15 copies a minute, and a second copy machine makes 10 copies a minute. If the two copiers work together, how long would it take them to make 1,000 copies?
A.20 minutes
B.30 minutes
C.40 minutes
D.50 minutes
Answer: C.40 minutes
Explanation: Total work done by both machines in a minute = 15 + 10 = 25 copies
Total number of copies required = 1000
Time = 1000/25 = 40 mins
Answer C
Question: If 5 people contributed a total of $20.00 toward a gift and each of them contributed at least $3.00, then the maximum possible amount any one person could have contributed is
A. $1.00
B. $1.25
C. $5.00
D. $8.00
Answer: D. $8.00
Explanation: D for me
4 people with 3$ each -> maximum = 8
Question: A retailer bought a shirt at wholesale and marked it up 80% to its initial price of $27. By how many more dollars does he need to increase the price to achieve a 100% markup?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: Let x be the wholesale price.
Then 1.8x= 27 and x = 27/1.8 = 15.
To achieve a 100% markup, the price needs to be $30.
The retailer needs to increase the price by $3 more.
The answer is C.
Question: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
A.99
B.98
C.97
D.96
Answer: D.96
Explanation: A prime factors are 3 and 11. 33<sqrt(99)? no
B prime factors are 2 and 7. 14<sqrt(98)? no
C prime number. its sqrt is never greater than itself
D A prime factors are 2 and 6. 6<sqrt(96)? yes
E prime factors are 5 and 19. 45<sqrt(95)? no
ANSWER:D
Question: A man can row his boat with the stream at 26 km/h and against the stream in 4 km/h. The man's rate is?
A.1 kmph
B.7 kmph
C.98 kmph
D.11 kmph
Answer: D.11 kmph
Explanation: DS = 26
US = 4
S = ?
S = (26 - 4)/2 = 11 kmph
Answer: D
Question: At what % above C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%?
A.49%
B.40%
C.48%
D.45%
Answer: B.40%
Explanation: Let C.P be Rs 100.then S.P be Rs 133
Let the market price be Rs x
Then 90% of x=133=>95x/100=133=>x=(133*100/95)=140
Market price = 40% above C.P
Answer is B.
Question: An article is bought for Rs.675 and sold for Rs.775, find the gain percent?
A.73%
B.14.8%
C.33 1/3%
D.93 1/3%
Answer: B.14.8%
Explanation: Explanation:
675 ---- 100
100 ---- ? => 14.8%
Answer:B
Question: There are 11 points marked on the circumference of a circle. How many hexagons can be formed by connecting 6 points of the 11 points?
A.450
B.454
C.458
D.462
Answer: D.462
Explanation: 11C6=462
The answer is D.
Question: A boy pays Rs. 369 for an article marked at Rs. 600, by enjoying two successive discounts. If the first discount is of 25%, how much should be the second discount?
A.20 %
B.10 %
C.25 %
D.18 %
Answer: D.18 %
Explanation: Explanation:
First discount = 25% of 600 = Rs. 150.
Thus, the reduced price = 600 – 150 = Rs. 450.
Since the person actually paid Rs. 369, the value of the second discount must be equal to Rs. 81 (450 – 369).
Let the second discount be x
Thus, we get, 81 = x of 450
( 81/450)*100 = 18%
ANSWER D
Question: When Rahul was born, his father was 26 years older than his brother and his mother was 23 years older than his sister. If Rahul's brother is 4 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
A.7 years
B.5 years
C.4 years
D.6 years
Answer: C.4 years
Explanation: When Rahul was born, his brother's age = 4 years; his father's age = (4 + 26) years = 30 years,
his mother's age = (30 - 3) years = 27 years;
his sister's age = (27 - 23) years = 4 years.
Answer: Option C
Question: The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
A.227
B.299
C.276
D.600
Answer: D.600
Explanation: Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 20 è x = 20 * 60 / 2 = 600
Answer: D
Question: Which of the following is a non-negative?
A.(b-0.9)(b-1)
B.(b-0.9)(b-0.9)
C.(b+0.9)(b+1)
D.(b+1)(b-1)
Answer: B.(b-0.9)(b-0.9)
Explanation: 5-sec approach:
D. (b-0.9)(b-0.9) = (b-0.9)^2. The square of a number is always non-negative.
Answer: B.
Question: When positive integer n is divided by 3, the remainder is 1. When n is divided by 11, the remainder is 9. What is the smallest positive integer k such that k+n is a multiple of 33?
A.2
B.4
C.6
D.8
Answer: A.2
Explanation: n = 3p + 1 = 11q + 9
n+2 = 3p + 3 = 11q + 11
n+2 is a multiple of 3 and 11, so it is a multiple of 33.
The answer is A.
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 39 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
A.36
B.2^4*3
C.24
D.38
Answer: D.38
Explanation: Working backward from the day it's covered:
day 39: fully covered
day 38: half covered
So 38 days
ANSWER:D
Question: a girl scout sold 5 macadamia cookies, 10 peanut butter cookies and 15 butter cookies. what is the ratio of the peanut butter cookies to the total sold?
A.1/2
B.1/3
C.5/10
D.10/15
Answer: B.1/3
Explanation: total # of cookies is 5+10+15=30; ratio of peanut butter cookies sold is 10/30 = 1/3
ANSWER:B
Question: If the volume of two cubes are in the ratio 125:1, the ratio of their edges is:
A.3:1
B.5:1
C.3:5
D.3:7
Answer: B.5:1
Explanation: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=125/1
=>(a/b)3=(5/1)3
a/b=5/1
=>a:b=5:1
Option B
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
A.9:10
B.9:8
C.3:4
D.39:49
Answer: B.9:8
Explanation: (3*6 + 6*6): (4*12)
54:48 => 9:8
ANSWER:B
Question: At what percentage above the C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%?
A.38%
B.40%
C.43%
D.48%
Answer: B.40%
Explanation: Let C.P = Rs. 100, Then S.P = Rs.133.
Let the marked price be x
Then , 95% of x = 133, 95 x/ 100 =133, x = 133*100/95 =140
Marked price = 40% above C.P
ANSWER:B
Question: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 336, which of the following could be equal to n?
A.38
B.39
C.40
D.41
Answer: A.38
Explanation: Since, there is no 48 in the answer choices (336/7 = 48), we know there is at least one 77.
336 - 77 = 259
259/7 = 37
37+1 = 38
If 38 wasn't there, I would have subtracted 77 from 259 and continued in a similar way.
Ans. A
Question: A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 36 minutes and a model N computer can complete the same task in 18 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model M computers were used?
A.12
B.11
C.10
D.9
Answer: A.12
Explanation: Let's say 1 work is processing 36 gb of data.
Model M : 1 gb per min
Model N : 2 gb per min
Working together, 1 M and 1 N = 3 gb per min
So, 12 times as many computers would work at 36 gb per min.
So no. of M =12
Answer is A
Question: How many positive integer solutions does the equation 5x+10y = 100 have?
A.2
B.33
C.38
D.35
Answer: A.2
Explanation: formula: (constant)/(lcm of two nos)
=100/(5*10)=2
ANSWER:A
Question: Two trains 200m and 300m long run at the speed of 70kmph and 50kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
A.10sec
B.15sec
C.18sec
D.20sec
Answer: B.15sec
Explanation: Relative speed = 70+50 = 120kmph * 5/18 = 100/3 m/s
Distance covered in crossing each other = 200+300 = 500m
Required time = 500*3/100 = 15sec
Answer is B
Question: If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ?
A.5
B.4
C.3
D.2
Answer: A.5
Explanation: Tried to locate a '0' ending multiple of 8 between 500599
Only 560 is present
560 is divisible by 8, so (560 - 8) is also divisible by 8 = 5
ANSWER A
Question: If 350!/10^n is an integer, what is the largest possible value of n?
A.88
B.82
C.86
D.87
Answer: C.86
Explanation: The question actually asks the highest power of 10 which divides 350! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)
10 = 2 x 5
350 factorial will have 86 as -
350/5 = 70
70/5 = 14
14/5 =2
So answer will be (C) 86
Question: A person travels through 5 cities - A, B, C, D, E. Cities E is 2 km west of D. D is 3 km north-east of A. C is 5 km north of B and 4 km west of A. If this person visits these citiesin the sequence B - C - A - E - D, what is the effective distance between cities B and D?
A.12
B.13
C.14
D.15
Answer: B.13
Explanation: make diagram first, then traverse according to B C A E D
u can find 5+4=9 (B to A)
A to E is not given but u can see it as 1.5 or 2 km so B to E is 10 km
now E to D is 2 km
total=5+4+1.5+2=12.5
or 5+4+2+2=13
ANSWER:B
Question: In a group of ducks and Cows, the total number of legs are 16 more than twice the no. of heads. Find the total no.of buffaloes.
A.10
B.12
C.8
D.12
Answer: C.8
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 16
=> 2x = 16 => x = 8
C
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 12%?
A.20%
B.29%
C.32%
D.80%
Answer: C.32%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 88
2/3 SP1 = 88
SP1 = 132
100 --- 32 => 32%
Answer: C
Question: If the cost price of 12 pencils is equal to the selling price of 8 pencils, the gain percent is:
A.30
B.40
C.50
D.60
Answer: C.50
Explanation: C
50%
Let C.P. of each pencil be $ 1.
Then, C.P. of 8 pencils = $8; S.P. of 8 pencils = $12.
Gain % = 4/8 * 100 = 50%
Question: A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
A.1/4
B.3/8
C.1/2
D.5/8
Answer: C.1/2
Explanation: The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);
P(OOO)=(1/2)^3;
P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);
So finally P=1/8+3/8=1/2.
Answer: C.
Question: If a 6 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?
A.300%
B.400%
C.500%
D.600%
Answer: C.500%
Explanation: The area A of the large cube is 6*6*6 = 216 square cm.
The area of the 216 small cubes is 216*6 = 6A, an increase of 500%.
The answer is C.
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 45 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.40
B.93
C.26
D.23
Answer: A.40
Explanation: Relative speed = 45 + 45 = 90 km/hr.
90 * 5/18 = 25 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 /25 = 40 sec.
Answer:A
Question: In how many ways can 6 people, A, B, C, D, E, F be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
A.384
B.396
C.576
D.624
Answer: D.624
Explanation: Total # of arrangements of 6 people in a row is 6!;
Now, let's find # of arrangements where C and D as well as A and B ARE seated next to each other. Consider them as a single unit: {AB}, {CD}, E, F. Now, these 4 units can be arranged in 4!, but we should multiply this number by 2*2 as A and B, as well as C and D within their unit can be arranged in two ways: {AB} or {BA}, and {CD} or {DC}. Hence total for this case is 4!*2*2;
So, {# of arrangements}={total}-{restriction}=6!-4!*2*2=624.
Answer: D.
Question: When four dice are thrown, what is the probability that the same number appears on each of them ?
A.1/36
B.1/18
C.1/216
D.1/5
Answer: C.1/216
Explanation: Explanation :
When four dice are rolled the total no of outcomes are : 64
All dice show up same number in the following cases: (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)
So in above six cases, all dice will show up the same number.
Required probability: 6/64 = 1/216
Answer : C
Question: If the least common multiple of two prime numbers x and y is 10, where x < y, then the value of 3x + y is
A.7
B.9
C.11
D.12
Answer: C.11
Explanation: LCM (x,y) = 10 and both x an y are prime.
The only values of x and y can be 2 and 5 (x = 2 and y = 5)
3x + y = 3*2 + 5 = 11
Correct Option: C
Question: The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
A.20,20
B.20,10
C.25,15
D.35,11
Answer: D.35,11
Explanation: Explanation:
Let their ages be x and (x + 24) years.
5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11.
Their present ages are 35 years and 11 years
Option D
Question: Express a speed of 36 kmph in meters per second?
A.10 mps
B.17 mps
C.97 mps
D.17 mps
Answer: A.10 mps
Explanation: 36 * 5/18
= 10 mps
Answer: A
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
A.Rs.81000
B.Rs.80000
C.Rs.75000
D.Rs.64000
Answer: A.Rs.81000
Explanation: 64000* 9/8 * 9/8 = 81000
ANSWER:A
Question: How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated?
A.20
B.40
C.60
D.80
Answer: C.60
Explanation: Three digit numbers will have unit's, ten's and hundred's place.
Out of 5 given digits any one can take the unit's place.
This can be done in 5 ways ------- (i)
After filling the unit's place, any of the four remaining digits can take the ten's place.
This can be done in 4 ways ------- (ii)
After filling in ten's place, hundred's place can be filled from any of the three remaining digits.
This can be done in 3 ways ------- (iii)
=> By counting principle, the number of 3 digit numbers =5Ã—4Ã—3==5Ã—4Ã—3= 60
ANSWER C
Question: 16 ltr of water is added with 24 ltr of a solution containing 90%of alcohol in the water. The %of alcohol in the new mixture is?
A.48%
B.52%
C.54%
D.60%
Answer: C.54%
Explanation: We have a 24 litre solution containing 90% of alcohol in the water.
=> Quantity of alcohol in the solution
=24Ã—90/ 100
Now 16 litre of water is added to the solution.
=> Total quantity of the new solution = 24 + 16 = 40
Percentage of alcohol in the new solution
=24Ã—90/100
40
Ã—
100
=24Ã—9010040Ã—100
=24Ã—2.25/100
=54%
C
Question: In how many ways can you seat 6 people on a bench if one of them does not want to sit at either end?
A.360
B.400
C.440
D.480
Answer: D.480
Explanation: One person can choose 4 possible chairs to sit. The remaining 5 people can sit in 5! ways.
The number of arrangements is 4*5! = 480.
The answer is D.
Question: Find the smallest number which should be divided with 3872 to make it a perfect square.
A.8
B.6
C.2
D.4
Answer: C.2
Explanation: 3872 = 11*11*2*2*2*2*2
Required smallest number = 2
2 is the smallest number which should be divided with 3872 to make it a perfect square.
ANSWER:C
Question: x is a positive integer less than 400. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
A.21
B.22
C.23
D.24
Answer: C.23
Explanation: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7k+1
this number when divided by 3 leaves remainder 2.
so,
(7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.
we now put the values of k starting from 0 to find first number divisible by 3
we find 1st number at k= 1
thus smallest number will be 7(1)+1 = 8
now,
next number will be = 8+ lcm of 37
i.e 29
now we will find number of all such values less than 500 by using the formula for last term of an a.p
8+(n-1)21=400
n=23.42
or n= 23
Answer:- C
Question: Robert's salary was decreased by 50% and subsequently increased by 50%. how much percentage does he lose?
A.10%
B.20%
C.25%
D.30%
Answer: C.25%
Explanation: let original salary be $100
new final salary = 150% of (50% of $100) = (150/100)*(50/100)*100 = $75
decrease = 25%
correct option is C
Question: A scuba diver descends at a rate of 40 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3000feet below the sea level..how long will he take to reach the ship?
A.70 minutes
B.72 minutes
C.75 minutes
D.76 minutes
Answer: C.75 minutes
Explanation: Time taken to reach = 3000/40= 75 minutes
ANSWER:C