RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In how many different ways can the letters of the word 'CORPORATMON' be arranged so that the vowels always come together?
A.40000
B.50000
C.50400
D.50700
Answer: C.50400
Explanation: The word 'CORPORATMON' has 11 letters. It has the vowels 'O','O','A','M','O' in it and
these 5 vowels should always come together. Hence these 5 vowels can be grouped
and considered as a single letter. that is, CRPRTN(OOAMO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and
rest of the letters are different.
Number of ways to arrange these letters = 7!2! = (7×6×5×4×3×2×1)/(2×1) = 2520
In the 5 vowels (OOAMO), 'O' occurs 3 and rest of the vowels are different.
Number of ways to arrange these vowels among themselves = 5!3! = (5×4×3×2×1)/(3×2×1) = 20
Hence, required number of ways = 2520 x 20 = 50400
C
Question: A car traveled from San Diego to San Francisco at an average speed of 51 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
A.24.
B.34.
C.36.
D.42.
Answer: B.34.
Explanation: Let the time taken be = x
One way distance = 51x
Total distance traveled = 2 * 51x = 102x
Total time taken = x + 2x = 3x
Average speed = 102x/3x = 34
Answer: B
Question: Analyze the number square carefully and find out what number fits in place of question mark.
35	20	14
9	17	42
2	8	?
A.12
B.6
C.18
D.2
Answer: D.2
Explanation: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(6
2/ 8) * 8 = 2*1= 2
D
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross-section is 690 sq m, the depth of cannel is?
A.39
B.28
C.27
D.69
Answer: D.69
Explanation: 1/2 * d (12 + 8) = 690
d = 69
Answer: D
Question: If each digit in the set of A = {1,2,3,4,5,6} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?
A.4*5!
B.6! - 5!
C.6! / 5!
D.6!* 5!
Answer: A.4*5!
Explanation: The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).
The number of ways to arrange 6 units is 6!
If we think of 2 and 5 as one single unit, the number of arrangements is 5!
Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*5!
The total number of valid arrangements is 6! - 2*5! = 6*5! - 2*5! = 4*5!
The answer is A.
Question: A part of Rs. 38800 is lent out at 6% per 6 months. The rest of the amount is lent out at 5% per annum after 1 year. The ratio of interest after 3 years from the time when first amount was lent out is 5:4. Find the second part that was lent out at 5%.
A.28800
B.27800
C.29800
D.26500
Answer: A.28800
Explanation: Let the 1st part that is lent out be x at 6%. then 2nd part will be (38800-x) at 5%.then the S.I1 of 1st part is (p*r*t)/100 = (x*6*6)/100 [t=6 becoz we r calculating till 3yrs & der is six 6months in 3yrs]
similarly S.I2 of 2nd part = {(38800-x)*5*2}/100 [t=2 since the 5% rate is to be calculated after the 1st year & per annum, so no. of years left is 2]therefore, S.I1/S.I2=5/4, by calculating it we get x=10000So, 2nd part is 38800-10000=28800
ANSWER:A
Question: A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
A.34
B.38
C.42
D.46
Answer: D.46
Explanation: 5/7*P are ponies with horseshoes, so P is a multiple of 7.
2/3*5/7*P = 10/21*P are Icelandic ponies with horseshoes, so P is a multiple of 21.
The minimum value of P is 21. Then H = P+4 = 25.
The minimum number of horses and ponies is 46.
The answer is D.
Question: Find The Missing Number in this sequence ?
1, 2, 6, 42, ? 3263442
A.2000
B.1806
C.4580
D.3546
Answer: B.1806
Explanation: B
1806
each number is multiplied by the number+1
1x2 = 2
2x3 = 6
6x7 = 42
42x43 = 1806
1806x1807 = 3263442
Question: It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?
A.2 hours and 45 minutes.
B.5 hours and 45 minutes.
C.3 hours and 45 minutes.
D.4 hours and 45 minutes.
Answer: C.3 hours and 45 minutes.
Explanation: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = 3 hours and 45 minutes.
correct answer C
Question: A boy is born when his father is 27 years old. How old will he be when he is exactly half his fathers' age?
A.23
B.24
C.25
D.27
Answer: D.27
Explanation: when son born:
son s=0
father f=27.
after x years:
son s=x
father f=f+x=27+x:
according to given condition
son age is exactly half his fathers' age...so
x=(27+x)/2---solve this
son age is 27
ANSWER:D
Question: What is the sum of all the prime numbers from 20 to 40?
A.279
B.100
C.278
D.120
Answer: D.120
Explanation: Explanation:
23 + 29 + 31 + 37 = 120
Answer: D
Question: a company has 17 office tasks 8 outdoor tasks and 7 misc. tasks for workers each worker can complete 4 tasks max what is he minimum number of workers required
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: Total subjects = 17+8+7=32
Max tasks by 1 worker = 4
So, min of workers required = 32/4 = 8
ANSWER:C
Question: Without stoppages, a train travels certain distance with an average speed of 80 km/h, and with stoppages, it covers the same distance with an average speed of 60 km/h. How many minutes per hour the train stops ?
A.15
B.18
C.10
D.16
Answer: A.15
Explanation: Due to stoppages, it covers 20 km less .
Time taken to cover 20 km = 20⁄80h = 1⁄4h
= 1⁄4 × 60 min = 15 min
Answer A
Question: Which values of ‘x’ satisfies the inequality
x2 - 3x + 2 > 2x - 4 ?
A.2< x < 3
B.x > 3 or x < 2
C.x ³ 3
D.x £ 2
Answer: B.x > 3 or x < 2
Explanation: Given expression is
x2 – 3x + 2 – 2x + 4 > 0
or, x2 – 5x + 6 > 0
or, x2 – 3x – 2x + 6 > 0
or, x(x – 3) – 2(x – 3) > 0
or, (x – 3)(x – 2) > 0
or, x > 3 or, x < 2
Answer B
Question: How many terms are in the G.P. 3, 6, 12, 24, ......., 96 ?
A.6
B.9
C.67
D.5
Answer: A.6
Explanation: Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 96 => a * r^(n-1) = 96
=> 3 * 2^(n-1) = 96 => 2^(n-1) = 32 = 2^(5)
=> n-1 = 5 => n = 6
Answer: A
Question: The speed of a boat in still water is 60kmph and the speed of the current is 15kmph. Find the speed downstream and upstream?
A.80,47 kmph
B.75,55 kmph
C.80,42 kmph
D.80,40 kmph
Answer: B.75,55 kmph
Explanation: Speed downstream = 60 + 15 = 75 kmph
Speed upstream = 60 - 15 = 55 kmph.Answer:B
Question: At a constant Rate of flow, it takes 30 minutes to fill a swimming pool if a large hose is used and 45 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
A.20
B.22
C.18
D.16
Answer: C.18
Explanation: time taken to fill the pool by Large Hose =30 minutes =L or 1/L=1/30 similarly 1/S=1/45
simultaneously it will take 1/L+1/S=1/30+1/45=5/90=18 minutes
Answer : C
Question: The area of a parallelogram is 128sq m.Then the area of a triangle formed by its diagonal is ----------?
A.128m
B.64m
C.64m^2
D.128m^2
Answer: B.64m
Explanation: b*h/2=128/2=64m. Ans:(B)
Question: If the sum of the interior angles of a regular polygon measures up to 1260 degrees, how many sides does the polygon have?
A.6
B.3
C.9
D.4
Answer: C.9
Explanation: 9 sides...answer is C
Question: 4 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
A.4 days
B.6 days
C.7 days
D.9 days
Answer: A.4 days
Explanation: 1 women's 1 day work = 1/28
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/28 + 10/140) = 1/4
5 women and 10 children will complete the work in 4 days.
Answer: A
Question: Raja and Abdul can finish the work 18 days if they work together. They worked together for 12 days and then Abdul left. Rja finished the remaining work in another 12 days. In how many days Raja alone can finish the work?
A.30 days
B.60 days
C.70 days
D.36 days
Answer: D.36 days
Explanation: Amount of work done by Raja and Abdul in 1 day = 1/18
Amount of work done by Raja and Abdul in 12 days = 12 Ã— (1/18) = 2/3
Remaining work â€“ 1 â€“ 2/3 = 1/3
Raja completes 1/3 work in 12 days
Amount of work JOHN can do in 1 day = (1/3)/12 = 1/36
=>Raja can complete the work in 36 days
Answer : D
Question: A cube painted red on two adjecent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size.How many cubes are there which have no face painted?
A.8
B.9
C.10
D.11
Answer: A.8
Explanation: If a painted cube is cut into 64 (4^3) smaller cubes then there will be
i. smaller cubes with three face painted (cubes at the corner)= 8
ii.smaller cubes with two face painted (cubes at the edges)= (4-2)*12= 24
iii.smaller cubes with one face painted (cubes at the faces)= ((4-2)^2)*6=24
iv.smaller cubes not painted = 64-(8+24+24)= 8
ANSWER:A
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
A.587 × 10<10>(exponent) miles
B.587 × 10<-12> (exponent) miles
C.587 × 10<-10>(exponent) miles
D.587 × 10<12>(exponent) miles
Answer: D.587 × 10<12>(exponent) miles
Explanation: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 ×10<12>(exponent) miles
Question: An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 40 miles per hour, then 50 miles per hour, then 60 miles per hour. If the test took 74 hours to complete, how many miles was the car driven during the entire test?
A.3600
B.3400
C.3300
D.3500
Answer: A.3600
Explanation: x is the segment to be traveled
x/40+x/50+x/60 =74
or 74x/1200 =74
x = 1200miles . total distance =3*1200 = 3600 miles
A
Question: There are, in a certain league, 50 teams, and each team face another team for a total of 4 times. How many games are played in the season?
A.6660
B.3600
C.2400
D.4900
Answer: D.4900
Explanation: By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 4900
Option D.
Question: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
A.Rs. 21,000
B.Rs. 22,500
C.Rs. 25,300
D.Rs. 25,800
Answer: C.Rs. 25,300
Explanation: sell at 18700 he got a loss of 15% means, This 18700 is 85% not 100%.
To get 1% : 18700/85=220; Then 220 is 1%.
To get 100% : 220x100=22000.
To get 115% : 220x115=25300
answer :C
Question: A certain smoothie A is three-fifths blueberries and 40% raspberries by weight. Another smoothie B is three-quarters banana and one-quarter raspberries by weight. If the mixed smoothie of A and B is 30% raspberries by weight, how much weight of this mixture belongs to smoothie A?
A.10%
B.33.33%
C.45%
D.50%
Answer: B.33.33%
Explanation: A is 40% raspberries;
B is 25% raspberries.
A and B is 30% raspberries;
30% raspberries in the mixed smoothie of A and B come from 40% raspberries in A and 25% raspberries in B, thus:
0.3(A+B)=0.4A+0.25B --> 0.1A=0.05B --> A/B=1/2 --> A/(A+B)=1/3.
Answer: B.
Question: There are 600 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
A.100
B.200
C.250
D.300
Answer: D.300
Explanation: There are 594 managers and 6 others. The 6 others would compose 2% of the total number of people if there were 300 people in the room. Thus 300 managers must leave.
The answer is D.
Question: For which of the following does f(r)−f(s)=f(r−s) for all values of r and s?
A.f(a)=a^2
B.f(a)=a/2
C.f(a)=a+5
D.f(a)=2a−1
Answer: B.f(a)=a/2
Explanation: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(r) = r^2 and f(s) = s^2
so L.H.S = r^2 - s^2
and R.H.S = (r-s)^2 ==> r^2 + s^2 -2rs.
so L.H.S not equal to R.H.S
with option 2. f(r) = r/2 and f(s) = s/2
L.H.S = r/2 - s/2 ==> 1/2(r-s)
R.H.S = (r-s)/2
so L.H.S = R.H.S which is the correct answer.
B
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
A.153
B.150
C.146
D.144
Answer: D.144
Explanation: Let x be the original 2-digit number.
If each digit is halved, then the sum of G and H is 3x/2.
Note the sum must be a multiple of 3 and less than 150.
Of these five choices, only 144 satisfies these two conditions.
The answer is D.
Question: Two goods trains each 625 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.40
B.45
C.48
D.60
Answer: D.60
Explanation: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 625 + 625 = 1250 m.
Required time = 1250 * 6/125 = 60 sec.
Answer: Option D
Question: What is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other?
A.3: 6
B.1.5: 1
C.3: 1.5
D.2: 1
Answer: B.1.5: 1
Explanation: d = 1.5d d = d
a√2 = 1.5d a√2 = d
a = 1.5d/√2 a = d/√2 => 1.5: 1
Answer: B
Question: A landlady has been paid $329,864 to her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to confirm that the money has been paid evenly by all 9 of her house rentors?
A.$1
B.$2
C.$3
D.$4
Answer: D.$4
Explanation: To find the least amount the landlady should add to her saving account to ensure that every rentor has paid evenly,
she needs to make the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Question: A company run by 20 men can produce 1000 pencils in a day. One-fifth of the pencils produced are defective and one-quarter of all pencils produced are rejected by quality control technician. If one-tenth of the nondefective pencils are rejected by mistake, and if all the pencils not rejected are sold, then what percent of the pencils sold by the company are defective?
A.4%
B.10%
C.8%
D.6%
Answer: A.4%
Explanation: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 4 of every 100 that are sold (not rejected) and defective, which implies Answer A.
Question: A train 270 m long passed a pole in 27 sec. How long will it take to pass a platform 650 m long?
A.92 sec
B.89 sec
C.54 sec
D.27 sec
Answer: A.92 sec
Explanation: Speed = 270/27 = 10 m/sec.
Required time = (270 + 650)/10
= 92 sec.
Answer: A
Question: The measurement of a rectangular box with lid is 50cmx30cmx38cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
A.288
B.4500
C.7200
D.864
Answer: B.4500
Explanation: d=30, r=15;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*15*15*15= 4500πcm3 ANSWER:B
Question: 70% of the employees of a company are men. 50% of the men in the company speak French and 40% of the employees of the company speak French. What is % of the women in the company who do not speak French?
A.4%
B.10%
C.83.33%
D.90.33%
Answer: C.83.33%
Explanation: No of employees=100(say)
Men=70
Women=30
Men speaking french=0.5*70=35
Employees speaking french=0.4*100=40
Therefore women speaking French=40-35=5
And women not speaking French=30-5=25
% of women not speaking French=25/30*100=83.33%
Answer C
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for three years?
A.29893
B.27773
C.29989
D.26100
Answer: D.26100
Explanation: Simple interest = (18000 * 3 * 15)/100 = Rs. 8100
Amount = P + I = 18000 + 8100 = Rs. 26100
Answer: D
Question: If P is a prime number greater than 3, find the remainder when P^2 + 13 is divided by 12.
A.6
B.1
C.0
D.2
Answer: D.2
Explanation: Every prime number greater than 3 can be written 6N+1 or 6N-1.
If P = 6N+1, then P^2 + 13 = 36N^2 + 12N + 1 + 13 = 36N^2 + 12N + 12 + 2
If P = 6N-1, then P^2 + 13 = 36N^2 - 12N + 1 + 13 = 36N^2 - 12N + 12 + 2
When divided by 12, it must leave a remainder of 2.
The answer is D.
Question: Ashok opened a shop investing Rs.60,000 and Madhuri joined him after 2 months investing Rs.90,000. They get a profit of Rs. 1,08,000 after one year. The share of Madhuri is
A.Rs.35,000
B.Rs.30,000
C.Rs.60,000
D.Rs.45,000
Answer: C.Rs.60,000
Explanation: 60000*12:90000*10=4:5
5/9(108000)=60000
ANSWER:C
Question: If 945*s is a perfect square then s can be which of the following numbers?
A.21
B.35
C.54
D.105
Answer: D.105
Explanation: For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 945 are 3 *3 *3 *5 * 7
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice D completes the pairing of 3, 5 and 7. It adds a "3", a "5", and a "7" to the prime factors of 945 (3*3*3*5*7) and makes it a perfect square.
Question: P = {22, 24, 26, 28, 30, 32}
Q = {2, 24, 25, 26, 27, 28}
R = {4, 7, 10, 13, 16, 19}
If p is the standard deviation of set P, q is the standard deviation of set Q, and r is the standard deviation of set R, which of the following must be true?
A.p<q<r
B.p<r<q
C.q<r<p
D.q<p<r
Answer: B.p<r<q
Explanation: P has difference by 2.
Q has difference of 22 between 2 and 24 and for other numbers we have difference by 1.
R has difference 3.
We need to take the SD as per the difference.
So Q > R > P. Option B has this set
ANSWER:B
Question: A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?
A.24
B.46
C.67
D.28
Answer: D.28
Explanation: 2/7 - 1/x = 1/4
x = 28
Answer: D
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
A.3/7
B.4/7
C.5/7
D.5/11
Answer: B.4/7
Explanation: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
B)
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
A.12 days
B.11 days
C.10 days
D.16 days
Answer: C.10 days
Explanation: C
10 days
Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days
Question: What is the probability of flipping a fair coin four times and the coin landing on heads on at least two flips?
A.1/16
B.15/16
C.9/16
D.11/16
Answer: D.11/16
Explanation: There are totally 16 outcomes
Chances of all being heads is 1/16
Chances of 3 heads is = 4c34c3 ways = 4/16
Chances of 2 heads is 4c24c2 ways = 6/16
hence 1/16+4/16+6/16=11/161/16+4/16+6/16=11/16
Ans: "D"
Question: There are total 15 people. 7 speaks French and 8 speaks Spanish 3 do not speak any language. Which part of total people speaks both languages.
A.3/4
B.1/5
C.1/6
D.3/8
Answer: B.1/5
Explanation: If x no of people speak both languages then
15 = 8+7-x+3
x=3
so part of total people speaks both languages = 3/15 =1/5
ANSWER:B
Question: The ages of two persons differ by 16 years. If 6 years ago , the elder one be 3 times as old as the younger one, find their present ages .
A.10 years and 18 years
B.18 years and 26 years
C.20 years and 28 years
D.14 years and 30 years
Answer: D.14 years and 30 years
Explanation: Explanation :
Sol. Let the age of the younger person be xx years
Then , age of the elder person = (x+16)(x+16) years
âˆ´âˆ´ 3(xâˆ’6)=(x+16âˆ’6)3(x-6)=(x+16-6)
â‡” 3x âˆ’18=x+10â‡” 3x -18=x+10
â‡” 2x=28â‡” 2x=28
â‡” x=14â‡” x=14
Hence, their present age are 14 years and 30 years .
ANSWER IS D
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 20%?
A.20%
B.30%
C.32%
D.73%
Answer: A.20%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 ---20 => 20%
Answer:A
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 40 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
A.80 lakh
B.50 lakh
C.40 lakh
D.64 lakh
Answer: D.64 lakh
Explanation: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+40/8x=5/4 ⇒ 20x + 160 = 40x
∴ x = 8
∴ Income of company B = 8x = 64 lakh
Answer D
Question: The dimensions of a rectangular solid are 4 inches, 5 inches, and 10 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
A. 10:17
B. 2:5
C. 10:19
D. 25:7
Answer: C. 10:19
Explanation: Answer: C.
Question: Dimitri weighs 2x-x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen’s weight?
A.y - x/2
B.2x - y/2
C.(y - x)/2
D.y - 2x
Answer: C.(y - x)/2
Explanation: These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs 2X-X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
Question: In how many ways can the letters of the word MECHANIC be arranged?
A.2580
B.2500
C.20160
D.2520
Answer: C.20160
Explanation: MECHANIC has 8 words, but C is repeated two times. Thus ways = 8! / 2! = 20160 ways
C
Question: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/2, then what is the value of abc/def ?
A. 27/4
B. 27/8
C. 3/4
D. 3/8
Answer: C. 3/4
Explanation: Say a = 3. Then:
a/b = 1/3 --> b = 9;
b/c = 2 --> c = 9/2;
c/d = 1/2 --> d = 9;
d/e = 3 --> e = 3;
e/f = 1/2 --> f = 6.
abc/def = (3*9*9/2)/(9*3*6) = 3/4.
Answer: C.
Question: A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work ?
A.4 days
B.5 days
C.6 days
D.7 days
Answer: C.6 days
Explanation: Explanation:
(A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work =
(1/4−1/12)=3−1/12=1/6
So B alone can complete the work in 6 days
Option C
Question: How many seconds will a 100 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.11 sec
B.6 sec
C.77 sec
D.14 sec
Answer: B.6 sec
Explanation: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 100 * 3/50
= 6 sec.
Answer: B