RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: 476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:
A.8 and 8
B.8 and 5
C.8 and 7
D.7 and 5
Answer: D.7 and 5
Explanation: Explanation:
Let the number be 476ab0
476ab0 is divisible by 3
=> 4 + 7 + 6 + a + b + 0 is divisible by 3
=> 17 + a + b is divisible by 3 ------------------------(i)
476ab0 is divisible by 11
[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11
=> [3 + (b - a)] is 0 or divisible by 11 --------------(ii)
Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.
if a=6 and b=2,
17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer
if a=8 and b=2,
17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)
[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer
if a=6 and b=5,
17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer
if a=8 and b=5,
17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1
[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2
Since these values satisfies both equation 1 and equation 2, this is the answer
Answer: D) 8 and 5
Question: Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission for each sale made. If each of her sales is for $2,000, what is the least number of sales she must make per year if she is not to lose money because of the job change?
A.57
B.133
C.178
D.377
Answer: B.133
Explanation: Lets say she sales x items so her commission will be : x * 2000*15/100 = 300x
Salary difference is: 85000 - 45000 = 40000
So commission must at least be equal to salary difference i.e. x = 40000/300= 133 (Approx).
Hence answer is B
Question: A train 80 m in length crosses a telegraph post in 6 seconds. The speed of the train is?
A.16 kmph
B.88 kmph
C.54 kmph
D.48 kmph
Answer: D.48 kmph
Explanation: S = 80/6 * 18/5
= 48 kmph
Answer: D
Question: At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 14th highest price and the 21st lowest price among the prices of the items sold, how many items were sold at the garage sale?
A.33
B.34
C.35
D.36
Answer: B.34
Explanation: There were 13 items sold at a higher price than the radio and 20 items sold at a lower price than the radio. Including the radio, there were 13 + 20 + 1 = 34 items sold.
The answer is B.
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
A.399 km
B.162 km
C.277 km
D.887 km
Answer: B.162 km
Explanation: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.Answer: B
Question: Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 10:00 am and Pipe B at 11:00 am, at what time will the pool be full?
A.22:00
B.20:00
C.21:00
D.18:00
Answer: B.20:00
Explanation: Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 10:00 a.m and Pipe B at 11:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 11:00 a.m
Pool filled after 1 hour with both the pipes on : 1/12
Pool filled after 9 hours with both pipes on : 9/12
Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1
Therefore, it takes 10 hrs to fill the pool
As Pipe A started at 10:00 a.m, pool is full at 20:00 hrs
Answer : B
Question: Tarun got 30% concession on the labelled price of an article and sold it for Rs. 8750 with 25% profit on the price he bought. What was the labelled price ?
A.10000
B.22438
C.28789
D.10002
Answer: A.10000
Explanation: Explanation:
Cost Price = = Rs. 7000. Let the labelled price be Rs. x.
Then,
= Rs.10000
Answer: A) 10000
Question: A basketball player succeeds with 50% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
A.0.585
B.0.625
C.0.75
D.0.875
Answer: D.0.875
Explanation: P(missing all 3 free throws) = 0.5^3 = 0.125
P(succeeding at least once) = 1 - 0.125 = 0.875
The answer is D.
Question: Commodious means ‘spacious’, large, voluminous and extensive.
A.22
B.28
C.277
D.199
Answer: A.22
Explanation: Answer:A
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4070. What is the difference between Rose ’s and Tom ’s share in the profit?
A.s.340
B.s.362
C.s.370
D.s.382
Answer: C.s.370
Explanation: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 4070 × 1/11 = Rs.370.
C)
Question: How many box's of length 40 Cm, width 30 Cm and height 10 Cm can be formed from a box of 6 m length, 4 m width and 2 m height.
A.2000
B.5000
C.7000
D.4000
Answer: D.4000
Explanation: (600×400×200)/(40×30×10) = 4000
Answer is D
Question: One copy machine can make 30 copies a minute, and a second copy machine makes 15 copies a minute. If the two copiers work together, how long would it take them to make 900 copies?
A.15 minutes
B.20 minutes
C.25 minutes
D.30 minutes
Answer: B.20 minutes
Explanation: Total work done by both machines in a minute = 30 + 15 = 45 copies
Total number of copies required = 900
Time = 900/45 = 20 mins
Answer B
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 41 kmph. For how many minutes does the bus stop per hour?
A.7 min
B.8 min
C.14.4 min
D.10 min
Answer: C.14.4 min
Explanation: Due to stoppages, it covers 13 km less.
Time taken to cover 13 km =(13/54)x60 = 14.4 min
answer : C
Question: 50 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.
A.190
B.200
C.1225
D.220
Answer: C.1225
Explanation: total no. of handshakes = 49+48+47+...+3+2+1 = 19*(19+1)/2 = 1225
or, if there are n persons then no. of shakehands = nC2 = 50C2 = 1225
Answer : C
Question: 385, 462, 572, 396, 421, 671, 264
A.385
B.421
C.671
D.264
Answer: B.421
Explanation: Solution
In each number except 421,the middle digit is the sum of the other two. Answer B
Question: An express traveled at an average speed of 120 km/hr, stopping for 4 min after every 85 kn. How long did it take to reach its destination 8400 km from the starting point?
A.5 hrs 21 min
B.4 hrs 21 min
C.6 hrs 41 min
D.7 hrs 32 min
Answer: D.7 hrs 32 min
Explanation: D
7 hrs 32 min
Time taken to cover 840 km = 840/120 = 7 hrs.
Number of stoppages = 840/85 - 1 = 8
Total time of stoppages = 4 * 8= 32 min
Hence, total time taken = 7 hrs 32 min.
Question: 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =
A. 3^7
B. 3^8
C. 3^14
D. 3^28
Answer: B. 3^8
Explanation: We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*3^7 we would have: sum=9*(2*3^7)=2*3^9=~3^10, so the actual sum is less than 3^10 and more than 3^7 (option A) as the last term is already more than that. So the answer is clearly B.
Answer: B.
Question: If (a-4)(b-2) =0, which of the following must be true ?
I. a=4 and b=2
II. if a is not = 4, then b=2
III. if a=4, then b is not=2
A.I only
B.II only
C.III only
D.I and II
Answer: B.II only
Explanation: (a-4)(b-2)=0
So either a=4 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.
The answer is B.
Question: Working alone, machine X can manufacture 1,200 nails in 12 hours. Working together, machines X and Y can manufacture 1,200 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
A.3 9/17
B.5 1/3
C.7
D.7 1/7
Answer: D.7 1/7
Explanation: rate of machine x = 1200/12
(1200/12 + y)5=1200
y=700/5
700/5 * t = 1000
t=7 1/7
D.
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 33 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 6 books, how many shelves does the bookcase have?
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: Let x be the number of shelves.
11x - 33 = 7(x-1) + 6
4x = 32
x = 8
The answer is C.
Question: Find the one which does not belong to that group?
A.16
B.36
C.21
D.64
Answer: C.21
Explanation: Explanation:
16, 36, 64 and 4 are perfect squares but not 21.
Answer:C
Question: How many kg of pure salt must be added to 30kg of 2% solution of salt and water to increase it to a 10% solution?
A.8/3
B.9/7
C.7/4
D.5/2
Answer: A.8/3
Explanation: Amount salt in 30kg solution = 2*30/100 = 0.6 kg
Let x kg of pure salt be added
then(0.6+x)/(30+x)=10/100
60+100x=300+10x
90x = 240
x = 8/3
Answer is A
Question: The dimensions of a field are 10 m by 10 m. A pit 10 m long, 5 m wide and 4 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
A.2 m
B.3 m
C.4 m
D.5 m
Answer: C.4 m
Explanation: The volume of the earth removed is 10*5*4 = 200 m^3.
The remaining area of the field is 10*10 - 10*5 = 50 m^2.
200 m^3 of the earth evenly spread over the area of 50 m^2 will rise the height by (height) = (volume)/(area) = 200/50 = 4 m.
Answer: C
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 6000, the number of valid votes that the other candidate got, was:
A.2800
B.2700
C.2160
D.2200
Answer: C.2160
Explanation: C
Number of valid votes = 80% of 6000 = 4800.
Valid votes polled by other candidate = 45% of 4800
= (45/100 x 4800) = 2160.
Question: Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit
A.Rs. 8510
B.Rs. 8620
C.Rs. 8730
D.Rs. 8820
Answer: D.Rs. 8820
Explanation: Explanation:
=>(8000×(1+5/100)2)
=>8000×21/20×21/20
=>8820
Option D
Question: The Speed of a boat in still water is 25 kmph. If it can travel 10 km upstream in 1 hr, What time it would take to travel the same distance downstream?
A.26 minutes
B.23 minutes
C.15 minutes
D.19 minutes
Answer: C.15 minutes
Explanation: Speed of boat in still water = 25 km/hr
Speed upstream = 10⁄1 = 10 km/hr
Speed of the stream = (25-10) = 15 km/hr
Speed downstream = (25+15) = 40 km/hr
Time taken to travel 10 km downstream = 10/40 hours=(10×60)/40= 15 minutes
Answer is C
Question: What is the smallest number which, when increased by 5, is divisible by 7, 8, and 24?
A.148
B.153
C.158
D.163
Answer: D.163
Explanation: LCM(7,8,24)=24x7=168
So the least divisible number is 168, and the number we are looking for is 168-5=163.
The answer is D.
Question: Ravi and Kavi start a business by investing â‚¹ 5000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
A.2 : 72
B.5 : 72
C.7 : 72
D.1 : 72
Answer: B.5 : 72
Explanation: Ratio of profit = Ratio of investments
= 5000 : 72000 = 5 : 72
Answer : B
Question: The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
A.22 years
B.30 years
C.32 years
D.44 years
Answer: C.32 years
Explanation: The total age of 10 students with average 20 = 200
The total age of 12 students with average 22 = 264
The total age of 2 new students = 64
Their average =32
ANSWER:C
Question: If x 2 – y 2 = 101, find the value of x 2 + y 2 ,
given that x and y are natural numbers.
A.5100
B.5101
C.5102
D.5103
Answer: B.5101
Explanation: x^2 – y^2 = 101
=> (x+y)*(x-y) = 101*1
x+y = 101
x-y = 1
so, x = 51, y = 50
(x^2 + y^2) = 51^2 + 50^2 = 5101
ANSWER:B
Question: Virginia, Adrienne, and Dennis have taught history for a combined total of 93 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?
A. 23
B. 32
C. 40
D. 41
Answer: C. 40
Explanation: Let number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D
V+A+D = 96
V= A+9
=>A = V-9
V= D-9
=> A = (D-9)-9 = D-18
D-9 + D-18 + D = 93
=> 3D = 93 + 27 = 120
=> D = 40
Answer C
Question: How many ODD integers n, where 100 <= n <= 200, are divisible neither by seven nor by nine?
A.37
B.38
C.39
D.40
Answer: C.39
Explanation: Total Integers from 100 to 200 inclusive = 101 (51 even and 50 odd)
Total Odd Integers from 100 to 200 = 50
Total No. that are multiple of 7 from 1-200 = 200/7 = 28 (i.e. 14 even and 14 odd)
Total No. that are multiple of 7 from 1-100 = 100/7 = 14 (i.e. 7 even and 7 odd)
Total No. that are ODD multiple of 7 from 100-200 = 14-7 = 7
Total No. that are multiple of 9 from 1-200 = 200/9 = 22 (i.e. 11 even and 11 odd)
Total No. that are multiple of 9 from 1-100 = 100/9 = 11 (i.e. 5 even and 6 odd)
Total No. that are ODD multiple of 9 from 100-200 = 11-6 = 5
Total No. that are odd multiple of 7 and 9 will be multiple of 63 and count of such numbers from 100-200 = 1
So Total No. that are odd multiple of 7 and/or 9 from 100-200 = 7+5-1 = 11
So Total No. that are NOT odd multiple of 7 and/or 9 from 100-200 = 50-11 = 39
Answer: Option C
Question: Find the lowest common multiple of 15, 25 and 35.
A.360
B.420
C.510
D.525
Answer: D.525
Explanation: LCM=3*5*5*7=525.
Answer is D
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
A.288
B.500
C.277
D.266
Answer: B.500
Explanation: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e.,
= 500 ways.
Answer: B
Question: The average of runs of a cricket player of 10 innings was 35. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
A.76
B.79
C.85
D.87
Answer: B.79
Explanation: Explanation:
Average = total runs / no.of innings = 35
So, total = Average x no.of innings = 35 x 10 = 350.
Now increase in avg = 4runs. So, new avg = 35+4 = 39runs
Total runs = new avg x new no. of innings = 39 x 11 = 429
Runs made in the 11th inning = 429 - 350 = 79 Answer: B
Question: 3 years ago the average age of a family of 5 members was 17 years. With the birth of a new baby, the average age of six members remains the same even today. Find the age of the new baby.
A.1 year
B.2 years
C.1 1⁄2 years
D.cannot be determined
Answer: B.2 years
Explanation: Sum of present ages of the six members
= (17 × 6) years = 102 years.
Sum of present ages of the 5 members (excluding baby)
= 5 × (17 + 3) years = 100 years.
∴ Age of the baby = 102 – 100 = 2 years
Answer B
Question: A boat covers a distance of 30 kms in 2 ½ hours running down streams. While returning, it covers the same distance in 3 ¾ hours. What is the speed of the boat in kmph?
A.12
B.8
C.14
D.10
Answer: D.10
Explanation: b+s=30*2/5
b-s=30*4/15
solving ths we get value of b
b=10
ANSWER:D
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.245
B.248
C.240
D.246
Answer: C.240
Explanation: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: Option C
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 63 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
A.2000
B.2100
C.2200
D.2300
Answer: B.2100
Explanation: 1 percent for 3 years= 63
1 percent for 1 year = 21
=> 100 percent = 2100
ANSWER:B
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
A.2:1
B.1:2
C.1:1
D.4:3
Answer: D.4:3
Explanation: Explanation:
5% of A + 4% of B
=2/3(6% of A + 8% of B)
A/B=4/3
A : B = 4 : 3
ANSWER IS D
Question: What is the sum of all the multiples of 10 between 0 and 85?
A.500
B.620
C.450
D.360
Answer: D.360
Explanation: The multiples of 10 between 0 and 85 are 10, 20, 30, 40, 50, 60, 70, 80. If these are all added together, the result is 360.
Final Answer:
D
Question: Which number can we add to 897326 to get a number exactly divisible by 456?
A.58
B.66
C.74
D.82
Answer: D.82
Explanation: 897326 / 456 = 1967 with a remainder of 374.
We need to add 456 - 374 = 82
The answer is D.
Question: A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 16000.
A.Rs. 25600
B.Rs. 5000
C.Rs. 7200
D.Rs. 8000
Answer: B.Rs. 5000
Explanation: Explanation:
A = 2B and B = 5C
=> A : B = 2:1 and B : C = 5 : 1
=> A : B : C = 10 : 5 : 1
Ratio of capitals of A, B and C = 10 : 5 : 1
B's share = Rs.[(5/16) × 16000] = Rs. 5000
Answer: Option B
Question: How many seconds does a train 130 meters long, traveling at 72 km/h, take to completely cross a bridge of 210 meters in length?
A.13
B.15
C.17
D.19
Answer: C.17
Explanation: 72 km/h = 72000/3600 = 20 m/s
Time = 340 / 20 = 17 seconds
The answer is C.
Question: The average age of a group of 14 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
A.22 years
B.30 years
C.36 years
D.32 years
Answer: C.36 years
Explanation: Answer
The average age of a group of 14 students is 20.
Therefore, the sum of the ages of all 14 of them = 14 * 20 = 280
When two new students join the group, the average age increases by 2. New average = 22.
Now, there are 16 students.
Therefore, the sum of the ages of all 16 of them = 16 * 22 = 352
Therefore, the sum of the ages of the two new students who joined = 352 - 280 = 72
And the average age of each of the two new students = 72/2 = 36 years.
Answer C
Question: Bill has d animals, 16 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?
A.6
B.12
C.18
D.24
Answer: D.24
Explanation: Total d animals, suppose each has price of x - total price = dx
now 16 were sold at profit of 10%, making equation - - 16*1.1x
now d-16 were sold at loss of 20%, making eqn --- (d-16)*0.8x
Now he made no profit or loss so,
dx = 16*1.1x + (d-16)*0.8x
solving for d, we get d=24
Ans D
Question: A train which has 300 m long, is running 80 kmph. In what time will it cross a person moving at 16 kmph in same direction ?
A.25 sec
B.35 sec
C.15 sec
D.45 sec
Answer: C.15 sec
Explanation: Time taken to cross a moving person = length of train/ relative speed
Time taken = 300/((80-16) (5/18) = 300/ 64*(5/18) = 300/20= 15 sec
Answer: C
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
A.16 sec
B.87 sec
C.12 sec
D.18 sec
Answer: C.12 sec
Explanation: D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer: 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 20%?
A.20%
B.90%
C.60%
D.40%
Answer: A.20%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.876 m
B.157 m
C.235 m
D.156 m
Answer: C.235 m
Explanation: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2
=> 2(140 + x) = 750 => x
= 235 m.
Answer: C
Question: A thief is noticed by a policeman from a distance of 225 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?
A.50 meter
B.100 meter
C.110 meter
D.125 meter
Answer: D.125 meter
Explanation: Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes =
1/60∗6=1/10=100meters
So distance between them after 6 minutes = 225 - 100
= 125 meters
Option D
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
A.28
B.20
C.998
D.21
Answer: B.20
Explanation: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km. Answer: B
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 35 revolutions, what will be the number of revolutions made by the larger wheel?
A.15
B.12
C.21
D.9
Answer: A.15
Explanation: Explanation:
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
(cogs) 6 : 14 :: x : 35
â‡’6Ã—35=14 Ã— x
â‡’x = 15
Answer: Option A
Question: 48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 46% of respondents did not use M. 42% used N. What percent of respondents used only N?
A.19.5%
B.21.5%
C.20%
D.18.5%
Answer: C.20%
Explanation: From the question, we can summarize the information as follows:
N Not N
M X
Not M Ans y 46
42 100
Then we can set a system of 3 equations 3 unknowns described below:
X + Y = 48
X + Ans = 42
Y + Ans = 46
Sum up all three equations to get 2X + 2Y + 2Ans = 136
Divide both sides by 2 to get X + Y + Ans = 68
Replace X + Y with 48 to get 48 + Ans = 68
Substract 48 from both sides to get Ans = 68 - 48 = 20
The answer must be C.
Question: Zayn is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 6 miles per hour and returns along the same route at an average speed of 8 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
A. 2.4
B. 5.8
C. 6.0
D. 6.3
Answer: A. 2.4
Explanation: to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here Zayn's uphill speed = 6 mph
Zayn's downhill speed = 8 mph
2*6*8/(6+8) = 96/40 = 2.4
Correct answer - A
Question: WHEN A PERSON SELLS TWO ITEMS $600 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:
A.1% loss
B.no loss no gain
C.4% loss
D.2% gain
Answer: C.4% loss
Explanation: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.
Answer : C
Question: What is the smallest number which when diminished by 8, is divisible by 9, 6, 12 and 18?
A.50
B.45
C.44
D.60
Answer: C.44
Explanation: Explanation:
Required number = LCM of (9, 6, 12 and 18) + 8
= 36 + 8 = 44
Answer: Option C
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
A.153
B.150
C.137
D.123
Answer: D.123
Explanation: let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
D satisfies
3x/ 2 = 123
=> x = 82
Verify. 82 + 41 = 123
Answer is D