RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Kevin plants corn and cotton. Once he harvests the crops, he has 30 pounds of corn and x
pounds of cotton. Corn sells for $5 per pound and cotton sells for $10 per pound. If Kevin sells
all his corn and cotton for a total of $640, then compute x.
A.39
B.49
C.59
D.69
Answer: B.49
Explanation: Kevin sells his corn for 305 dollars and his cotton for x10 dollars. Thus 30-5+x*10 =
640, so x = 640-30*5/10 = 490/10 = 49 .
correct answer B
Question: A batsman in his 9th inning makes a score of 75 and their by increasing his average by 7. What is his average after the 9th inning?
A.12
B.19
C.26
D.33
Answer: B.19
Explanation: 8x + 75 = 9(x + 7)
x = 12 + 7 = 19
Answer:B
Question: P runs 20% faster than Q so P gives Q a 300 meter head start. If the race ends in a tie, how far (in meters) did P run in the race?
A.1500
B.1600
C.1700
D.1800
Answer: D.1800
Explanation: Let D be the race distance that P ran.
Let T be the time it took to complete the race.
Let V be Q's speed.
T = D/1.2V = (D-300) / V
D=1.2D-360
0.2D=360
D=1800 meters.
The answer is D.
Question: How many positive integers between 1 and 100 are there such that they are multiples of 13?
A.6
B.5
C.4
D.7
Answer: D.7
Explanation: Multiples of 13 = 13,26,39,-----91
Number of multiples of 13 => 13*7= 91
Answer is D
Question: Which is the following is divisible by 11
A.A)3052
B.B)4825
C.C)4805
D.D)4905
Answer: A.A)3052
Explanation: Explanation:
Sum of first 'n' natural numbers = n(n + 1)/2
Sum of first 8 natural numbers = 7(7+ 1)//2 = 7 x 4 = 28
Sum of first 88 natural numbers = 77(77 + 1)//2 = 77 x 40 = 3080
3080 - 28= 3052
Answer: Option A
Question: In how many different number of ways a combination of 3 men and 2 children can be selected from 6 men and 5 children ?
A.20
B.22
C.24
D.26
Answer: A.20
Explanation: 6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20.
A)
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?
A.1 : 2
B.2 : 3
C.2 : 5
D.3 : 5
Answer: A.1 : 2
Explanation: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A
Question: Ayesha's father was 28 years of age when she was born while her mother was 15 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A.12 years
B.17 years
C.16 years
D.18 years
Answer: B.17 years
Explanation: Explanation:
Mother's age when Ayesha's brother was born = 15 years.
Father's age when Ayesha's brother was born = (28 + 4) years = 32 years.
Required difference = (32 - 15) years = 17 years.
Answer: B
Question: Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time ,the rate of interest being the same ?
A.Rs. 10
B.Rs. 10.40
C.Rs. 15.20
D.Rs. 13
Answer: B.Rs. 10.40
Explanation: Solution
S.I. on Rs. (260-20) for a given time =Rs. 7.34.
S.I. on Rs. 240 for half the time = Rs.10.
T.D. on Rs. 250 = Rs. 10.
∴ T.D. on Rs. 260 = Rs. ( 10/250 x260 ) = Rs. 10.40.
Answer B
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was
A.13years
B.14years
C.15years
D.16years
Answer: D.16years
Explanation: Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21.
Son's age 5 years back (21 - 5) = 16 years.
D)
Question: An article is bought for Rs.675 and sold for Rs.1200, find the gain percent?
A.87%
B.88%
C.78%
D.75%
Answer: C.78%
Explanation: 675 ---- 525
100 ---- ? =>
=78%
Answer:C
Question: Working in a North Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
A. 3 and 1/3 weeks
B. 3 weeks
C. 2 and 1/2 weeks
D. 2 and 1/3 weeks
Answer: A. 3 and 1/3 weeks
Explanation: VERITAS PREPOFFICIAL SOLUTION:
Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don’t have to read the question all over again to get started. You should be thinking:
Working in a North Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.
Rate (K) = 1 album / 5 weeks
Working at his own constant rate, Common can drop a full-length platinum LP in x weeks.
Rate (C) = 1 album / x weeks
If the two emcees work together…
I’m adding these rates, so their combined rate is 1/5 + 1/x
…they can drop a full-length platinum compilation LP in 2 weeks.
And they’re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2
Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
I’m using that equation to solve for Common’s time, so I’m solving for x.
Now by this point, that slow motion has paid off – your equation is set, your variable is assigned, and you know what you’ve solving for. Your job is to solve for x, so:
1/5 + 1/x = 1/2, so let’s get the x term on its own:
1/x = 1/2 – 1/5. and we can combine the two numeric terms by finding a common denominator of 10:
1/x = 5/10 – 2/10
1/x = 3/10, and from here you have options but let’s cross multiply:
10 = 3x, so divide both sides by 3 to get x alone:
10/3 = x, and that doesn’t look like the answer choices so let’s convert to a mixed number: 3 and 1/3 (there’s that number again), for answer choice A.
Question: One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?
A.10 km
B.12 km
C.16 km
D.17 km
Answer: C.16 km
Explanation: Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So, x + (61 -x) = 9
4 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.
C
Question: Which number can we add to 425897 to get a number exactly divisible by 456?
A.3
B.5
C.7
D.9
Answer: C.7
Explanation: 425897 / 456 = 933 with a remainder of 449.
We need to add 456 - 449 = 7
The answer is C.
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'U', then how many triangles can be determined with the 15 points that contain the point U?
A.182
B.105
C.185
D.210
Answer: A.182
Explanation: Fist point is U which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2=A
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 750 m long?
A.78sec
B.83sec
C.95sec
D.99sec
Answer: D.99sec
Explanation: Speed = 240/24 = 10 m/sec.
Required time = (240 + 750)/10 = 99 sec.
Answer:D
Question: If x is a positive integer such that (x-1)(x-3)(x-5)....(x-93) < 0, how many values can x take?
A.47
B.23
C.46
D.21
Answer: B.23
Explanation: Solution
If x takes any value greater than 93, the expression will definitely be positive.
Therefore, the set of values that x takes should be from the set of positive integers upto 93
The expression(x-1)(x-3)(x-5)....(x-93) has a total of 47 terms.
When x = 1, 3, 5,7 ....93 the value of the express will be zero. i.e., for odd values of x, the expression will be zero.
We need to evaluate whether the expression will be negative for all even numbers upto 93
Let x = 2; first term (x-1) > 0; remaining 46 terms < 0.
The product of one positive number and 46 negative numbers will be positive (product of even number of negative terms will be positive).
So, x = 2 does not satisfy the condition.
Let x = 4; (x-1) and (x-3) are positive; the remaining 45 terms < 0.
The product of two positive numbers and 45 negative numbers will be negative. So, x = 4 satisfies the condition.
Let x = 6; first 3 terms (x-1), (x-3), and (x-5) are positive and the remaining 44 terms are negative.
Their product > 0. So, x = 6 does not satisfy the condition.
Let x = 8; first 4 terms positive; remaining 43 terms < 0. Their product < 0. x = 8 satisfies the condition.
Extrapolating what we have oberved with these 4 terms, we could see a pattern.
The expression takes negative values when x = 4, 8, 12, 16 ..... 92 (multiples of 4)
92, the last value that x can take is the 23rd multiple of 4. Hence, number of such values of x = 23
Answer B
Question: Walking at 8KMPH From Point E to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point E to Railway station?
A.A)9KM
B.B)6.66KM
C.C)7.25KM
D.D)12.40KM
Answer: B.B)6.66KM
Explanation: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point E and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point E and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Question: A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
A.3 hrs 15 min
B.3 hrs 45 min
C.4 hrs
D.4 hrs 15 min
Answer: B.3 hrs 45 min
Explanation: Time taken by one tap to fill the tank = 3 hrs.
Part filled by the taps in 1 hour = 4 * 1/6 = 2/3
Remaining part = 1 - 1/2 = 1/2
2/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min
So, total time taken = 3 hrs 45 min.
ANSWER:B
Question: If p is an even integer and q is an odd integer, which of the following must be an odd integer?
A.p/q
B.pq
C.2p+q
D.2(p+q)
Answer: C.2p+q
Explanation: A. p/q
p = 6, q = 3 => p/q is odd integer
p = 4, q=3 =>p/q is not integer
B. pq
Must be even
C. 2p+q
2p must be even, q is odd=> 2p+q must be ODD: CORRECT
D. 2(p+q)
must be even
E. 3p/q
Same A
Answer: C
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.18 of money?
A.1800
B.1992
C.9921
D.2798
Answer: A.1800
Explanation: P = 18(100/10)2
=> P = 1800
Answer: A
Question: A can give B 80 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
A.130.12
B.130.43
C.130.22
D.111.0
Answer: B.130.43
Explanation: A runs 1000 m while B runs 920 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/920
= 869.56 m
B can give C = 1000 - 869.56
=130.43m.
Answer:B
Question: A man is trying to fill up his pool and he has three different water sources, if he uses faucet A it takes 5 hours to fill up the pool, if he used faucet B it takes 20 hours to fill it up. He first runs the water from source A for 2 hours, then turning that off, he continues with faucet B for 10 hours. Then turning that off as well he uses Faucet C and in 3 hours the pool is filled up. How long does it take to fill up the pool only using the faucet C?
A.10 hours
B.20 hours
C.30 hours
D.40 hours
Answer: C.30 hours
Explanation: 2/5 +10/20 + 3/x = 1 x = 30ANSWER =C
Question: A and B invests Rs.6000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
A.32:99
B.82:31
C.24:45
D.34:89
Answer: C.24:45
Explanation: A : B
(6000*4)+(3000*8) : (9000*6)+(6000*6)
48000 : 90000
24 : 45
Answer:C
Question: If y exceeds x by 20%, then x is less than y by?
A.16 2/38%
B.16 3/3%
C.16 2/3%
D.18 2/3%
Answer: C.16 2/3%
Explanation: X=100	y=120
120------20
100-------? => 16 2/3%
Answer: C
Question: Calculate the fourth proportional to 7.4, 8.1 and 9.8?
A.10.73
B.13.73
C.15.73
D.11.73
Answer: A.10.73
Explanation: Explanation:
Formula = Fourth propotional = (b × c)/a
A = 7.4 , B = 8.1 and C = 9.8
(8.1 × 9.8)/7.4 = 10.73
Answer: Option A
Question: The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:
A.20
B.30
C.60
D.70
Answer: B.30
Explanation: B
30
Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 × y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 × y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30.
Question: Dominos charges $6.25 for a veg pizza of std size that costs a total of $2.85 to make. Pizza Hut charges $5.80 for a similar pizza that costs $1.80 to make. If Dominos sells 2,000 pizzas, how many must Pizza Hut sell to make at least as much in total gross profit as its competitor does?
A.858
B.1875
C.14,667
D.63,840
Answer: B.1875
Explanation: Dominos : Profit/pizza = 6.25-2.85 = 3.75
: No of pizza = 2,000
: Gross Profit = 2,000*3.75 = 7,500
Pizza Hut : Profit/pizza = 4
: Gross Profit = 7,500
: No of Cups = 7,500/4 = 1875
Answer B
Question: What should come in the place of the question mark(?) in the following equation?
45(2)×27(2)/135(2)=?
A.81
B.1
C.243
D.9
Answer: A.81
Explanation: ? = 45×45×27×27 /135×135=81
Answer A
Question: If n=4p where p is a prime number greater than 3, how many different positive even divisors does n have, including n?
A.2
B.6
C.4
D.8
Answer: C.4
Explanation: We're told that N = 4P and that P is a prime number greater than 3. Let's TEST P = 4; so N = 16
The question now asks how many DIFFERENT positive EVEN divisors does 16 have, including 16?
16:
1,16
2,8
4,4
How many of these divisors are EVEN? 2,8,4,16…..4 even divisors.
ANSWER:C
Question: If Henry were to add 6 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?
A.25
B.48
C.64
D.80
Answer: B.48
Explanation: 7/8x-3/4x=6galls
1/8*x=6gallons
x=48 gallons
Answer B
Question: The average of four consecutive even numbers is 27. find the largest of these numbers?
A.10
B.20
C.30
D.40
Answer: C.30
Explanation: let the numbers be x,x+2,x+4 andx+6. then,
(x+(x+2)+(x+4)+(x+6))/4) = 27
(4x+12)/4 = 27
x+3=27
x=24.
Therefore the largest number=(x+6)=24+6=30.
Option C
Question: There are 2 sections with 6 questions each. If two questions are selected from each section, the chance of getting different questions is________
A.10
B.100
C.240
D.225
Answer: D.225
Explanation: we have to select two questions from each section so the chances are 6C2.6C2=225
ANSWER:D
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 28 white marbles. How many red marbles could be in bag A?
A.1
B.3
C.4
D.6
Answer: C.4
Explanation: # of Red marbles in Bag A can be either 2 or 6. No 2 in the choices, so 6. D.
Bag A:
R:W:B = 2:6:9
Bag B
R:W = 1:4
6X + 4Y = 28 i.e 3X + 2Y = 14
X has to be odd to make an odd sum from the eq.
X = 2 , Y = 4 OR X = 4, Y = 1
So R can be 2X i.e 4 or 8.
Answer C
Question: From a corner of a ground of 20m*30m, a boy hits a ball that travels maximum 14m. What is the area of the football ground through which the ball can pass by the hit of that boy from that corner ?
A.132
B.140
C.150
D.154
Answer: D.154
Explanation: Area covered by ball = Pi*r^2/4 ( here we divide by 4 because ball is hit from the corner of the ground and only 1/4 part the ball can go)
where r= 14 m = length of pass
So area = (22/7)*14*14/4 =154 sq m
answer :D
Question: If n is a multiple of 5, n=p^2q, where p and q are prime numbers. Which of the following must be a multiple of 25?
A.p^2
B.q^2
C.pq
D.p^2q^2
Answer: D.p^2q^2
Explanation: You are given that n = p^2 * q, which is a multiple of 5. Therefore p^2 * q is a multiple of 5. Since 5 is a prime number, p OR q must be a multiple of 5. Therefore, in order to be a multiple of 25, you must have a MINIMUM of p^2 * q^2 in the answer, since you don't know whether p or q is the multiple of 5. The only answer which satisfies this condition is D. The answer is D: p^2*q^2.
Question: (x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. 3
II. -6
III. 2
IV. 5
A.I and II only
B.I and III only
C.II and III only
D.II and IV only
Answer: B.I and III only
Explanation: (x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only 3 and 2 satisfy both inequalities.
Answer: B.
Question: 6persons enter a lift on the ground floor of a 9floor apartment. Assuming that each of them independently & with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the 6persons are leaving the lift at different floors?
A.7P6/8^6
B.5P6/8^6
C.8P6/8^6
D.9P6/8^2
Answer: C.8P6/8^6
Explanation: Apart from the ground floor, there are 8 floors
Let's find out the total number of ways in which all the six persons can leave the
lift at eight different floors
The 1st person can leave the lift in any of the 8 floors (8 ways)
The 2nd person can leave the lift in any of the remaining 7 floors (7 ways)
The 3nd person can leave the lift in any of the remaining 6 floors (6 ways)
...
The 6th person can leave the lift in any of the remaining 3 floors (3 ways)
Total number of ways = 8 × 7 × 6 × 5 × 4 × 3 = 8P6
(In fact, from the definition of permutations itself,
we will be able to directly say that the number of ways in which all the six persons
can leave the lift at 8 different floors = 8P6)
n(E)= Total Number of ways in which all the six persons can leave the lift at eight
different floors = 8P6
Now we will find out the total number of ways in which each of the six persons
can leave the lift at any of the eight floors
The 1st person can leave the lift in any of the 8 floors (8 ways)
The 2nd person can leave the lift in any of the 8 floors (8 ways)
The 3nd person can leave the lift in any of the 8 floors (8 ways)
...
The 6th person can leave the lift in any of the 8 floors (8 ways)
Total number of ways = 8 × 8 × 8 × 8 × 8 × 8 = 86
i.e., The total number of ways in which each the six persons can leave the lift
at any of the eight floors = n(S) = 86
P(E) = n(E)n(S)=8P6/8^6
C
Question: An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 20000 people who applied for the army and 196 were finally selected, what was the value of N?
A.4
B.5
C.6
D.8
Answer: D.8
Explanation: step(1) 8000 accepted.
step(2) another 40%of 8000=3200 accepted.
here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.
so i would get to second stage of recruitment where 50 % is accepted
step(3) 50% of 3200=1600
step(4) 50% of 1600=800
step(5) 50% of 800=400
Step(6) 50% of 400=200
70% of 400=280
and last step of accepting 70% of 280=196(our target)
total 8 steps required.
Ans D
Question: 1254,1254,627,209,52.25,?
A.1.29
B.10.45
C.3.58
D.4.96
Answer: B.10.45
Explanation: Explanation :
Terms are continuously divided by 1,2,3 ,4, and so on
1254
1254 Ã· 1 = 1254
1254 Ã· 2 = 627
627 Ã· 3 = 209
209 Ã· 4= 52.25
52.25Ã·5=10.45
Answer : Option B
Question: How many integer values R are there for x such that 1 < 3x + 5 < 17?
A.Two
B.Three
C.Four
D.Five
Answer: D.Five
Explanation: 1 < 3x + 5 < 17
=> -4 < 3x < 12
=> -4/3 < x < 4
x can take integer values R -1,0 , 1 , 2 , 3
Answer D
Question: Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is
A.6/19%
B.6/17%
C.5 5/11%
D.3 5/11%
Answer: C.5 5/11%
Explanation: Explanation:
Whenever we get this type of question, we should have formula in mind that,
Gain% = (gain/cost)*100
Cost = 4700 + 800 = Rs. 5500
S.P. = Rs. 5800
Profit = 5800 - 5500 = 300
Gain%=300/5500∗100=5 5/11%
Option C
Question: How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet)
A.37×260^2
B.36×260^2
C.36×270^2
D.10^2×26^3
Answer: B.36×260^2
Explanation: We are given that License plate could be either of the form DDLLL or DDDLL
Now, every D could be filled in 10 ways and every L could be filled in 26 ways.
or Number of ways for DDLLL = 10 * 10 * 26 * 26 * 26 --(1)
Number of ways for DDDLL = 10 *10*10*26*26 --(2)
Total ways = (1) +
(2)
= \(36×260^2\)
Answer s B.
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
A.26
B.27
C.29
D.32
Answer: B.27
Explanation: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
B
Question: If -2x+3y=8 and 4x-3y=20, what is the sum of x and y?
A.24
B.28
C.18
D.26
Answer: D.26
Explanation: Given -2x+3y=8 ---Eq 1
4x -3y =20 -- Eq 2
Sum both eqns we get 2x = 28 => x = 14
Sub 2x in eq 1 => -28 + 3y = 8.
=> y = 12
Now X+Y = 12 + 14 = 26
Option D is correct answer.
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum W of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
A. 6x
B. 4x
C. 5x/3
D. 3x/2
Answer: B. 4x
Explanation: Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<W<5x --> only option B fits.
Answer: B.
Question: In how many different number of ways 4 men and 2 women can sit on a bench?
A.690
B.700
C.720
D.740
Answer: C.720
Explanation: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
C
Question: The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 40 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?
A.20 ft
B.25 ft
C.600ft
D.900 ft
Answer: C.600ft
Explanation: Point to note: Both the wheels would have traveled the same distance.
Now consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).
Equating the distance traveled by front wheel to back wheel: (x+5)*30 = x * 40. (Formula for calculating the distance traveled by each wheel is: # of revolutions * circumference.)
Solving this eqn. gives x=15.
Sub x=15 either in (x+5)*30 or in x * 40 to get the distance, which is 600. So the correct choice is C.
Question: A train speeds past a pole in 15 seconds and a platform 130 meters long in 25 seconds. What is the length of the train (in meters)?
A.175
B.185
C.195
D.205
Answer: C.195
Explanation: Let the length of the train be x meters.
The speed of the train is x / 15.
Then, x + 130 = 25*(x / 15)
10x = 1950
x = 195 meters
The answer is C.
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length?
A.18.9 sec
B.88.9 sec
C.22.9 sec
D.30.00 sec
Answer: D.30.00 sec
Explanation: D = 110 + 390 = 500 m
S = 60 * 5/18 = 50/3
T = 500 * 3/50 = 30 sec
Answer: D